problem solving insight psychology

Insight Learning (Definition+ 4 Stages + Examples)

Have you ever been so focused on a problem that it took stepping away for you to figure it out? You can’t find the solution when you’re looking at all of the moving parts, but once you get distracted with something else - “A-ha!” you have it.

When a problem cannot be solved by applying an obvious step-by-step solving sequence, Insight learning occurs when the mind rearranges the elements of the problem and finds connections that were not obvious in the initial presentation of the problem. People experience this as a sudden A-ha moment.

Humans aren’t the only species that have these “A-ha” moments. Work with other species helped psychologists understand the definition and stages of Insight Learning. This video is going to break down those stages and how you can help to move these “a-ha” moments along.

What Is Insight Learning?

Insight learning is a process that leads to a sudden realization regarding a problem. Often, the learner has tried to understand the problem, but steps away before the change in perception occurs. Insight learning is often compared to trial-and-error learning, but it’s slightly different.

Rather than just trying different random solutions, insight learning requires more comprehension. Learners aim to understand the relationships between the pieces of the puzzle. They use patterns, organization, and past knowledge to solve the problem at hand.

Is Insight Learning Only Observed In Humans?

Humans aren’t the only species that learn with insight. Not all species use this process - just the ones that are closest to us intellectually. Insight learning was first discovered not by observing humans, but by observing chimps.

In the early 1900s, Wolfgang Köhler observed chimpanzees as they solved problems. Köhler’s most famous subject was a chimp named Sultan. The psychologist gave Sultan two sticks of different sizes and placed a banana outside of Sultan’s cage. He watched as Sultan looked at the sticks and tried to reach for the banana with no success. Eventually, Sultan gave up and got distracted. But it was during this time that Köhler noticed Sultan having an “epiphany.” The chimp went back to the sticks, placed one inside of the other, and used this to bring the banana to him.

Since Köhler’s original observations took place, psychologists looked deeper into the insight process and when you are more likely to experience that “a-ha” moment. There isn’t an exact science to insight learning, but certain theories suggest that some places are better for epiphanies than others.

Four Stages of Insight Learning

But how does insight learning happen? Multiple models have been developed, but the four-stage model is the most popular. The four stages of insight learning are preparation, incubation, insight, and verification.

Preparation

The process begins as you try to solve the problem. You have the materials and information in front of you and begin to make connections. Although you see the relationships between the materials, things just haven’t “clicked” yet. This is the stage where you start to get frustrated.

During the incubation period, you “give up” for a short period of time. Although you’ve abandoned the project, your brain is still making connections on an unconscious level.

When the right connections have been made in your mind, the “a-ha” moment occurs. Eureka! You have an epiphany!

Verification

Now, you just have to make sure that your epiphany is right. You test out your solution and hopefully, it works! This is a great moment in your learning journey. The connections you make solving this problem are likely to help you in the future.

Examples of Insight Learning

Insight learning refers to the sudden realization or understanding of a solution to a problem without the need for trial-and-error attempts. It's like a "light bulb" moment when things suddenly make sense. Here are some examples of insight learning:

The Matchstick Problem : Realizing you can light a match and use it to illuminate a dark room instead of fumbling around in the dark.
Sudoku Puzzles : Suddenly seeing a pattern or number placement that you hadn't noticed before, allowing you to complete the puzzle.
The Two Rope Problem : In an experiment, a person is given two ropes hanging from the ceiling and is asked to tie them together. The solution involves swinging one rope like a pendulum and grabbing it with the other.
Opening Jars : After struggling to open a jar, you remember you can tap its lid lightly or use a rubber grip to make it easier.
Tangram Puzzles : Suddenly realizing how to arrange the geometric pieces to complete the picture without any gaps.
Escape Rooms : Having an "aha" moment about a clue that helps you solve a puzzle and move to the next challenge.
The Nine Dot Problem : Connecting all nine dots using only four straight lines without lifting the pen.
Cooking : Realizing you can soften butter quickly by grating it or placing it between two sheets of parchment paper and rolling it.
Math Problems : Suddenly understanding a complex math concept or solution method after pondering it for a while.
Guitar Tuning : Realizing you can use the fifth fret of one string to tune the next string.
Traffic Routes : Discovering a faster or more efficient route to your destination without using a GPS.
Packing Suitcases : Figuring out how to fit everything by rolling clothes or rearranging items in a specific order.
The Crow and the Pitcher : A famous Aesop's fable where a thirsty crow drops pebbles into a pitcher to raise the water level and drink.
Computer Shortcuts : Discovering a keyboard shortcut that makes a task you frequently do much quicker.
Gardening : Realizing you can use eggshells or coffee grounds as a natural fertilizer.
Physics Problems : After struggling with a concept, suddenly understanding the relationship between two variables in an equation.
Art : Discovering a new technique or perspective that transforms your artwork.
Sports : Realizing a different way to grip a tennis racket or baseball bat that improves your game.
Language Learning : Suddenly understanding the grammar or pronunciation rule that was previously confusing.
DIY Projects : Figuring out a way to repurpose old items in your home, like using an old ladder as a bookshelf.

Where Is the Best Place to Have an Epiphany?

But what if you want to have an epiphany? You’re stuck on a problem and you can’t take it anymore. You want to abandon it, but you’re not sure what you should do for this epiphany to take place. Although an “a-ha” moment isn’t guaranteed, studies suggest that the following activities or places can help you solve a tough problem.

The Three B’s of Creativity

Creativity and divergent thinking are key to solving problems. And some places encourage creativity more than others. Researchers believe that you can kickstart divergent thinking with the three B’s: bed, bath, and the bus.

Sleep

“Bed” might be your best bet out of the three. Studies show that if you get a full night’s sleep, you will be twice as likely to solve a problem than if you stay up all night. This could be due to the REM sleep that you get throughout the night. During REM sleep , your brain is hard at work processing the day’s information and securing connections. Who knows - maybe you’ll dream up the answer to your problems tonight!

Meditation

The word for “insight” in the Pali language is vipassana. If you have ever been interested in meditation , you might have seen this word before. You can do a vipassana meditation at home, or you can go to a 10-day retreat. These retreats are often silent and are set up to cultivate mind-body awareness.

