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How Mental Sets Can Prohibit Problem Solving

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A mental set is a tendency to only see solutions that have worked in the past. This type of fixed thinking can make it difficult to come up with solutions and can impede the problem-solving process. For example, that you are trying to solve a math problem in algebra class. The problem seems similar to ones you have worked on previously, so you approach solving it in the same way. Because of your mental set, you may be unable to see a simpler solution that is unique to this problem.

When we are solving problems, we tend to fall back on solutions that have worked in the past. In many cases, this is a useful approach that allows us to quickly come up with answers. In some instances, however, this strategy can make it difficult to think of new ways of solving problems .

Mental sets can lead to rigid thinking and create difficulties in the problem-solving process .

Functional Fixedness

Functional fixedness is a specific type of mental set where people are only able to see solutions that involve using objects in their normal or expected manner. Mental sets are definitely useful at times. By using strategies that have worked before, we are often able to quickly come up with solutions. This can save time and, in many cases, the approach does yield a correct solution.

While in many cases it is beneficial to use our past experiences to solve issues we face, it can also make it difficult to see novel or creative ways of fixing current problems. For example, imagine your vacuum cleaner has stopped working. When it has stopped working in the past, a broken belt was the culprit. Since past experience has taught you the belt is a common issue, you immediately replace the belt again. But, this time the vacuum continues to malfunction.

However, when you ask a friend to come to take a look at the vacuum, they quickly realize one of the hose attachments was not connected, causing the vacuum to lose suction. Because of your mental set, you failed to notice a fairly obvious solution to the problem.

Impact of Past Experiences

In daily life, a mental set may prevent you from solving a relatively minor problem (like figuring out what is wrong with your vacuum cleaner). On a larger scale, mental sets can prevent scientists from discovering answers to real-world problems or make it difficult for a doctor to determine the cause of an illness.

For example, a physician might see a new patient with symptoms similar to certain cases they have seen in the past, so they might diagnose this new patient with the same illness. Because of this mental set, the doctor might overlook symptoms that would actually point to a different illness altogether. Such mental sets can obviously have a dramatic impact on the health of the patient and possible outcomes.

Necka E, Kubik T. How non-experts fail where experts do not: Implications of expertise for resistance to cognitive rigidity . Studia Psychologica . 2012;54(1):3-14.

Valee-Tourangeau F, Euden G, Hearn V. Einstellung defused: Interactivity and mental set . Quarterly Journal of Experimental Psychology . 2011;64(10):1889-1895. doi:10.1080/17470218.2011.605151

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

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Mental Set: Psychology Definition, History & Examples

In psychology, the concept of a mental set refers to a person’s inclination to approach situations in a fixed way based on their previous experiences and perceptions. This cognitive framework influences how individuals solve problems and can both aid and hinder the decision-making process.

The history of mental set as a psychological construct extends back to the early 20th century, with significant contributions from gestalt psychologists who studied patterns of thought and problem-solving.

Over the years, numerous examples have been documented that illustrate how mental sets can lead to both efficient problem resolution and to cognitive rigidity that precludes alternative solutions.

Understanding mental sets is crucial for comprehending human behavior and cognition , and has implications for fields ranging from education to cognitive therapy.

Table of Contents

A mental set is a cognitive framework that influences how a person approaches problem-solving based on their past experiences and successes. It can be helpful by promoting efficiency and confidence, but it can also limit creativity and adaptability.

Mental sets are rooted in heuristics, which are mental shortcuts that expedite decision-making but may hinder critical evaluation and innovative thinking.

The concept of a mental set originated in the early 20th century within the field of psychology. It was primarily developed by Gestalt psychologists, who focused on the role of perception in problem-solving. These psychologists believed that cognitive processes were not simply reactions to stimuli but were influenced by inherent patterns and structures within the human mind.

The term ‘mental set’ was later expanded upon to describe a predisposition to approach a problem in a fixed manner, based on past experiences and habitual patterns of thinking. This concept emerged as a result of various studies and experiments conducted by key figures in psychology.

Two notable psychologists associated with the development of the mental set concept are Karl Duncker and Wolfgang Köhler. Their methodical examination of historical experiments shed light on how mental sets can both aid and hinder problem-solving. Their analyses played a significant role in understanding how prior knowledge and learned strategies could limit the consideration of alternative solutions.

One significant event that contributed to the evolution of the mental set concept was the research conducted by Duncker in the 1930s. His studies focused on the phenomenon of functional fixedness, which is a type of mental set that inhibits the ability to see objects or concepts beyond their typical or familiar uses. Duncker’s experiments demonstrated how mental sets can restrict problem-solving by creating a narrow focus on previously learned associations.

Another influential study was conducted by Köhler in the 1920s. His research with chimpanzees demonstrated insight problem-solving, which challenged the prevailing behaviorist view that all problem-solving was based solely on trial and error. Köhler’s work highlighted the importance of mental sets in facilitating creative problem-solving by breaking away from fixed patterns of thinking.

These significant events and studies contributed to the evolution of the mental set concept within psychology. Today, mental sets continue to be a fundamental aspect of cognitive psychology, helping researchers understand how our past experiences and preconceived notions can influence our problem-solving abilities.

Several examples can help us understand how mental sets shape our approach to problem-solving and influence our behavior in everyday life.

For instance, imagine you’re trying to fix a leaky faucet in your kitchen. You’ve always used a specific method that worked in the past, so you automatically assume it’s the best way to solve the problem. However, there might be a simpler solution available, like replacing a worn-out washer. Your rigid mental set prevents you from considering alternative approaches and hinders your ability to find a quicker and easier fix.

On the other hand, let’s consider a different scenario. Imagine you’re an experienced chef who specializes in making pasta dishes. Over the years, you’ve developed a mental set of different cooking techniques, ingredient combinations, and flavor profiles that work well together. This mental set allows you to efficiently recognize patterns and apply established strategies, resulting in delicious and successful pasta dishes.

In an educational context, mental sets also play a role. Imagine a teacher who always uses the same teaching method for every lesson. This approach may work well for some students, but it can hinder the learning process for others who might need a different approach to grasp the material. A teacher who recognizes the influence of mental sets would vary their instructional methods, providing different problem-solving strategies to cater to the diverse learning needs of their students. This approach fosters a more adaptive and robust learning environment , allowing students to develop a broader set of problem-solving skills.

Related Terms

Understanding mental sets is greatly enhanced by examining a few key psychological concepts that share connections with this phenomenon.

‘Cognitive rigidity’, for instance, denotes an individual’s resistance to change in thought patterns, which is inherently linked to the persistence of a mental set despite new information. Cognitive rigidity is similar to a mental set in that it involves a rigid adherence to existing cognitive frameworks or ways of thinking. However, while a mental set specifically refers to a fixed mindset or approach to problem-solving, cognitive rigidity encompasses a broader range of inflexible thinking patterns.

Similarly, ‘functional fixedness’ is a cognitive bias that limits a person to using an object only in the way it is traditionally used, reflecting a type of mental set focused on problem-solving. Functional fixedness and mental sets are closely related as they both involve a narrow focus on familiar problem-solving strategies or restricted views of object functions. However, functional fixedness specifically refers to the inability to see alternative uses for an object, while a mental set can encompass broader cognitive frameworks beyond object usage.

‘Confirmation bias’, the tendency to process information by looking for, or interpreting, information that is consistent with one’s existing beliefs, also ties into the rigidity of mental sets. Confirmation bias and mental sets are linked as they both involve a tendency to maintain existing cognitive frameworks and resist information that challenges those frameworks. However, confirmation bias is a broader phenomenon that applies to belief systems in general, while mental sets specifically pertain to problem-solving approaches.

Each term reflects facets of cognitive inflexibility, underscoring the breadth of mental set implications in various cognitive processes. While cognitive rigidity, functional fixedness, and confirmation bias all share similarities with mental sets, they each provide distinct perspectives on the rigidity of cognitive processes and the influences on decision-making and problem-solving.

Scholarship on mental sets draws from a wide range of reputable sources that have significantly contributed to our understanding of this psychological term. These sources include seminal works by early 20th-century psychologists, such as Gestalt psychologists Max Wertheimer and Wolfgang Köhler, who laid the groundwork for the concept of mental sets (Wertheimer, 1923; Köhler, 1947).