You certainly don’t have to sign up for a 10-day silent retreat to solve a problem that is bugging you. (Although, you may have a series of breakthroughs!) Try meditating for 20 minutes at a time. Studies show that this can increase the likelihood of solving a problem.

Laugh!

How do you feel when you have an epiphany? Good, right? The next time you’re trying to solve a problem, check in with your emotions. You are more likely to experience insight when you’re in a positive mood. Positivity opens your mind and gives your mind more freedom to explore. That exploration may just lead you to your solution.

Be patient when you’re trying to solve problems. Take breaks when you need to and make sure that you are taking care of yourself. This approach will help you solve problems faster and more efficiently!

Insight Vs. Other Types Of Learning.

Learning by insight is not learning by trial and error, nor by observation and imitation. Learning by insight is a learning theory accepted by the Gestalt school of psychology, which disagrees with the behaviorist school, which claims that all learning occurs through conditioning from the external environment.

Gestalt is a German word that approximately translates as ‘an organized whole that has properties and elements in addition to the sum of its parts .’ By viewing a problem as a ‘gestalt’ , the learner does not simply react to whatever she observes at the moment. She also imagines elements that could be present but are not and uses her imagination to combine parts of the problem that are presently not so combined in fact.

Insight Vs. Trial And Error Learning

Imagine yourself in a maze-running competition. You and your rivals each have 10 goes. The first one to run the maze successfully wins $500. You may adopt a trial-and-error strategy, making random turning decisions and remembering whether those particular turns were successful or not for your next try. If you have a good memory and with a bit of luck, you will get to the exit and win the prize.

Completing the maze through trial and error requires no insight. If you had to run a different maze, you would have no advantage over running previous mazes with different designs. You have now learned to run this particular maze as predicted by behaviorist psychologists. External factors condition your maze running behavior. The cash prize motivates you to run the maze in the first place. All maze dead ends act as punishments , which you remember not to repeat. All correct turns act as rewards , which you remember to repeat.

If you viewed the maze running competition as a gestalt, you might notice that it doesn't explicitly state in the competition rules that you must run along the designated paths to reach the exit.

Suppose you further noticed that the maze walls were made from cardboard. In that case, you may combine those 2 observations in your imagination and realize that you could just punch big holes in the walls or tear them down completely, to see around corners and directly run to the now visible exit.

Insight Vs. Learning Through Observation, Imitation, And Repetition

Observation, imitation, and repetition are at the heart of training. The violin teacher shows you how to hold your bow correctly; you practice your scales countless times before learning to play a sonata from Beethoven flawlessly. Mastering a sport or a musical instrument rarely comes from a flash of insight but a lot of repetition and error correction from your teacher.

Herbert Lawford, the Scottish tennis player, and 1887 Wimbledon champion, is credited for being the first player to play a topspin. Who could have taught it to him? Who could he have imitated? One can only speculate since no player at that time was being coached on how to hit topspin.

He could have only learned to play a topspin by having a novel insight. One possibility is that he played one by accident during training, by mistakenly hitting the ball at a flatter angle than normal. He could then have observed that his opponent was disorientated by the flatter and quicker bounce of the ball and realized the benefit of his ‘mistake’ .

Behaviorist theories of learning can probably explain how most successful and good tennis players are produced, but you need a Gestalt insight learning theory to explain Herbert Lawford.

Another interesting famous anecdote illustrating insight learning concerned Carl Friedrich Gauss when he was a 7-year-old pupil at school. His mathematics teacher seems to have adopted strict behaviorism in his teaching since the original story implies that he beat students with a switch.

One day the teacher set classwork requiring the students to add up all the numbers from 1 to 100. He expected his pupils to perform this calculation in how they were trained. He expected it to be a laborious and time-consuming task, giving him a long break. In just a few moments, young Gauss handed in the correct answer after having to make at most 2 calculations, which are easy to do in your head. How did he do it? Gauss saw the arithmetic sequence as a gestalt instead of adding all the numbers one at a time: 1+2+3+4…. +99+100 as he expected.

He realized that by breaking this sequence in half at 50, then snaking the last number (100) under the first number (1), and then adding the 2 halves of the arithmetic sequence like so:

1 + 2 + 3 + 4 + 5 + …………. + 48 + 49 + 50

100 + 99 + 98 + 97 + 96 + …………... + 53 + 52 + 51

101 + 101 + 101 + 101 + 101 + ……………. + 101 + 101 + 101

Arranged in this way, each number column adds up to 101, so all Gauss needed to do was calculate 50 x 101 = 5050.

Can Major Scientific Breakthroughs be made through observation and experiment alone?

Science is unapologetically an evidence-based inquiry. Observations, repeatable experiments, and hard, measurable data must support theories and explanations.

Since countless things can be observed and comparisons made, they cannot be done randomly for observations and experiments to advance knowledge. They must be guided by a good question and a testable hypothesis. Before performing actual experiments and observations, scientists often first perform thought experiments . They think of ideal situations by imagining ways things could be or imaging away things that are.

Atoms were talked about long before electron microscopes could observe them. How could atoms be seriously discussed in ancient Greece long before the discoveries of modern chemistry? Pre-Socratic philosophers were puzzled by a purely philosophical problem, which they termed the problem of the one and many .

People long observed that the world was made of many different things that didn't remain static but continuously changed into other various things. For example, a seed different from a tree changed into a tree over time. Small infants change into adults yet remain the same person. Boiling water became steam, and frozen water became ice.

Observing all of this in the world, philosophers didn’t simply take it for granted and aimed to profit from it practically through stimulus-response and trial and error learning. They were puzzled by how the world fit together as a whole.

To make sense of all this observable changing multiplicity, one needed to imagine an unobservable sameness behind it all. Yet, there is no obvious or immediate punishment or reward. Therefore, there seems to be no satisfying behaviorist reason behind philosophical speculations.

Thinkers such as Empedocles and Aristotle made associations between general properties in the world wetness, dryness, temperature, and phases of matter as follows:

Earth : dry, cold
Fire: dry, hot
Water: wet, cold
Air: hot or wet, depending on whether moisture or heat prevails in the atmosphere.

These 4 primitive elements transformed and combined give rise to the diversity we see in the world. However, this view was still too sensually based to provide the world with sought-for coherence and unity. How could a multiplicity of truly basic stuff interact? Doesn't such an interaction presuppose something more fundamental in common?

The ratio of these 4 elements was thought to affect the properties of things. Stone contained more earth, while a rabbit had more water and fire, thus making it soft and giving it life. Although this theory correctly predicted that seemingly basic things like stones were complex compounds, it had some serious flaws.

For example, if you break a stone in half many times, the pieces never resemble fire, air, water, or earth.

To account for how different things could be the same on one level and different on another level, Leucippus and his student Democritus reasoned that all things are the same in that they were made from some common primitive indivisible stuff but different due to the different ways or patterns in which this indivisible stuff or atoms could be arranged.

For atoms to be able to rearrange and recombine into different patterns led thinkers to the insight that if the atom idea was true, then logically, there had to be free spaces between the atoms for them to shift into. They had to imagine a vacuum, another phenomenon not directly observable since every nook and cranny in the world seems to be filled with some liquid, solid, or gas.

This ancient notion of vacuum proved to be more than just a made-up story since it led to modern practical applications in the form of vacuum cleaners and food vacuum packing.

This insight that atoms and void exist makes no sense from a behaviorist learning standpoint. It cannot be explained in terms of stimulus-response or environmental conditioning and made no practical difference in the lives of ancient Greeks.

For philosophers to feel compelled to hold onto notions, which at the time weren’t directly useful, it suggests that they must have felt some need to understand the universe as an intelligible ‘gestalt’ One may even argue that the word Cosmos, from the Greek word Kosmos, which roughly translates to ‘harmonious arrangement’ is at least a partial synonym.

The Historical Development Of The Theory of Insight Learning

Wolfgang Kohler , the German gestalt psychologist, is credited for formulating the theory of insight learning, one of the first cognitive learning theories. He came up with the theory while first conducting experiments in 1913 on 7 chimpanzees on the island of Tenerife to observe how they learned to solve problems.

In one experiment, he dangled a banana from the top of a high cage. Boxes and poles were left in the cage with the chimpanzees. At first, the chimps used trial and error to get at the banana. They tried to jump up to the banana without success. After many failed attempts, Kohler noticed that they paused to think for a while.

After some time, they behaved more methodically by stacking the boxes on top of each other, making a raised platform from which they could swipe at the banana using the available poles. Kohler believed that chimps, like humans, were capable of experiencing flashes of insight, just like humans.

In another experiment, he placed a peanut down a long narrow tube attached to the cage's outer side. The chimpanzee tried scooping the peanut out with his hand and fingers, but to no avail, since the tube was too long and narrow. After sitting down to think, the chimp filled its mouth with water from a nearby water container in the cage and spat it into the tube.

The peanut floated up the tube within the chimp's reach. What is essential is that the chimp realized it could use water as a tool in a flash of insight, something it had never done before or never shown how to do . Kohler's conclusions contrasted with those of American psychologist Edward Thorndike , who, years back, conducted learning experiments on cats, dogs, and monkeys.

Through his experiments and research, Thorndike concluded that although there was a vast difference in learning speed and potential between monkey dogs and cats, he concluded that all animals, unlike humans, are not capable of genuine reasoned thought. According to him, Animals can only learn through stimulus-response conditioning, trial and error, and solve problems accidentally.

Kohler’s 4 Stage Model Of Insight Learning

From his observations of how chimpanzees solve complex problems, he concluded that the learning process went through the following 4 stages:

Preparation: Learners encounter the problem and begin to survey all relevant information and materials. They process stimuli and begin to make connections.
Incubation: Learners get frustrated and may even seem to observers as giving up. However, their brains carry on processing information unconsciously.
Insight: The learner finally achieves a breakthrough, otherwise called an epiphany or ‘Aha’ moment. This insight comes in a flash and is often a radical reorganization of the problem. It is a discontinuous leap in understanding rather than continuous with reasoning undertaken in the preparation phase.
Verification: The learner now formally tests the new insight and sees if it works in multiple different situations. Mathematical insights are formally proved.

The 2 nd and 3 rd stages of insight learning are well described in anecdotes of famous scientific breakthroughs. In 1861, August Kekulé was contemplating the structure of the Benzene molecule. He knew it was a chain of 6 carbon atoms attached to 6 hydrogen atoms. Still, He got stuck (incubation phase) on working out how they could fit together to remain chemically stable.

He turned away from his desk and, facing the fireplace, fell asleep. He dreamt of a snake eating its tail and then spinning around. He woke up and realized (insight phase) that these carbon-hydrogen chains can close onto themselves to form hexagonal rings. He then worked out the consequences of his new insight on Benzene rings. (Verification phase)

Suitably prepared minds can experience insights while observing ordinary day-to-day events. Many people must have seen apples fall from trees and thought nothing of it. When Newton saw an apple fall, he connected its fall to the action of the moon. If an unseen force pulls the apple from the tree top, couldn't the same force extends to the moon? This same force must be keeping the moon tethered in orbit around the earth, keeping it from whizzing off into space. Of course, this seems counterintuitive because if the moon is like the apple, should it not be crashing down to earth?

Newton's prepared mind understood the moon to be continuously falling to earth around the horizon's curve. Earth's gravitational pull on the moon balanced its horizontal velocity tangential to its orbit. If the apple were shot fast enough over the horizon from a cannon, it too, like the moon, would stay in orbit.

So, although before Newton, everyone was aware of gravity in a stimulus-response kind of way and even made practical use of it to weigh things, no one understood its universal implications.

Applying Insight Learning To The Classroom

The preparation-incubation-insight- verification cycle could be implemented by teachers in the classroom. Gestalt theory predicts that students learn best when they engage with the material; they are mentally prepared for age, and maturity, having had experiences enabling them to relate to the material and having background knowledge that allows them to contextualize the material. When first presenting content they want to teach the students, teachers must make sure students are suitably prepared to receive the material, to successfully go through the preparation stage of learning.