Additionally, contemporary cognitive science journals like Cognitive Psychology and Journal of Experimental Psychology: Learning, Memory , and Cognition have published numerous peer-reviewed articles that delve into the intricacies of mental sets (e.g., Smith & Kosslyn, 2007; Lleras & Von Mühlenen, 2004).

Cross-references from related disciplines such as neuroscience and education also contribute to our understanding of mental sets. For example, studies using neuroimaging techniques have provided valuable insights into the neural mechanisms underlying mental sets (e.g., Krawczyk, Gazzaley, & D’Esposito, 2007). Similarly, educational research has explored how mental sets affect learning and problem-solving in various educational contexts (e.g., Perkins, 1986).

It is important to note that the reference list for a comprehensive study on mental sets is not just a collection of citations, but rather a curated map of the intellectual terrain. Each source is carefully evaluated for its methodological rigor, relevance to the topic, and contribution to the understanding of mental set phenomena. This ensures that the references cited provide a solid foundation for further reading and enable readers to navigate the complexities of cognitive processes and their implications.

References:

Gestalt psychologists. (1923). Gestalt theory . Psychological Bulletin, 20(12), 531-585.

Köhler, W. (1947). Gestalt psychology: An introduction to new concepts in modern psychology. New York, NY: Liveright.

Krawczyk, D. C., Gazzaley, A., & D’Esposito, M. (2007). Reward modulation of prefrontal and visual association cortex during an incentive working memory task. Brain Research, 1141, 168-177.

Lleras, A., & Von Mühlenen, A. (2004). Spatial context and top-down strategies in visual search. Spatial Vision, 17(4-5), 465-482.

Perkins, D. N. (1986). Knowledge as design. Hillsdale, NJ: Lawrence Erlbaum Associates.

Smith, E. E., & Kosslyn, S. M. (2007). Cognitive psychology: Mind and brain. Upper Saddle River, NJ: Pearson/Prentice Hall.

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Unconditional Perseveration of the Short-Term Mental Set in Chunk Decomposition

A mental set generally refers to the brain’s tendency to stick with the most familiar solution to a problem and stubbornly ignore alternatives. This tendency is likely driven by previous knowledge (the long-term mental set) or is a temporary by-product of procedural learning (the short-term mental set). A similar problem situation is considered the factor required for perseveration of the long-term mental set, which may not be essential for the short-term mental set. To reveal the boundary conditions for perseveration of the short-term mental set, this study adopted a Chinese character decomposition task. Participants were asked to perform a practice problem that could be solved by a familiar loose chunk decomposition (loose solution) followed by a test problem, or they were asked to repeatedly perform 5–8practice problems followed by a test problem; the former is the base-set condition, and the latter is the enhanced-set condition. In Experiment 1, the test problem situation appeared to be similar to the practice problem and could be solved using the reinforced loose solution and also an unfamiliar tight chunk decomposition (tight solution) (a 2-solution problem). In Experiment 2, the test problem situation differed from the practice problem and could only be solved using an unfamiliar tight solution (a 1-solution problem). The results showed that, when comparing the enhanced-set and base-set conditions, both the accuracy rate and the response times for solving the test problem with a tight solution were worse in Experiment 1, whereas the response times were worse in Experiment 2. We concluded that perseveration of the short-term mental set was independent of the similarity between problem situations and discuss the differences in perseveration between two types of fixation.

Introduction

A mental set is also known as the Einstellung effect, which represents a form of rigidity in which an individual behaves or believes in a certain manner. In the field of psychology, this effect has typically been examined in the process of problem solving and specifically refers to the brain’s tendency to stick with the most familiar solution and to stubbornly ignore alternatives ( Schultz and Searleman , 2002 ). Both prior knowledge and a similar problem situation were considered the factors required to induce an attentional bias toward the familiar solution ( Lovett and Anderson, 1996 ). In addition, the mental set is also likely formed and strengthened by repeatedly practicing a particular solution in a short time and can be interpreted as a temporary by-product of procedural learning ( Ohlsson, 1992 ; Ollinger et al., 2008 ). However, whether a similar problem situation is an essential factor for perseveration of the short-term mental set remains largely unknown.

The mental set is likely driven by previous knowledge, particularly expertise in a domain ( Wiley, 1998 ; Ricks et al., 2007 ; Ellis and Reingold, 2014 ), which can be defined as the long-term mental set. This mental set always occurs when people are confronted with a problem situation that is similar to previously experienced problem situations. Previously acquired knowledge likely helps problem solvers to understand, interpret and solve problems quickly and also likely has a negative impact. For example, most errors that doctors make are not connected to their inadequate medical knowledge but rather to the tendency to form opinions quickly based on previous experience. Once the initial diagnosis is formed, it guides doctors in the search for supporting evidence, which in turn introduces a risk of missing important aspects unrelated to the initial diagnosis.

In a laboratory experiment, chess players were required to find a checkmate position with the fewest number of moves. If players were given a 2-solution problem that had two possible solutions, a familiar solution that took five moves and a less familiar solution that took three moves (the optimal solution), then most of the players selected the familiar but non-optimal solution and failed to notice the shorter solution ( Bilalić et al., 2008 ). Eye tracking technology revealed that the cognitive mechanism underlying this phenomenon was attentional bias, where previous knowledge likely directs attention toward relevant information and away from irrelevant information. Accordingly, players rapidly fixated on the target region that was associated with the familiar but longer solution (i.e., checkmate in five moves) and spent more time looking at these squares rather than those relevant to the shortest solution (i.e., checkmate in three moves), even when they reported that they were searching for alternative solutions in an open-minded manner ( Bilalić et al., 2008 , 2010 ; Sheridan and Reingold, 2013 ). Thus, the search for a solution became self-fulfilling as the familiar solution was consistent with previously acquired knowledge and was more likely to be utilized ( Bilalić et al., 2008 , 2010 ; citealpBR1). If a problem situation is different from previous experiences, then no cues will elicit retrieval of previously acquired knowledge and no attentional bias will occur.

In addition, the mental set is also likely strengthened by repeated practice in a short time and can be interpreted as a temporary by-product of procedural learning ( Ohlsson, 1992 ). One of the most famous examples is the so-called water jar problem, which was originally developed by Luchins ( Luchins, 1942 ; Luchins and Luchins, 1969 ). Participants are presented with three jars (A, B, and C), each of which holds a certain amount of water. The goal is to determine how the jars can be used to obtain a designated amount of water. A series of practice problems can only be solved using a complicated strategy (e.g., A – B – 2C), which participants learn quickly. Subsequently, the participants are provided a test problem (called the 2-solution problem) that could be solved using either the complicated strategy or a much easier strategy (e.g., A – C). Typically, most participants continue to use the complicated strategy instead of the simple strategy. In this case, fixation is induced by repeatedly reinforcing a small number of similar problems in people who have never experienced the task before, which can be defined as the short-term mental set.

In previous studies, the short-term mental effect has been demonstrated in both the laboratory and real-life settings using a range of different problem-solving tasks ( Schultz and Searleman, 2002 ). However, the neurocognitive mechanism underlying this effect and its boundary conditions remain largely unknown. One possibility is that the reinforced solution gradually realizes mechanization, which likely becomes automatically activated during the next problem when the problem situation is similar to the former practice problems. Accordingly, problem solvers progressively require less time to solve problems with a reinforced solution but also experience greater difficulties in searching for alternative solutions ( Neroni et al., 2017 ). Meanwhile, mechanization of a particular solution likely implies that people’s brains lost flexibility to manage novel stimuli or tasks. Therefore, although the next problem situation was different from the former practice problems, negative influences of the short-term mental set likely remained. More generally, regardless of whether the next problem is similar to the former practice problems, problem solving will be hindered when people try to use alternative solutions rather than the reinforced solution.