Teachers should present the material holistically and contextually. For example, when teaching about the human heart, they should also teach where it is in the human body and its functional importance and relationship to other organs and parts of the body. Teachers could also connect other fields, such as comparing hearts to mechanical pumps.

Once the teacher has imparted sufficient background information to students, they should set a problem for their students to solve independently or in groups. The problem should require the students to apply what they have learned in a new way and make novel connections not explicitly made by the teacher during the lesson.

However, they must already know and be familiar with all the material they need to solve the problem. Students must be allowed to fumble their way to a solution and make many mistakes , as this is vital for the incubation phase. The teacher should resist the temptation to spoon-feed them. Instead, teachers should use the Socratic method to coax the students into arriving at solutions and answers themselves.

Allowing the students to go through a sufficiently challenging incubation phase engages all their higher cognitive functions, such as logical and abstract reasoning, visualization, and imagination. It also habituates them to a bit of frustration to build the mental toughness to stay focused.

It also forces their brains to work hard in processing combining information to sufficiently own the insights they achieve, making it more likely that they will retain the knowledge they gained and be able to apply it across different contexts.

Once students have written down their insights and solutions, the teacher should guide them through the verification phase. The teacher and students need to check and test the validity of the answers. Solutions should be checked for errors and inconsistencies and checked against the norms and standards of the field.

However, one should remember that mass education is aimed at students of average capacity and that not all students are always equally capable of learning through insight. Also, students need to be prepared to gain the ability and potential to have fruitful insights.

Learning purely from stimulus-response conditioning is insufficient for progress and major breakthroughs to be made in the sciences. For breakthroughs to be made, humans need to be increasingly capable of higher and higher levels of abstract thinking.

However, we are not all equally capable of having epiphanies on the cutting edge of scientific research. Most education aims to elevate average reasoning, knowledge, and skill acquisition. For insight, learning must build on rather than replace behaviorist teaching practices.

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Concrete Operational Stage (3rd Cognitive Development)

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Insight Learning Theory: Definition, Stages, and Examples

Categories Learning

Insight learning theory is all about those “lightbulb moments” we experience when we suddenly understand something. Instead of slowly figuring things out through trial and error, insight theory says we can suddenly see the solution to a problem in our minds.

This theory is super important because it helps us understand how our brains work when we learn and solve problems. It can help teachers find better ways to teach and improve our problem-solving skills and creativity. It’s not just useful in school—insight theory also greatly impacts science, technology, and business.

The four stages of insight learning theory

Table of Contents

What Is Insight Learning?

Insight learning is like having a lightbulb moment in your brain. It’s when you suddenly understand something without needing to go through a step-by-step process. Instead of slowly figuring things out by trial and error, insight learning happens in a flash. One moment, you’re stuck, and the next, you have the solution.

This type of learning is all about those “aha” experiences that feel like magic. The key principles of insight learning involve recognizing patterns, making connections, and restructuring our thoughts. It’s as if our brains suddenly rearrange the pieces of a puzzle, revealing the big picture. So, next time you have a brilliant idea pop into your head out of nowhere, you might just be experiencing insight learning in action!

Three Components of Insight Learning Theory

Insight learning, a concept rooted in psychology, comprises three distinct properties that characterize its unique nature:

1. Sudden Realization

Unlike gradual problem-solving methods, insight learning involves sudden and profound understanding. Individuals may be stuck on a problem for a while, but then, seemingly out of nowhere, the solution becomes clear. This sudden “aha” moment marks the culmination of mental processes that have been working behind the scenes to reorganize information and generate a new perspective .

2. Restructuring of Problem-Solving Strategies

Insight learning often involves a restructuring of mental representations or problem-solving strategies . Instead of simply trying different approaches until stumbling upon the correct one, individuals experience a shift in how they perceive and approach the problem. This restructuring allows for a more efficient and direct path to the solution once insight occurs.

3. Aha Moments

A hallmark of insight learning is the experience of “aha” moments. These moments are characterized by a sudden sense of clarity and understanding, often accompanied by a feeling of satisfaction or excitement. It’s as if a mental lightbulb turns on, illuminating the solution to a previously perplexing problem.

These moments of insight can be deeply rewarding and serve as powerful motivators for further learning and problem-solving endeavors.

Four Stages of Insight Learning Theory

Insight learning unfolds in a series of distinct stages, each contributing to the journey from problem recognition to the sudden realization of a solution. These stages are as follows:

1. Problem Recognition

The first stage of insight learning involves recognizing and defining the problem at hand. This may entail identifying obstacles, discrepancies, or gaps in understanding that need to be addressed. Problem recognition sets the stage for the subsequent stages of insight learning by framing the problem and guiding the individual’s cognitive processes toward finding a solution.

2. Incubation

After recognizing the problem, individuals often enter a period of incubation where the mind continues to work on the problem unconsciously. During this stage, the brain engages in background processing, making connections, and reorganizing information without the individual’s conscious awareness.

While it may seem like a period of inactivity on the surface, incubation is a crucial phase where ideas gestate, and creative solutions take shape beneath the surface of conscious thought.

3. Illumination

The illumination stage marks the sudden emergence of insight or understanding. It is characterized by a moment of clarity and realization, where the solution to the problem becomes apparent in a flash of insight.

This “aha” moment often feels spontaneous and surprising, as if the solution has been waiting just below the surface of conscious awareness to be revealed. Illumination is the culmination of the cognitive processes initiated during problem recognition and incubation, resulting in a breakthrough in understanding.

4. Verification

Following the illumination stage, individuals verify the validity and feasibility of their insights by testing the proposed solution. This may involve applying the solution in practice, checking it against existing knowledge or expertise, or seeking feedback from others.

Verification serves to confirm the efficacy of the newfound understanding and ensure its practical applicability in solving the problem at hand. It also provides an opportunity to refine and iterate on the solution based on real-world feedback and experience.

Famous Examples of Insight Learning

Examples of insight learning can be observed in various contexts, ranging from everyday problem-solving to scientific discoveries and creative breakthroughs. Some well-known examples of how insight learning theory works include the following:

Archimedes’ Principle

According to legend, the ancient Greek mathematician Archimedes experienced a moment of insight while taking a bath. He noticed that the water level rose as he immersed his body, leading him to realize that the volume of water displaced was equal to the volume of the submerged object. This insight led to the formulation of Archimedes’ principle, a fundamental concept in fluid mechanics.

Köhler’s Chimpanzee Experiments

In Wolfgang Köhler’s experiments with chimpanzees on Tenerife in the 1920s, the primates demonstrated insight learning in solving novel problems. One famous example involved a chimpanzee named Sultan, who used sticks to reach bananas placed outside his cage. After unsuccessful attempts at using a single stick, Sultan suddenly combined two sticks to create a longer tool, demonstrating insight into the problem and the ability to use tools creatively.

Eureka Moments in Science

Many scientific discoveries are the result of insight learning. For instance, the famed naturalist Charles Darwin had many eureka moments where he gained sudden insights that led to the formation of his influential theories.

Everyday Examples of Insight Learning Theory

You can probably think of some good examples of the role that insight learning theory plays in your everyday life. A few common real-life examples include:

Finding a lost item : You might spend a lot of time searching for a lost item, like your keys or phone, but suddenly remember exactly where you left them when you’re doing something completely unrelated. This sudden recollection is an example of insight learning.
Untangling knots : When trying to untangle a particularly tricky knot, you might struggle with it for a while without making progress. Then, suddenly, you realize a new approach or see a pattern that helps you quickly unravel the knot.
Cooking improvisation : If you’re cooking and run out of a particular ingredient, you might suddenly come up with a creative substitution or alteration to the recipe that works surprisingly well. This moment of improvisation demonstrates insight learning in action.
Solving riddles or brain teasers : You might initially be stumped when trying to solve a riddle or a brain teaser. However, after some time pondering the problem, you suddenly grasp the solution in a moment of insight.
Learning a new skill : Learning to ride a bike or play a musical instrument often involves moments of insight. You might struggle with a certain technique or concept but then suddenly “get it” and experience a significant improvement in your performance.
Navigating a maze : While navigating through a maze, you might encounter dead ends and wrong turns. However, after some exploration, you suddenly realize the correct path to take and reach the exit efficiently.
Remembering information : When studying for a test, you might find yourself unable to recall a particular piece of information. Then, when you least expect it, the answer suddenly comes to you in a moment of insight.

These everyday examples illustrate how insight learning is a common and natural part of problem-solving and learning in our daily lives.

Exploring the Uses of Insight Learning

Insight learning isn’t an interesting explanation for how we suddenly come up with a solution to a problem—it also has many practical applications. Here are just a few ways that people can use insight learning in real life:

Problem-Solving

Insight learning helps us solve all sorts of problems, from finding lost items to untangling knots. When we’re stuck, our brains might suddenly come up with a genius idea or a new approach that saves the day. It’s like having a mental superhero swoop in to rescue us when we least expect it!

Ever had a brilliant idea pop into your head out of nowhere? That’s insight learning at work! Whether you’re writing a story, composing music, or designing something new, insight can spark creativity and help you come up with fresh, innovative ideas.

Learning New Skills

Learning isn’t always about memorizing facts or following step-by-step instructions. Sometimes, it’s about having those “aha” moments that make everything click into place. Insight learning can help us grasp tricky concepts, master difficult skills, and become better learners overall.

Insight learning isn’t just for individuals—it’s also crucial for innovation and progress in society. Scientists, inventors, and entrepreneurs rely on insight to make groundbreaking discoveries and develop new technologies that improve our lives. Who knows? The next big invention could start with someone having a brilliant idea in the shower!

Overcoming Challenges

Life is full of challenges, but insight learning can help us tackle them with confidence. Whether it’s navigating a maze, solving a puzzle, or facing a tough decision, insight can provide the clarity and creativity we need to overcome obstacles and achieve our goals.

The next time you’re feeling stuck or uninspired, remember: the solution might be just one “aha” moment away!

Alternatives to Insight Learning Theory

While insight learning theory emphasizes sudden understanding and restructuring of problem-solving strategies, several alternative theories offer different perspectives on how learning and problem-solving occur. Here are some of the key alternative theories:

Behaviorism

Behaviorism is a theory that focuses on observable, overt behaviors and the external factors that influence them. According to behaviorists like B.F. Skinner, learning is a result of conditioning, where behaviors are reinforced or punished based on their consequences.

In contrast to insight learning theory, behaviorism suggests that learning occurs gradually through repeated associations between stimuli and responses rather than sudden insights or realizations.

Cognitive Learning Theory

Cognitive learning theory, influenced by psychologists such as Jean Piaget and Lev Vygotsky , emphasizes the role of mental processes in learning. This theory suggests that individuals actively construct knowledge and understanding through processes like perception, memory, and problem-solving.

Cognitive learning theory acknowledges the importance of insight and problem-solving strategies but places greater emphasis on cognitive structures and processes underlying learning.

Gestalt Psychology

Gestalt psychology, which influenced insight learning theory, proposes that learning and problem-solving involve the organization of perceptions into meaningful wholes or “gestalts.”

Gestalt psychologists like Max Wertheimer emphasized the role of insight and restructuring in problem-solving, but their theories also consider other factors, such as perceptual organization, pattern recognition, and the influence of context.

Information Processing Theory

Information processing theory views the mind as a computer-like system that processes information through various stages, including input, processing, storage, and output. This theory emphasizes the role of attention, memory, and problem-solving strategies in learning and problem-solving.

While insight learning theory focuses on sudden insights and restructuring, information processing theory considers how individuals encode, manipulate, and retrieve information to solve problems.