To reveal the boundary conditions of perseveration of the short-term mental set, a chunk decomposition task was adopted in this study. As a possible means to solve insight problems, chunk decomposition refers to decomposing familiar patterns into their components such that they can be regrouped in a different and meaningful manner ( Knoblich et al., 1999 ). Based on whether the components of the chunks to be decomposed are themselves meaningful perceptual patterns, chunk decomposition can be divided into loose and tight levels. Decomposing the numeral “VI” into “V” and “I” is an example of loose chunk decomposition, and decomposing ‘X’ into “/” and “∖” is an example of tight chunk decomposition because ‘VI’ is composed of meaningful small chunks (‘V’ and ‘I’), whereas ‘X’ is composed of meaningless small chunks (“/” and “∖”) ( Knoblich et al., 1999 ). Generally, participants are more familiar with loose chunk decomposition rather than tight chunk decomposition due to previous knowledge about chunks ( Knoblich et al., 1999 ; Wu et al., 2013 ; Huang et al., 2015 ), but the latter strategy is critical to solving insight problems. Moreover, previous studies have demonstrated that performance in solving mathematical problems with loose chunk decomposition (a loose solution) was improved by repeated practice in the set ( Knoblich et al., 2001 ; Chi and Snyder, 2011 ), i.e., the short-term mental set of chunk decomposition was formed and strengthened by intense practice. After repeatedly solving 5∼8 practice mathematical problems using a loose solution, participants were asked to solve a test mathematical problem, which was different from the practice problem and could only be solved by tight chunk decomposition (a tight solution), in the experimental condition; or else participants were asked to perform a test mathematical problem after repeatedly solving several anagrams in the control condition ( Ollinger et al., 2008 ). Results showed no significant difference in the performance of the test problem between two conditions. Researchers believe that the short-term mental set did not perseverate in the test problem since it was insightful ( Ollinger et al., 2008 ) and different from the practice problem situation. However, another possibility is that perseveration of the short-term mental set was independent on the problem situation similarity, and was happened in both the experimental condition and the control condition; or the short-term mental set likely perseverate in a totally different problem situation.

To further reveal the boundary condition of the short-term mental set, we selectively adopted the design of Ollinger et al. (2008) in this study. Participants were asked to repeatedly perform 5–8 practice problems that could be solved using a loose solution, followed by a test problem, or they were asked to perform a single practice problem followed by a test problem; the former is the enhanced-set condition, and the latter is the base-set condition. In Experiment 1, the test problem situation appeared to be similar to the practice problem and could be solved by the reinforced loose solution and also an unfamiliar tight solution (a 2-solution problem). In Experiment 2, the test problem situation was different from the practice problem and could only be solved by an unfamiliar tight solution (a 1-solution problem). By comparing the success probability and response time of solving the test problem with an unfamiliar tight solution between the enhanced- and base-set conditions, the influences of the short-term mental set on the unfamiliar tight solution were revealed, allowing examination of whether perseveration of the short-term mental set was independent of the situation similarity between the practice problems and the test problem.

We assumed that the short-term mental set would be formed and strengthened after repeatedly solving several similar practice problems using the loose solution and would negatively influence solving of the test problem with an unfamiliar tight solution. The accuracy rates and response times associated with the tight solution for the test problem would be worse in the enhanced-set condition versus the base-set condition regardless of whether the test problem situation was similar to the practice problems.

Experiment 1

Participants.

Thirty-two paid participants (18 males between the ages of 18 and 22 years; mean age 20.11 ± 1.31 years) recruited from the Jiangxi Normal University participated in the task as paid volunteers. They were all native Chinese speakers and had normal or corrected-to-normal vision. Before the experiment, all participants signed the informed consent form approved by the institutional review board of the Jiangxi Normal University.

Tasks, Design, and Procedure

Example of the Chinese character decomposition task in this study.

Two conditions were created in this study, namely, the base-set and enhanced-set conditions, and their presentation sequences were random. In the base-set condition, the participants were asked to perform a practice problem that could be solved only by a loose solution (decompose and remove radicals), followed by a test problem that could be solved by a loose solution and also a tight solution (decompose and remove strokes). In the enhanced-set condition, the participants were asked to continuously perform 5∼8 similar practice problems, followed by one test problem; the range was designed to prevent participants from anticipating. In both conditions, the test problem situation was similar to the practice problems in which the character to be decomposed had a radical element that was closely associated with the loose solution. In total, 24 practice problems and 24 test problems were included in the base-set condition, and 156 practice problems and 24 test problems were included in the enhanced-set condition. Each problem was a Chinese character that was highly familiar to the participants, who were native Chinese speakers.

The time course of each trial is shown below (see Figure ​ Figure2). 2 ). After a period of 500∼800 ms that was designed to reduce expectation, the character to be decomposed appeared in the center of the screen for up to 3,000 ms. During this period, the participants were instructed to consider the answers one by one and to press a response key with the right index finger as soon as they determined an answer. Then, an input box appeared on the screen, and the participants were given an unlimited period of time to enter their answers using a keyboard and then press the “Enter” key to complete the task. Subsequently, the same character again appeared in the center of the screen for up to 10,000 ms minus the reaction time for the first encounter, and the participants were given an unlimited amount of time to enter their answers using a keyboard, or the participants could press the “Space” key to end the trial if they believed that no other answer was possible. Thus, both the character to be decomposed and the answer input box appeared twice since two answers were required for the test problem, and the same procedure was applied to the practice problem for coherence. After the participants finished a practice problem and a test problem or 5∼8 practice problems and a test problem in the set, a 3∼5-s interval was included as a break. The random length was designed to reduce the impact of expectation and preparation.

Example of the experimental trial timeline in Experiment 1.

To demonstrate the influences of the short-term mental set on chunk decomposition, we compared the response times and accuracy rates of the loose solution for both the practice and test problems and the tight solution for the test problem between the enhanced-set condition and the base-set condition.

For the accuracy rate, a 2 (condition: base-set, enhanced-set) × 2 (solution: loose, tight) repeated-measures analysis of variance (ANOVA) revealed significant effects of the condition [ F (1,31) = 6.58, p = 0.015, η 2 = 0.18], the solution [ F (1,31) = 940.16, p < 0.001, η 2 = 0.97], and the interaction effect [ F (1,31) = 11.00, p = 0.002, η 2 = 0.26]. The participants achieved fewer correct responses for the tight solution in the test task in the enhanced-set condition than in the base-set condition [ t (31) = 9.42, p = 0.004], but no significant differences emerged between the enhanced-set condition and the base-set condition for the loose solution [ t (31) = 0.24, p = 0.63] (Figure ​ (Figure3 3 ).

The panel shows the mean accuracy rate and the mean response times for loose and tight solutions for character decomposition in both the base-set and enhanced-set conditions in Experiment 1. Error bars represent the 95% confidence interval. The asterisks indicate significant differences between conditions ( ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001).

For the mean response times, a 2 (condition: base-set, enhanced-set) × 2 (solution: loose, tight) repeated-measures ANOVA showed significant effects of the condition [ F (1,31) = 7.75, p = 0.009, η 2 = 0.20], the solution [ F (1,31) = 203.25, p < 0.001, η 2 = 0.87] and the interaction effect [ F (1,31) = 5.67, p = 0.024, η 2 = 0.16]. The reaction times of the tight-level solution for the test task were longer in the enhanced-set condition than those in the base-set condition [ t (31) = 6.87, p = 0.013], but no difference in response time for the loose solution for both tasks was found in either condition [ t (31) = 0.74, p = 0.40] (Figure ​ (Figure3 3 ).

Experiment 2

Twenty-eight participants (20 males between the ages of 18 and 22 years; mean age 19.93 ± 1.36 years) recruited from the Jiangxi Normal University participated in the task as paid volunteers. They were all native Chinese speakers and had normal or corrected-to-normal vision. Before the experiment, all participants signed the informed consent forms approved by the institutional review board of the Jiangxi Normal University.

The time course for each trial was as follows (see Figure ​ Figure4). 4 ). After 500∼800 ms, the character to be decomposed appeared in the center of the screen for up to 10,000 ms. During this period, the participants were asked to press a response key with the right index finger as soon as they determined an answer. Subsequently, an input box appeared on the screen, and the participants were given an unlimited amount of time to enter their answers using a keyboard and press the “Enter” key to complete the task. After the participants finished a practice problem and a test problem or 5∼8 practice problems and a test problem in the set, a 3∼5-s interval was provided as a break.

Example of the experimental trial timeline in Experiment 2.