Restructuring processes and Aha! experiences in insight problem solving

Jennifer Wiley ORCID: orcid.org/0000-0002-2590-7392 1 &
Amory H. Danek ORCID: orcid.org/0000-0002-2849-8774 2

Nature Reviews Psychology volume 3 , pages 42–55 ( 2024 ) Cite this article

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Insightful solution processes represent cases of problem solving in which the emergence of a new interpretation allows for an abrupt shift from bewilderment to clarity. One approach to researching insight problem solving emphasizes cognitive restructuring of the problem representation as a defining feature of the insightful solution process. By contrast, another approach emphasizes phenomenological Aha! experiences. In this Review, we summarize both approaches, considering the restructuring processes involved in finding a solution and the Aha! experiences that might accompany solutions. We then consider the extent to which Aha! experiences co-occur with restructuring, and the critical observation that sometimes they do not. We conclude by proposing avenues for future research that combine the methodologies used to study restructuring and Aha! experiences to better understand the cognitive and phenomenological underpinnings of insight problem solving and the connections between them.

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The authors thank I. K. Ash, P. J. Cushen, T. George, A. F. Jarosz, T. S. Miller and S. Ohlsson for discussion on these topics.

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Wiley, J., Danek, A.H. Restructuring processes and Aha! experiences in insight problem solving. Nat Rev Psychol 3 , 42–55 (2024). https://doi.org/10.1038/s44159-023-00257-x

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MINI REVIEW article

Current understanding of the “insight” phenomenon across disciplines.

Messerli Research Institute, University of Veterinary Medicine, Medical University of Vienna, University of Vienna, Vienna, Austria

Despite countless anecdotes and the historical significance of insight as a problem solving mechanism, its nature has long remained elusive. The conscious experience of insight is notoriously difficult to trace in non-verbal animals. Although studying insight has presented a significant challenge even to neurobiology and psychology, human neuroimaging studies have cleared the theoretical landscape, as they have begun to reveal the underlying mechanisms. The study of insight in non-human animals has, in contrast, remained limited to innovative adjustments to experimental designs within the classical approach of judging cognitive processes in animals, based on task performance. This leaves no apparent possibility of ending debates from different interpretations emerging from conflicting schools of thought. We believe that comparative cognition has thus much to gain by embracing advances from neuroscience and human cognitive psychology. We will review literature on insight (mainly human) and discuss the consequences of these findings to comparative cognition.

Introduction

A 7years old girl is standing at a table into which psychologists have fixed a vertical transparent tube containing a small basket with a handle and a sparkly sticker inside. On the table, alongside the tubes, lie a long straight piece of pipe-cleaner and a colorful string. After inserting her finger which only reaches down about a third of the tube, the girl immediately grabs the pipe-cleaner and attempts several times to use it to press the handle of the basket against the tube wall and pull it up. The tube is too narrow and the attempts remain unsuccessful. With a hesitant movement, the colorful string is also briefly dangled into the tube before she seems to get distracted ( Isen et al., 1987 ; Subramaniam et al., 2009 ). Her gaze seems lost for a moment ( Segal, 2004 ; Kohn and Smith, 2009 ) when suddenly her pupils dilate ( Salvi et al., 2020 ) and a smile appears ( van Steenburgh et al., 2012 ). She expresses a drawn-out and slightly soaring “Aaahhhh!” and immediately grabs the pipe-cleaner, bends a little hook into one of its distal ends, inserts the hooked end of the pipe-cleaner back into the tube, hooks the handle of the basket, pulls the basket over the rim, and claims her reward with determination ( Stuyck et al., 2021 ).

The hook bending paradigm is a so-called ill-structured innovation task in which the path to the solution is missing information about how to get from its start to its goal state ( Cutting et al., 2014 ). Interestingly, children that are seven or older find the entire multistep solution to this problem very suddenly rather than in an incremental way. Notably, the hook bending task has similarly been used to test tool innovation in large brained birds and apes, which show a rather ratchet-like improvement upon solving the task for the first time (rarely failing after first success; Weir, 2002 ; Bird and Emery, 2009a ; Laumer et al., 2017 , 2018 ).

The moment just before the little girl tackles the problem, or what Hermann von Helmholtz referred to as a “happy idea” ( Wallas, 1926 ), may be a familiar sentiment to most of us. Such moments of so-called insight are also a recurringly described (and romanticized) phenomenon in scientific history: Newton and that apple, Archimedes in the bathtub, and Poincaré stepping on the bus; all of them have a common pattern: someone with accumulated experience escapes for a moment from the problem to be solved and suddenly finds themselves surprised (without knowing how or why) with the solution.

Insight As a Global Phenomenon

Although there are cultural differences in the importance we attribute to insight as a source of creative output ( Rudowicz and Yue, 2000 ; Niu and Sternberg, 2006 ; Shao et al., 2019 ), the traditional description of the stages of the creative process is very similar in European psychology (four stage model by Wallas, 1926 ) and Eastern philosophy (Yoga Sutras; Maduro, 1976 ; Shao et al., 2019 ). Insight itself also has an important bearing in Eastern cultures. For example, in Theravada Buddhism, the goal of vipassana meditation is to reach a sudden understanding, abhisamaya (insight), which contrasts with gradually attained understanding (anapurva). Both the description of the phenomenon and the way in which it is achieved, fit with the popular Western notion of insight ( Laukkonen and Slagter, 2021 ).

Although we can have reasonable confidence that insight is a global phenomenon and not a myth specific to western culture (a WEIRD one; Henrich et al., 2010 ), it still holds many mysteries regarding its mechanisms and function ( Shen et al., 2018 ), as well as its evolution and presence (and level of expression) in other species ( Call, 2013 ).

Scientific Insight

Given the importance of the subjectively perceived components of insight, the phenomenon is certainly easier to study in humans than in non-human animals, both because of the possibility to report verbally (the subject might describe the suddenness of the solution’s appearance and the emotions involved, but also specific difficulties with aspects of the task, and how close the subject believes he or she is to the solution at any given moment) and the methodology (because of test diversity and the relative ease of applying neuroimaging technology).