To demonstrate the influences of the short-term mental set on chunk decomposition, we compared the response times and accuracy rates of the loose solution for all practice problems and the tight solution for the test problem between the enhanced-set condition and the base-set condition.

For the accuracy rate, a 2 (condition: base-set, enhanced-set) × 2 (solution: loose, tight) repeated-measures ANOVA revealed significant effects of the solution [ F (1,27) = 107.41, p < 0.001, η 2 = 0.80], indicating that the participants had fewer correct responses for the tight solution versus the loose solution, whereas the main effects of the condition [ F (1,27) = 0.02, p = 0.89, η 2 = 0.001] and the interaction effect [ F (1,27) = 0.06, p = 0.81, η 2 = 0.002] were not significant (Figure ​ (Figure5 5 ).

The panel shows the mean accuracy rate and the mean response times for the practice and test problems in both the base-set and enhanced-set conditions in Experiment 2. Error bars represent the 95% confidence interval. The asterisks indicate significant differences between conditions ( ∗∗∗ p < 0.001).

For the mean response times, a 2 (condition: base-set, enhanced-set) × 2 (solution: loose, tight) repeated-measures ANOVA showed the significant effects of the condition [ F (1,27) = 16.12, p < 0.001, η 2 = 0.37], the solution [ F (1,27) = 371.25, p < 0.001, η 2 = 0.93] and the interaction effect [ F (1,27) = 29.50, p < 0.001, η 2 = 0.52]. The reaction times of the tight solution were longer in the enhanced-set condition than those in the base-set condition [ t (27) = 23.85, p < 0.001], but no difference in response time for the loose solution was found between the two conditions [ t (27) = 1.18, p = 0.29] (Figure ​ (Figure5 5 ).

To reveal the boundary conditions of perseveration of the short-term mental set, this study adopted a Chinese character decomposition task. Participants were asked to perform a practice problem that could be solved by a familiar loose solution followed by a test problem, or they were asked to repeatedly perform 5–8 practice problems followed by a test problem; the former task is the base-set condition, and the latter task is the enhanced-set condition. The test problem situation was similar to the practice problem, which included a character with a radical structure, and could be solved by the reinforced loose solution and also an unfamiliar tight solution (Experiment 1), or the situation was different from the practice problem, which included a character without a radical structure, and could only be solved using an unfamiliar tight solution (Experiment 2). The results showed that the participants’ performance in solving the test problems with the unfamiliar tight solution was worse in the enhanced-set condition than in the base-set condition regardless of whether the test problem situation was similar to the practice problems.

For the 2-solution test problem in both the base- and enhanced-set conditions of Experiment 1, all of the participants selected the loose solution as their first choice even though no cue toward a loose or tight solution was provided in the experimental instructions, and the probability of using the loose solution was much higher than that of using the tight solution. This result was consistent with the chunk decomposition hypothesis that chunk decomposition begins with loose chunks, and that the probability that a chunk will be decomposed is inversely proportional to the tightness of the chunk ( Knoblich et al., 1999 ). The processing tendency toward loose chunk decomposition likely reflected the long-term mental set, which originated from previous knowledge about chunks. In particular, Chinese characters are composed of radicals, which are composed of strokes. Because radicals are meaningful elements and can be viewed as independent units, people likely consider removing radicals as the first choice in the process of chunk decomposition when a radical structure is present in the characters ( Luo and Knoblich, 2007 ; Luo et al., 2008 ). In other words, previous knowledge biased attention toward the radical structure and the corresponding loose solution, which was likely prioritized first when performing the Chinese characters decomposition task.

Compared with the base-set condition of Experiment 1, the participants had a lower probability of identifying and required more time to search for the tight solution for the test problem in the enhanced-set condition, reflecting the negative influence of the short-term mental set. As a temporary by-product of procedural learning, the short-term mental set was formed and strengthened with repeated practice of a particular solution. The solution that was satisfactory for all of the practice problems resulted in gradual realization of mechanization, which was likely automatically activated in the problem situation that was similar with prior practice problems ( Lovett and Anderson, 1996 ). Accordingly, problem solvers become faster at solving similar consecutive problems ( Ollinger et al., 2008 ). In this study, performance in solving the practice problem did not increase in the enhanced-set condition compared with the base-set condition, likely because of a ceiling effect. More importantly, performance in solving the test problem by the unfamiliar tight solution was decreased in the enhanced-set condition versus the base-set condition. Two possible mechanisms may underlie this phenomenon. First, reinforced practice enhanced the attentional bias toward the loose solution since a radical structure was present in the test problem situation and in the practice problems. Second, a particular solution realizing mechanization indicates that cognitive and neural adaptation occurred, and the participants may have lost the flexibility to shift their attention to search for other solutions.

For the 1-solution test problem in both conditions of Experiment 2, no radical element was present for retrieval of the loose solution, and the loose solution did not interfere with the tight solution. Therefore, the accuracy rate of solving the test problem with an unfamiliar tight solution was relatively high. Compared with the base-set condition, the participants showed poorer performance in solving the test problem by the tight solution after repeatedly solving the practice problems by the loose solution. This result revealed that the short-term mental set persisted in a different problem situation even though no attentional bias toward the radical structure and its corresponding loose solution likely occurred. The only possible explanation is that mechanization of a particular solution decreased cognitive flexibility, which likely increased the switching costs from the practiced problems to a totally different problem. Therefore, perseveration of the short-term mental set was independent of the similarity between the problem situations. Regardless of whether the next problem situation is similar to the previously practiced problems, problem solving will be hindered when people try to explore alternative solutions rather than using the repeatedly reinforced solution.

Although the formation mechanisms of the long-term mental set and the short-term mental set are completely different, these two kinds of fixation likely occur at the same time. In particular, the short-term mental set can be formed and strengthened on the basis of the long-term mental set. As in this study, the short-term mental set of chunk decomposition was formed and strengthened after the participants repeatedly solved several practice problems with the loose solution, which was driven by the long-term mental set originating from previous knowledge about Chinese character chunks. Then, when the next problem situation was similar to the previously practiced problems, influences from both the long-term mental set and also the short-term mental set manifested. The former set likely decreased the accuracy rate of solving the test problem with the tight solution due to an attentional bias toward the familiar loose solution, whereas the latter set likely increased the response times of solving the test problem with the tight solution since cognitive flexibility was lost after a particular process realizing mechanization. Therefore, both the accuracy and the response time in solving the test problem with an alternative solution were worse in the enhanced-set condition than those in the base-set condition (in Experiment 1). If the next problem situation was not similar to the previously practiced situation, then the influence from the short-term mental set leads to cognitive inflexibility, which likely affected performance on the switching task. Consequently, the participants spent considerably more time searching for and executing the solution in the enhanced-set condition versus the base-set condition (in Experiment 2). The different influences of the test problem on performance in the two experiments also demonstrated the differences in perseveration of the long-term mental set and the short-term mental set.

In sum, the short-term mental set that was formed and strengthened by repeated reinforcement of a particular solution to solve a set of similar practice problems not only likely increased the attentional bias toward the familiar solution when the test problem situation was similar to the practice problems but also likely decreased cognitive flexibility and increased the switching costs from the practice problems to a totally different test problem. Perseveration of the short-term mental set was independent of the similarity between problem situations. Therefore, the short-term mental set was different from the long-term mental set since the latter can only be induced when a similar situation activates previous knowledge. This study largely broadens our general understanding of the mental set and not only distinguished two types of mental sets on the basis of the forming processes but also revealed the differences in the necessary conditions for perseveration. In future research, the neurocognitive mechanism underlying the two types of fixation should be further investigated.

Ethics Statement

This study was carried out in accordance with the recommendations of Norms for human behavior experiments in Jiangxi Normal University with written informed consent from all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the institutional review board of the Jiangxi Normal University.

Author Contributions

FH and ST designed the experiments. ST collected and analyzed the data. FH, ST, and ZH wrote the manuscript.

Conflict of Interest Statement

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

Funding. This work was supported by funding programs from the National Natural Science Foundation of China (Grant Nos. 31700956 and 31860278), a project funded by the China Postdoctoral Science Foundation (Grant Nos. 2018M632598 and 2018T110657), the Natural Science Foundation of Jiangxi, China (Grant No. 20181BAB214010), and the Science and Technology Research Project of the Educational Department in Jiangxi Province, China (Grant No. GJJ160343).