A review by Kounios and Beeman (2014) defines insight as any sudden comprehension, realization, or problem solution that involves a reorganization of the elements of a subject’s mental representation of a stimulus, situation, or event to yield a non-obvious or nondominant interpretation. Note, however, that there are various definitions of insight with some considering it as a dynamic process, and others as an end state ( Call, 2013 ; Kounios and Beeman, 2014 ; Shen et al., 2018 ). Insight is further frequently linked to a number of traits (such as an impasse or a pleasant feeling of surprise) that may or may not be considered essential to some authors, resulting in variation in the respective definitions (as reviewed in Kounios and Beeman, 2014 ; and the reason we are using their definition). While neuroscience has been hampered by some inconsistencies in definitions of insight (see Kounios and Beeman, 2014 for examples), experimental evidence (especially due to advances in neuroimaging; e.g., Shen et al., 2018 ) has helped to guide research along a convergent path ( Stuyck et al., 2021 ), suggesting that innovation achieved through insight-like experiences can be clearly distinguished from other problem solving strategies ( van Steenburgh et al., 2012 ).

Despite the success within neuroscience, the topic of insight and even the use of the term in animal behavior has caused significant theoretical debates in comparative cognition (e.g., Kacelnik, 2009 ; von Bayern et al., 2009 ; Emery, 2013 ). Notably, few animal studies are included the recent literature on human problem solving or neuroscience ( Shettleworth, 2012 ; Call, 2013 ).

First Scientific Approximations To Insight

In 1925–1926, Wolgang Köhler and Graham Wallas independently published two books that had long lasting effects on the general perception of problem solving: The Mentality of Apes, by Köhler, and The Art of Thoughts, by Wallas.

Wallas, inspired by the ideas of Hermann von Helmholtz and Henri Poincare, proposed four stages of progression for a creative process ( Wallas, 1926 ). Helmholtz, during a banquet held for his 70th birthday in 1891, revealed how he had reached his best ideas; always after first researching a problem in detail, letting it rest, and seeking a pleasant distraction. This way he was often surprised by a solution in the form of a pleasant experience. Wallas named these stages preparation (investigative stage), incubation (temporally discarding the problem from conscious thought), and illumination (the sudden arrival of a new “happy idea”), to which he added a fourth, the verification of the solution. These four stages have been recurrently used as a framework for studying insight in the psychological literature ( Luo and Niki, 2003 ; Jung-Beeman et al., 2004 ; Sandkühler and Bhattacharya, 2008 ; Weisberg, 2013 ). Although Wallas’ work covers the creative process in rather broad terms, its relevance to the study of insight is remarkable, due to the close proximity and similarity in conceptualization, measures, and processes ( Shen et al., 2017 , 2018 ).

Almost at the same time, Wolfgang Köhler, one of the pioneers of Gestalt psychology, introduced the term insight into comparative psychology (although this way of problem solving was already described before him in non-human animals; Turner, 1909 ; Köhler, 1925 ; Weisberg, 2006 ; Galpayage Dona and Chittka, 2020 ). Gestalt psychologists proposed that insight depends on different mechanisms to trial and error learning, which, according to Thorndike (1911) , was the only way in which animals could solve problems ( Köhler, 1925 ; Koffka, 1935 ; Duncker, 1945 ; Wertheimer, 1959 ). Köhler worked for years at the Casa Amarilla in Tenerife (Canary Islands, Spain) with seven chimpanzees, testing them in experiments where they had to find unusual methods to reach food (see Figure 1 ). In those experiments, Köhler found problem solving strategies that did not seem compatible with classical associative learning routines: After an unsuccessful period of trial and error, in which the chimpanzees used familiar strategies, they stopped trying. Nevertheless, after a while some of them returned with a completely different and, this time, immediately successful strategy. After their first success, the animals could immediately retrieve the correct sequence of steps on the following occasions when they faced the same problem. Köhler, at the time, described these strategies as cognitive trial and error and insight, rather than associative processes.

(A) The Crow and the Pitcher, illustrated by Milo Winter (1919; Public Domain). Stones must be dropped into water to have access to the liquid, or to a floating object. (B) String-pulling; “Still Life with Fruit and a Goldfinch,” Abraham Mignon (1660; Public Domain). Goldfinch’s detail, right side. To have access to the hanging object, the string must be pulled first; as seem in Jacobs and Osvath (2015) . (C) Three-boxes experiment; “Grande on an insecure construction” The Mentality of Apes, Köhler (1925 ; CC) To get the banana, the chimpanzees must pile the boxes. (D) Early representation of the nine-dot problem; Egg of Columbus, Sam Loyds Cyclopedia of Puzzles (1914; Public Domain). Nine dots, arranged in three parallel lines, must be linked with four connected straight lines. (E) Candle problem; Duncker (1945 ; Public Domain) A candle must be attached to the wall; subjects are given a box of tacks, a candle, and matches. Problem on top, solution, below. (F) Compound Remote Associates Test test; developed by Mednick and Mednick (1967) . Subjects are given the three words on top and have to find one to link with each one of them (as the one in brackets). All Public Domain and Creative Commons (CC) images can be found in Wikimedia Commons.

Other Gestalt psychologists adapted Köhler’s problem solving methodology to study insight in humans. Duncker (1945) , for example, designed situations in which everyday objects had to be used in unusual ways to solve a task (e.g., the candle problem, see Figure 1 ; Duncker, 1945 ). Notably, if he asked the subjects to use these objects in their usual way before the test, the success rate was reduced. Duncker and other Gestalt psychologists (e.g., Maier, 1930 ; Luchins, 1942 ; Scheerer, 1963 ) concluded that the repeated application of incorrectly selected knowledge could prevent the deep conceptual understanding necessary to achieve insight. This phenomenon is now known as functional fixedness ( Duncker, 1945 ).

It was, however, the British ornithologist W. H. Thorpe who coined in his book Learning and Instinct in Animals (1956) the most prevalent definition of insight in psychology today; “ the sudden production of a new adaptive response not arrived at by trial behaviour or the solution of a problem by the sudden adaptive reorganization of experience .” We will later explain how an over-emphasis on the absence of trial and error learning, and a lack of attention to the “reorganization of experience,” may have affected the interpretation of insight in comparative cognition.