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• DOI: 10.1027/1618-3169.55.4.269
• Corpus ID: 612598

Investigating the effect of mental set on insight problem solving.

• M. Ollinger , Gary Jones , G. Knoblich
• Published in Experimental Psychology 7 May 2008

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Content area

Introduction.

• Studies of Mental Set and Insight
• The Representational Change Theory of Insight and the Matchstick Arithmetic Domain
• The Goals of the Study
• Experiment 1
• Participants
• Materials and Apparatus
• Solution Frequencies for Test Problems
• Solution Time for Set Problems
• Solution Time for Set Problems Preceding and Succeeding a Test Problem
• Experiment 2
• Material and Apparatus
• Procedure and Design
• Experiment 3
• General Discussion
• Figure 1
• Figure 2
• Figure 31
• Table 1
• Table 2
• Table 3

Mental set is the tendency to solve certain problems in a fixed way based on previous solutions to similar problems. The moment of insight occurs when a problem cannot be solved using solution methods suggested by prior experience and the problem solver suddenly realizes that the solution requires different solution methods. Mental set and insight have often been linked together and yet no attempt thus far has systematically examined the interplay between the two. Three experiments are presented that examine the extent to which sets of noninsight and insight problems affect the subsequent solutions of insight test problems. The results indicate a subtle interplay between mental set and insight: when the set involves noninsight problems, no mental set effects are shown for the insight test problems, yet when the set involves insight problems, both facilitation and inhibition can be seen depending on the type of insight problem presented in the set. A two process model is detailed to explain these findings that combines the representational change mechanism with that of proceduralization.

Mental set and insight are two elementary processes within problem solving. Both concepts are significant for understanding and explaining a broad range of human problem solving behavior, and yet to date there has been little research that examines both within a single problem solving task. Mental set is the tendency to solve certain problems in a fixed way...

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• Open access
• Published: 09 February 2022

Overcoming cognitive set bias requires more than seeing an alternative strategy

• Sarah M. Pope-Caldwell 1 &
• David A. Washburn 2  

Scientific Reports volume  12 , Article number:  2179 ( 2022 ) Cite this article

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• Human behaviour

Determining when to switch from one strategy to another is at the heart of adaptive decision-making. Previous research shows that humans exhibit a ‘cognitive set’ bias, which occurs when a familiar strategy occludes—even much better—alternatives. Here we examined the mechanisms underlying cognitive set by investigating whether better solutions are visually overlooked, or fixated on but disregarded. We analyzed gaze data from 67 American undergraduates (91% female) while they completed the learned strategy-direct strategy (LS-DS) task, which measures their ability to switch from a learned strategy (LS) to a more efficient direct strategy (DS or shortcut). We found that, in the first trial block, participants fixated on the location of the shortcut more when it was available but most (89.6%) did not adopt it. Next, participants watched a video demonstrating either the DS ( N  = 34 Informed participants) or the familiar LS (N = 33 Control s). In post-video trials, Informed participants used the DS more than pre-video trials and compared to Controls . Notably, 29.4% of Informed participants continued to use the LS despite watching the DS video. We suggest that cognitive set in the LS-DS task does not stem from an inability to see the shortcut but rather a failure to try it.

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Introduction.

Humans live in a range of diverse and dynamic environments. Adaptive decision-making hinges on cognitive flexibility, the ability to select between known strategies and innovated or acquired novel strategies to meet changing demands 1 , 2 . When a known solution stops working, switching to another is clearly beneficial. Even from a young age, humans are adept at switching when instructed to do so 3 , 4 or after receiving feedback that a current strategy is no longer effective 5 . However, these forced-switch contexts are not the only time when changing tact is beneficial. In dynamic environments, the effectivity of a strategy is likely to change over time and although a familiar strategy continues to be useful, alternatives may eventually be better. Under optional-switch contexts, when a current strategy works but others are available, it can be difficult to know if, or when, to switch to an alternative.

Moreover, searching for an alternative strategy can be time-consuming or risky, and even if a viable alternative is found, the time invested in finding and learning a new strategy might easily outweigh the benefits of using it—especially in the short-term. Balancing the tradeoffs of exploiting a current strategy and exploring alternatives is a fundamental challenge that plagues diverse fields ranging from ecology 6 , 7 to data science 8 , 9 . Humans minimize the cognitive resources spent deciding when to stay and when to switch strategies by relying on rules-of-thumb, or heuristics 10 , 11 . However, this ‘mechanized’ approach can lead us astray.

In optional-switch contexts, humans often exhibit a ‘cognitive set’ bias, which occurs when a familiar strategy occludes—even much better—alternatives 12 , 13 . For example, after learning to solve a set of ‘water jar’ math problems using a four-step method, Luchins 14 found that thousands of participants, from a variety of age-groups and backgrounds, were blinded to a better one-step alternative. This finding has been widely replicated 15 , 16 , 17 , 18 , 19 and extends beyond mathematics to other areas of cognition, including strategic reasoning 20 , 21 , 22 design and engineering 23 , 24 , 25 , spatial navigation 14 , 26 , tool-use 27 , 28 , 29 , as well as insight 30 , 31 , lexical 14 , 32 , and sequential problem solving 12 , 13 , 33 , 34 , 35 . Cognitive set bias is pervasive, but its underlying mechanisms remain unclear.

One hypothesis is that cognitive set affects visual search, such that more time is spent looking at stimuli relevant to the familiar method than alternatives. In other words, once a strategy is adopted, alternatives are to some extent overlooked. For example, Bilalić et al. 20 found that chess experts’ gaze remained primarily focused on pieces involved in a familiar checkmate pattern, the smothered mate, rather than a better alternative—despite reporting that they were looking for other solutions. Similarly, Knoblich et al. 36 found that when presented with ‘matchstick’ arithmetic problems, where moving a single line is necessary to balance an equation (e.g. IV = III + III, solution: VI = III + III), participants who struggled to solve problems that required the disassembly of operators (e.g. using + to create =) looked at the key operators no more than would be expected by chance. These studies support the idea that cognitive set is accompanied by visual or attentional bias towards familiar solutions. However, efforts to reduce cognitive set by increasing the saliency of alternatives, show limited success 14 , 18 , 37 .

Another hypothesis is that cognitive set arises from an unwillingness to search for alternatives. This might be due to an assumption that the current strategy is the only, or best, available strategy, and therefore, the cost of searching for another is prohibitive. In other words, cognitive set arises from a prediction error stemming from similar prior experience or assumptions about the current situation. Luchins 14 found that participants who were told “Don’t be blind” prior to being given the water jar problems used the shorter method more than controls, who persisted with the familiar long solution. He noted that cognitive set (referred to as “Einstellung”) may have arisen because “[Participants] were not accustomed to being taught one method and [then] expected to seek for, or use other methods.” For example, after Luchins showed participants the shorter method, some replied, "You did not teach us that method," or "You should have shown the other way, too, if you wanted us to use it," (p. 90) . Likewise, Knoblich et al. 36 suggested that cognitive set in matchstick problems likely stems from participants’ prior experience with operators as “constant elements” (p. 1008) .

In the current study, we investigated whether cognitive set arises because better solutions are visually overlooked, or fixated on but disregarded. Participants completed the Learned Strategy-Direct Strategy (LS-DS) task, a nonverbal, nonmathematical adaptation of Luchins’ 14 water jar task, which measures their propensity to switch from a learned strategy (LS) to a more efficient direct strategy (DS or shortcut) when it becomes available. The LS-DS task has been shown to elicit high rates of cognitive set in American participants, but interestingly, several non-human primate species seem relatively unaffected 12 , 13 , 34 , 35 . Here, we tracked participants’ gaze while they completed the LS-DS task to test the hypothesis that cognitive set is driven by a visual/attentional bias occluding the shortcut. Additionally, in the second half of the experiment, we measured shortcut-use following a video demonstration of the DS, compared to controls who saw a video of the LS, to assess whether cognitive set would be broken if we removed the costs of searching for a new strategy.

Participants

Data were collected from 72 participants, recruited from the pool of undergraduate students at Georgia State University through the SONA Experiment Management System. Originally, the minimum sample-size was determined to be 60 participants, based on a frequentist power analysis (power = 0.85, cohen’s f = 0.25); although we later decided to use Bayesian modeling, this sample-size yielded satisfactory model fits throughout the analyses. Participants were pseudo-randomly assigned to the Control and Informed conditions, with the requirement that an equal number of males and females were assigned to each. Five participants were excluded from all analyses as a result of either technical malfunctions ( N  = 3), opting out ( N  = 1), or not passing training ( N  = 1). The final data set includes 67 participants [mean 20.2 (SD 4.0) years, 91% female]. Previous research using the LS-DS task has found no evidence of sex-differences in participants’ strategy-use 13 , 34 , 35 ; but it should be noted that the current sample is heavily biased towards female participants and is therefore not demographically representative of the underlying population. For three participants, no eye tracking data were available due to system error; however, their response data were included in non-gaze analyses.

The study was approved by the Georgia State University Institutional Review Board for human subjects and all methods were performed in accordance with the applicable institutional, national, and international guidelines for ethical human research. Informed consent was obtained prior to testing. Testing occurred on Georgia State University campus in a private room with dimmed lights. Participants sat approximately 60 cm from a 19inch monitor (1280 × 1040 Native Resolution; 33.8 × 27.1 cm display size; 1915L Desktop Touchmonitor, Elo Touch Solutions). Responses were collected via mouse clicks to minimize movement. Gaze was captured by the Eye Tribe Tracker (The Eye Tribe), using 16-point gaze calibration. The experiment was conducted in OpenSesame Experiment Builder (version 3.1.1; Mathot et al. 38 ), with the PyGaze plugin (version 0.6.0a16; default settings). Prior to testing, participants were informed of the audio and visual cues for correct and incorrect responses and told that they would need to “select the shapes to figure out the right answer.” Incorrect cues appeared immediately following any incorrect selection during a participants’ response, followed by a 3 s delay and a new trial. Correct cues were only elicited after participants had correctly completed the trial, (i.e. correct intermediate steps were not indicated, except by the lack of incorrect feedback). To start each trial, participants looked at the fixation cross (within a 1.5° threshold) while pressing the SPACE bar; this was enforced by the PyGaze drift-correct feature. If, at any point during the task, the eye tracker was unable to detect fixation after several attempts, the experiment was paused and gaze recalibrated. No further instructions were provided and the experimenter remained in an adjacent room (out of sight) unless recalibration was required.

The LS-DS task

The LS-DS task began with three training levels, in which participants learned the three-step LS (Square1 → Square2 → Triangle) through trial-and-error. Throughout training and testing, the twenty-four possible configurations for the locations of Square1 (10 × 11 cm), Square2 (10 × 11 cm), and the Triangle (10 × 11 cm) were randomly presented. Participants progressed through training by achieving ≥ 80% accuracy, assessed every 8 trials. Training 1, 2, and 3 required a median of 8 (range 8–168), 8 (range 8–24), and 8 (range 8–32) trials, respectively.

After training, participants completed the first 48 experimental trials (Supplementary Fig. S1 ) while gaze was recorded (sample rate = 30 Hz). Experimental trials were presented in random order, and consisted of 24 baseline (BASE) trials, wherein the Triangle was not revealed until after Square 1 and Square 2 had been correctly selected, and 24 test (PROBE) trials, wherein the Triangle appeared alongside the Square 1 → Square 2 demonstration and remained visible throughout participants’ response. Crucially, on PROBE trials, participants could either continue to use the full LS (Square1 → Square2 → Triangle) sequence or they could skip Square1 → Square2 and simply select the Triangle (DS or shortcut). Thus, the LS-DS task assessed participants’ propensity to forego their learned response, the LS, in order to adopt the more efficient shortcut, the DS, when it was available (i.e. PROBE trials). Note that throughout training and testing, participants received immediate negative feedback after choosing any incorrect Square; however, selection of the Triangle–whenever it was available–always elicited the correct feedback cues. See Pope et al. 12 for detailed task description.

After the first 48 (PRE) experimental trials, participants were given a questionnaire asking them to describe the role of various task components (e.g. the red Squares, Triangle, fixation cross) and their thoughts regarding the goal of the task in general. Once the participants completed the questionnaire (~ 5 to 10 min), they were shown a brief video twice, demonstrating either the DS [ Informed group, N = 34, mean 20.8 (SD 5.1) age in years, 91% female] or the LS [ Control group, N  = 33, mean 19.6 (SD 2.3) years, 91% female] being performed in four consecutive PROBE trials. After the video, participants completed an additional 48 (POST) trials, again consisting of 24 BASE and 24 PROBE trials, randomly presented, followed by another, identical questionnaire. Thus, each participant completed the three training levels, 48 PRE trials, a PRE questionnaire, 48 POST trials, and a POST questionnaire, with eye-tracking recorded during all PRE and POST trials.

Data processing

Gaze data were separated into mutually exclusive trial-parts: demo1, when the location of Square1 was shown; demo2, when the location of Square2 was shown; response1, the time until the participant’s first selection, response2, the time until the participant’s second selection; response3, the time until the participant’s third selection. For example, response1 consisted of all gaze data collected from the onset of the response screen until the first response. Fixations were determined based on the default Pygaze settings, which utilize the initial calibration procedure to detect fixations versus saccadic movements that exceed a participant-specific precision threshold (see Dalmaijer et al. 39 ). All non-fixations were excluded. Fixations were categorized into four regions of interest, corresponding to each quadrant of the screen: top left, top right, bottom left, and bottom right—excluding those that fell into the middle 30 pixels extending across the screen both vertically and horizontally, including the central fixation cross (Supplementary Fig. S2 ).

For all correct trials, we marked whether the LS (Square1 → Square2 → Triangle) or DS (Triangle) was used. However, on rare occasions, fewer than 1% of trials, a subset of participants (N = 11) selected Square 1, skipped Square 2, and then selected the Triangle—previously referred to as the “switch strategy” or SS 35 . Because Square1 → Triangle is a partial shortcut, we opted to group SS trials with DS trials for behavioral analyses. However, unlike typical DS trials, the first response is not the Triangle; thus, we excluded them from gaze and response time analyses performed on response1 data.

Questionnaires (both PRE and POST) were analyzed for indications that participants (1) noticed the Triangle appearing earlier in PROBE trials, or (2) ascribed more importance to the Triangle than other task components. For example, statements like “the triangle was sometimes a distraction” were categorized as noticing the early presence of the Triangle in PROBE trials. Responses noting that the Triangle was “how to progress to the next trial”, “how you knew you were correct”, or “the goal” were considered indications of ascribing importance to the Triangle. Participants received two scores for both PRE and POST questionnaires: noticed (yes) or not (no) and ascribed importance (yes) or not (no). The experimenter was blind to video condition during coding and a subset (21%) of the questionnaires were re-coded by another, condition-blind experimenter. A Spearman rank order correlation between the two observers indicated that scoring was reliable ( r s  = 0.781, p  < 0.001).

Data analysis

All models were fit in R version 4.0.3 using the brms (version 2.14.4 40 , 41 interface with r stan 42 . Competing models were compared using the Widely Applicable Information Criterion (WAIC) 43 . Deidentified data are available here .

First, we assessed whether participants looked at the Triangle shortcut when it was available. Participants’ gaze data were used to determine if they fixated on the location of the Triangle (1) or not (0), prior to their first response. Using binary logistic regression models, we assessed whether Triangle fixations occurred more often in PROBE compared to BASE trials. Recall that the Triangle was not visible during response1 in BASE trials, so this comparison controls for random fixations on the Triangle’s location. Data were filtered to include only PRE trials in which the LS was used, to avoid video-condition or response strategy effects. Model 1.0 (Supplementary Table S1 ) included only the random effect of subject number. Model 1.1 also included the main effect of trial type (BASE or PROBE). Identical investigation of Square1, Square2, and Foil fixations are included in supplementary analyses (Supplementary Table S2 ).

Next, we investigated how shortcut-use was influenced by watching the video of either the DS ( Informed ) or the LS ( Control ). Using binary logistic regression models, we looked at whether participants’ use of the shortcut (1) vs the LS (0) differed between PRE and POST trial blocks, and as a function of their video condition ( Informed vs Control ). Trials with incorrect responses were excluded (PRE: mean 3.5, SD 3.7, max 18 trials; POST: mean 2.5, SD 2.5, max 10 trials). Model 2.0 (Supplementary Table S3 ) included only the random effect of subject number. Model 2.1 also included the main effects of block (PRE and POST) and video condition ( Informed vs Control ). Model 2.2 also included the interaction effect of block * video condition. Additionally, we ran a series of point-biserial correlations to investigate whether participants’ reports of noticing the Triangle (noticed) or ascribing importance to it (valued) correlated with shortcut use (Supplementary Table S4 ).

Next, we ran a set of Gamma regression models on overall trial times, to confirm that LS trials took longer than DS or SS trials. Responses shorter than 200 ms or longer than 3 times subjects’ total trial time standard deviation were excluded. Model 3.0 (Supplementary Table S5 ) included only the random effect of subject number on total trial time. Model 3.1 also included the main effect of strategy-used (LS, SS, or DS).

Finally, we explored whether switching between the LS and the DS resulted in switch costs, which are deficits in response time or accuracy that occur when switching from one strategy to another, compared to repeating the same strategy 44 , 45 . We fit a series of Gamma regression models, to see if the latency to first response was shorter in trials where participants repeated their previous strategy (DS preceded by DS, or LS preceded by LS) compared to trials where they switched strategies (DS preceded by LS, or LS preceded by DS). Responses shorter than 200 ms or longer than 3 times subjects’ response1 standard deviation were excluded. Only consecutive PROBE DS ( N  = 464) or BASE LS ( N  = 557) trials from participants that used the DS in more than 50% of trials during that trial block ( N PRE  = 6, N Post  = 27) were analyzed. Model 4.0 (Supplementary Table S6 ) included only the random effect of subject number on response time. Model 4.1 also included the main effects of trial type (BASE or PROBE) and switch type (stay or switch). Model 4.2 also included the interaction effect of trial type * switch type.

In PRE trials, participants used the shortcut in a mean 9.56% (SD 25.39%) of correct PROBE trials. Only 7 out of 67 participants (10.45%; N Informed  = 4, N Control  = 3) used the shortcut in more than 50% of PROBE trials (Table S7 ); this is in line with previous findings 13 , 34 , 35 and our expectations.

Triangle fixations

First, we investigated whether participants continued to use the LS in PRE-PROBE trials because they did not see that the Triangle was already available. Model 1.1 had the lowest WAIC value (Supplementary Table S1 ). It found that, prior to using the LS, participants were more likely to fixate on the Triangle’s location in PROBE ((μ PROBE ) = 0.53, CI = [0.34, 0.72]) compared to BASE trials (Fig.  1 ). This indicates that participants likely saw the Triangle in PROBE trials, but continued to use the LS. The converse was also true, Model S1 found that participants were slightly less likely to fixate on Square 1’s location in PROBE compared to BASE trials ((μ PROBE ) = − 0.17, CI = [− 0.33, − 0.01]). There was no effect of trial type on fixations directed at Square 2 or Foil locations (Supplementary Table S2 ).

Gaze data during the LS-DS task. ( a ) All fixations, including those directed at the midline, that occurred prior to participants’ first response were compiled across all participants during the top left (Square1), bottom left (Square2), top right (Triangle) BASE and PROBE trial configurations, in PRE and POST trial blocks and ( b ) the proportion of PRE trials that participants fixated on each item, prior to using the LS, in BASE and PROBE trials.

Video information

Next, we looked at whether watching the video demonstration of the shortcut increased participants’ ability to use it. In POST trials, Control and Informed participants used the shortcut in a mean 9.12% (SD 25.13%) and 65.25% (SD 42.88%) of correct PROBE trials, respectively. Only 3/33 (9.09%) participants that watched the video of the LS ( Control group) used the shortcut in more than 50% of their correct trials. In stark contrast, 24/34 (70.59%) Informed participants used the shortcut in more than 50% of their correct POST trials (Table S7 ). Model 2.2 had the lowest WAIC value (Supplementary Table S3 ). It confirmed that, in POST trials, Informed participants were far more likely to use the DS ((μ POST Informed ) = 6.06, CI = [5.23, 6.93]) than PRE Control , PRE Informed or POST Control participants (Fig.  2 ). However, note that 10/34 (29.41%) of Informed participants saw the video of the DS but still did not adopt it.

Shortcut-use during the LS-DS task. Mean proportion of trials that a shortcut (DS or SS) was used, for each subject in Informed and Control conditions, in PRE and POST trial blocks. Solid and dashed lines represent group means and standard deviations, respectively. Participants who used the shortcut in fewer than 5% of trials have been aggregated into counts at the bottom.

Shortcut-use and self reports

We found no correlation between shortcut-use and noticing ( r (67) = 0.17, p  = 0.17) or valuing ( r (67) = 0.19, p  = 0.13) the Triangle in PRE trials. However, in POST trials, there was a small positive correlation between shortcut-use and noticing ( r (67) = 0.30, p  = 0.01) and especially for valuing ( r (67) = 0.45, p  < 0.001) the Triangle. See Tables 1 and S4 .

Costs and benefits of shortcut-use

We confirmed that LS trial durations were much longer than DS ((μ LS ) = − 0.82, CI = [− 0.90, − 0.74]) and SS trial durations ((μ LS ) = − 0.38, CI = [− 0.65, − 0.11]; Supplementary Table S5 ); in other words, using either shortcut resulted in a faster trial. Finally, we looked at the switch costs associated with using the shortcut. Model 4.1 had the lowest WAIC values (Supplementary Table S6 ). It suggests, although tentatively, that switching between LS and DS strategies resulted in a slightly slower first response time ((μ LS ) = 0.09, CI = [− 0.01, 0.20]) compared to trials in which participants repeated their previous strategy. However, these results should be interpreted cautiously.

The current study replicated previous reports of cognitive set in the LS-DS task 12 , 13 , 34 , 35 . Specifically, 89% of American adult participants persisted with an inefficient but familiar strategy—the LS, despite the availability of the more efficient shortcut—the DS. We tracked participants’ gaze while they completed the LS-DS task to test the hypothesis that cognitive set stems from visual bias towards familiar strategies, resulting in the shortcut being overlooked. However, this was not supported. Prior to using the LS, participants often fixated on the location of the Triangle, suggesting that they saw the shortcut but still did not use it. Next, we measured shortcut-use following a video demonstration of the DS, to look at whether cognitive set would be broken once participants learned that the DS was a viable alternative. These Informed participants were 24 × times as likely to use the shortcut as Controls , who were shown a video of the LS. However, for 10 Informed participants (29.4%), shortcut-use remained negligible, mean 0.85% (SD 1.80%) of correct POST trials.

Our finding that participants continued to use their familiar solution even after fixating on the Triangle, is contradictory to previous reports. Specifically, using chess and arithmetic paradigms, prior studies concluded that participants’ cognitive set arose because they were not looking for alternatives, as indicated by their gaze 20 , 36 . We suggest that in these paradigms, the alternative strategy was no more visually salient than the familiar approach, making it difficult to discern between participants’ not seeing the alternative versus not looking for it. However, in the LS-DS task the shortcut is very salient—the Triangle is the only icon on the screen during the response phase of PROBE trials (Fig.  1 a). The current study found that, prior to using the LS, participants were 1.5 × more likely to fixate on the Triangle’s location during PROBE trials. Although fixations are only proxies for visual attention, and fixations on the Triangle might reasonably occur simply because of its saliency or role as the third response item when using the LS, our findings indicate that seeing the Triangle was not enough to prompt its use as a shortcut. Instead, we propose that cognitive set on the LS-DS task stems from a reluctance to explore alternative solutions.

Sampling alternatives can be time-consuming and risky. If a working strategy is already in place, these costs may not be outweighed by the mere possibility of a better solution. One way that humans mitigate the risks of decision-making under uncertainty, is by using problem-solving heuristics or rules-of-thumb that are based on previous experience with similar situations 10 , 11 and are subject to individual differences 46 . Specifically, in problem spaces or environments which change often or are otherwise uncertain, alternative strategies may be sampled frequently 47 , 48 or reliance on other sources of information, like socially-acquired strategies can increase 49 .

We suggest that in the LS-DS task, and likely many other instances of cognitive set, failure to use the alternative strategy stems from a prediction error that leads participants to overestimate the stability or predictability of the problem space—in other words, participants believe that the best strategy at the beginning of the game will continue to be the best strategy throughout the game . Indeed, Pope et al. 12 found that telling participants “Don’t be afraid to try new things”, resulted in a substantial increase in shortcut use for American participants. Similarly, Luchins noted that higher rates of cognitive set were often found in children enrolled in remedial arithmetic, wherein rote practice was used extensively 14 . The current study recruited undergraduate students from a Western, Educated, Industrialized, Rich, Democratic (WEIRD) 50 , urban context, and tested them on university property. Perhaps it is not surprising that, even after watching the video of the DS, 29.4% of Informed participants did not break away from their familiar strategy. We suggest that prior experience with school-like testing, or other stable problem-solving situations may play a key role in cognitive set bias. Future studies should directly test this.

It is also possible that, on the LS-DS task, cognitive set is driven by a desire to respond “appropriately”, rather than efficiently 51 . In other words, we did not distinguish between participants believing that they could not versus should not use the shortcut. However, from the questionnaires, it seemed that even participants who reported noticing the difference between BASE and PROBE trials and/or valuing the Triangle, did not consider the shortcut a viable solution until after watching the DS video (Supplementary Table S4 ). Additionally, none of participants’ responses suggested active avoidance of the shortcut.

We conclude that cognitive set on the LS-DS task is not attributable to an inability to detect the alternative but rather to participants’ understanding of the problem space and their (un)willingness to explore alternatives. We suggest that prior experience with rule-based problem solving, especially in the context of formal education, might lead to increased set. The impact of rote memorization and mechanized rule-use, typical of Western educational approaches, on cognitive inflexibility should be clearly elucidated in future studies.

“When the individual does not adequately deal with problems but views them merely from the frame of reference of a habit; when he applies a certain habituated behavior to situations which have a better solution or which, in fact, are not even solvable by the just working habit; when, in a word, instead of the individual mastering the habit, the habit masters the individual – then mechanization is indeed a dangerous thing.” (Luchins, 1942, p. 93)

Data availability

Data is publicly available through the Harvard Dataverse here .

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Acknowledgements

Thanks to Lindsay Mahovetz, who contributed her time to the interrater reliability coding. SP received funding in support of this project from the Kenneth W. and Georganne F. Honeycutt Fellowship and Second Century Initiative Primate Social Cognition, Evolution, and Behavior fellowship. DW received support for this project from National Institutes of Health Grant HD-60563.

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S.M.P. designed the study, collected and analyzed the data, and wrote the manuscript. D.W. provided critical feedback on the study design and manuscript. All authors approved the final version of the manuscript for submission.

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Pope-Caldwell, S.M., Washburn, D.A. Overcoming cognitive set bias requires more than seeing an alternative strategy. Sci Rep 12 , 2179 (2022). https://doi.org/10.1038/s41598-022-06237-0

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Investigating the effect of mental set on insight problem solving.

Mental set is the tendency to solve certain problems in a fixed way based on previous solutions to similar problems. The moment of insight occurs when a problem cannot be solved using solution methods suggested by prior experience and the problem solver suddenly realizes that the solution requires different solution methods. Mental set and insight have often been linked together and yet no attempt thus far has systematically examined the interplay between the two. Three experiments are presented that examine the extent to which sets of non-insight and insight problems affect the subsequent solutions of insight test problems. The results indicate a subtle interplay between mental set and insight: when the set involves non-insight problems, no mental set effects are shown for the insight test problems, yet when the set involves insight problems, both facilitation and inhibition can be seen depending on the type of insight problem presented in the set. A two process model is detailed to explain these findings that combines the representational change mechanism with that of proceduralisation.

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Insight in problem solving occurs when the problem solver fails to see how to solve a problem and then – “aha!” – there is a sudden realization how to solve it. Two contemporary theories have been proposed to explain insight. The representational change theory (e.g., Knoblich et al., 2001) proposes that insight occurs through relaxing self-imposed constraints on a problem, and by decomposing chunked items in the problem. The progress monitoring theory (e.g., MacGregor et al., 2001) proposes that insight is only sought once it becomes apparent that the distance to the goal is unachievable in the moves remaining. These two theories are tested in an unlimited move problem, to which neither theory has previously been applied. The results lend support to both, but experimental manipulations to the problem suggest that the representational change theory is the better indicator of performance. The findings suggest that testable opposing predictions can be made to examine theories of insight, and that the use of eye movement data is a fruitful method of both examining insight and testing theories of insight.

This article reports 2 experiments that investigated performance on a novel insight problem, the 8-coin problem. The authors hypothesized that participants would make certain initial moves (strategic moves) that seemed to make progress according to the problem instructions but that nonetheless would guarantee failure to solve the problem. Experiment 1 manipulated the starting state of the problem and showed that overall solution rates were lower when such strategic moves were available. Experiment 2 showed that failure to capitalize on visual hints about the correct first move was also associated with the availability of strategic moves. The results are interpreted in terms of an information-processing framework previously applied to the 9-dot problem. The authors argue that in addition to the operation of inappropriate constraints, a full account of insight problem solving must incorporate a dynamic that steers solution-seeking activity toward the constraints.

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The feeling of insight in problem solving is typically associated with the sudden realization of a solution that appears obviously correct (Kounios et al., 2006). Salvi et al. (2016) found that a solution accompanied with sudden insight is more likely to be correct than a problem solved through conscious and incremental steps. However, Metcalfe (1986) indicated that participants would often present an inelegant but plausible (wrong) answer as correct with a high feeling of warmth (a subjective measure of closeness to solution). This discrepancy may be due to the use of different tasks or due to different methods in the measurement of insight (i.e., using a binary vs. continuous scale). In three experiments, we investigated both findings, using many different problem tasks (e.g., Compound Remote Associates, so-called classic insight problems, and non-insight problems). Participants rated insight-related affect (feelings of Aha-experience, confidence, surprise, impasse, and pleasure) on continuous scales. As expected we found that, for problems designed to elicit insight, correct solutions elicited higher proportions of reported insight in the solution compared to non-insight solutions; further, correct solutions elicited stronger feelings of insight compared to incorrect solutions.

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Expertise as mental set: The effects of domain knowledge in creative problem solving

• Published: July 1998
• Volume 26 , pages 716–730, ( 1998 )

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• Jennifer Wiley 1  

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Experts generally solve problems in their fields more effectively than novices because their wellstructured, easily activated knowledge allows for efficient search of a solution space. But what happens when a problem requires a broad search for a solution? One concern is that subjects with a large amount of domain knowledge may actually be at a disadvantage, because their knowledge may confine them to an area of the search space in which the solution does not reside. In other words, domain knowledge may act as a mental set, promoting fixation in creative problem-solving attempts. A series of three experiments in which an adapted version of Mednick’s (1962) remote associates task was used demonstrates conditions under which domain knowledge may inhibit creative problem solving.

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This article is based on a dissertation submitted to the University of Pittsburgh in partial fulfillment of the requirements for a Ph.D.

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Wiley, J. Expertise as mental set: The effects of domain knowledge in creative problem solving. Memory & Cognition 26 , 716–730 (1998). https://doi.org/10.3758/BF03211392

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Received : 20 February 1997

Accepted : 11 July 1997

Issue Date : July 1998

DOI : https://doi.org/10.3758/BF03211392

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Expertise as mental set: the effects of domain knowledge in creative problem solving

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• 1 University of Pittsburgh, Pennsylvania, USA. [email protected]
• PMID: 9701964
• DOI: 10.3758/bf03211392

Experts generally solve problems in their fields more effectively than novices because their well-structured, easily activated knowledge allows for efficient search of a solution space. But what happens when a problem requires a broad search for a solution? One concern is that subjects with a large amount of domain knowledge may actually be at a disadvantage, because their knowledge may confine them to an area of the search space in which the solution does not reside. In other words, domain knowledge may act as a mental set, promoting fixation in creative problem-solving attempts. A series of three experiments in which an adapted version of Mednick's (1962) remote associates task was used demonstrates conditions under which domain knowledge may inhibit creative problem solving.

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