Our Current Understanding of Insight

Insight is often conceptualized as a process in which a subject has a sudden realization of how to solve a novel problem ( Schooler et al., 1995 ; Sheth et al., 2009 ). Thereby specific elements of a subject’s mental representation of various stimuli, situations, or events are reorganized to yield a nonobvious or nondominant interpretation ( Kounios and Beeman, 2014 ). Insight is associated with a number of characteristic phases that set it apart from other mental processes employed in problem solving, such as a distinctive subjective momentary experience of surprise and delight, the “aha” or “eureka” moment ( Bowden et al., 2005 ).

Neuroscience typically contrasts insight with analytical reasoning within problem solving. A directly perceivable difference between the two seems to be a more or less gradual progress toward a solution in analytical thinking ( Smith and Kounios, 1996 ), while individuals are abruptly surprised by the latter during an insightful solution ( Metcalfe and Wiebe, 1987 ). Thus, insight is believed to depend by a large degree (but not completely) on unconscious mental processing, as we will see in the next sections ( Sandkühler and Bhattacharya, 2008 ; Shen et al., 2013 , 2018 ; Weisberg, 2013 ).

Convergent Insight Process Theories

The main theoretical proposals to explain insight largely differ with regards to the amount of conscious processing they describe involved in an insightful event. For example, approaches, such as the representational change theory (also called the redistribution theory; ( Ohlsson, 1992 , 2011 ; Knoblich et al., 1999 ), advocate a completely unconscious redistribution of information ( Knoblich et al., 1999 ; Ohlsson, 2011 ), whereas the progress monitoring theory (or criterion for satisfactory progress theory; MacGregor et al., 2001 ; Chu et al., 2007 ) proposes insight through a conscious process: searching consciously among a pool of possible solutions during which wrongful presumptions are dropped in favor of a working solution.

In an attempt to find a bridge between the strengths of both previous theories, Weisberg proposed an integrated theory of insight comprising several phases: the individual would first attempt to find a solution by using strategies based on long-term memory; if this fails, the subject would use rules of thumb or more complex heuristics to acquire information about the problem before re-confronting its long-term memory; then, a conscious solution via a restructuring of old and new information may thereby be achieved; and if the process reaches an impasse and new information is no longer acquired, an unconscious restructuration of knowledge would take place ( Weisberg, 2015 ). Interestingly, the four stages of Weisberg's (2015) proposal bear some parallels to those suggested by Wallas in the mid twentieth century ( Wallas, 1926 ). “Preparation” would comprise the first three phases of the integrated insight theory, while “incubation” and “illumination” could be interpreted as part of the fourth, where insight is achieved through an unconscious process (see above, section four, to find Wallas’ proposal).

Fixation and Impasse

The fixation and impasse (the repetition of incorrect strategies, and the following temporary withdrawal of action), as already described by Duncker (1945) , are likely the result of an inappropriate knowledge base ( Wiley, 1998 ) or incomplete heuristics ( Knoblich et al., 1999 , 2001 ). Knoblich et al. (1999) found that expertise in algebra can negatively affect insightful arithmetic problem solving. Similarly, great apes have trouble innovating a solution to a problem when the tools or objects at their disposal were previously used in a different way ( Hanus et al., 2011 ; Ebel et al., 2020 ). Such “functional fixedness” may be one of the factors responsible for the fixation leading to an impasse.

It is important to highlight at this point that there are no insight problems but only insight solutions: any problem solved by insight could also be solved analytically ( van Steenburgh et al., 2012 ), and that an impasse (although common) is not required for insight to occur ( MacGregor et al., 2001 ; Ormerod et al., 2002 ; Kounios and Beeman, 2014 ). However, the design of a problem is highly important as it determines the nature of its solution/s. Experimental subjects in classical insight challenges, such as Duncker’s candle problem (e.g., Duncker, 1945 ; Knoblich et al., 2001 ; Huang, 2017 ), often encounter an impasse prior to the solution. This is much less common in so-called CRAT-based challenges (a specific type of word puzzle, see Figure 1 ; e.g., Cranford and Moss, 2012 ; Webb et al., 2019 ) even if they are also solved by insight. This could be because classical tests often have misleading structures and/or contain elements that may provoke functional fixedness ( Duncker, 1945 ; Hanus et al., 2011 ; Stuyck et al., 2021 ). Nevertheless, the scientific approach for detecting an impasse may also be problematic ( Stuyck et al., 2021 ): Studies that found no impasse before insightful solutions mostly relied on verbal reports (e.g., Webb et al., 2019 ), while when other methods were used an impasse was more likely to be detected (e.g., eye tracking, Huang, 2017 ; neurophysiological measurements, Shen et al., 2018 ).

Incubation/Restructuring and Illumination

An impasse is usually followed by an incubation/restructuring stage, which is suspected to constitute the insight’s core ( Wallas, 1926 ; Sandkühler and Bhattacharya, 2008 ; Sio and Ormerod, 2009 ; Cranford and Moss, 2012 ; Weisberg, 2013 ). Although restructuring can of course be done consciously ( Weisberg, 2015 ), it may also happen at a time during which a subject consciously withdraws from the problem at hand ( van Steenburgh et al., 2012 ; Kounios and Beeman, 2014 ; Shen et al., 2018 ). We know that insight-like responses improve when participants take a break after reaching an impasse (or when the task is simply removed from their sight; Kohn and Smith, 2009 ), regardless of the duration of the break, and particularly when the break is occupied with a different, cognitively demanding task; Segal, 2004 ).

Human neuroimaging and electrophysiology-based studies suggest a significant function of the prefrontal cortex in the process of overcoming impasse to reach incubation (e.g., Qiu et al., 2010 ; Zhao et al., 2013 ; Seyed-Allaei et al., 2017 ; Shen et al., 2018 ). The right inferior frontal gyrus plays a role in evaluating possible solutions while the left gyrus seems to control the suppression of inappropriate mental sets or dominantly activated associations (e.g., Jung-Beeman et al., 2004 ; Shen et al., 2013 , 2018 ; Wu et al., 2015 ). This corresponds with studies reporting brain asymmetries in insight tests. Studies using insight and priming with word hints (where the left hemisphere typically has an advantage; van Steenburgh et al., 2012 ), the left visual field (right hemisphere) has shown a strong advantage over the right, with primed participants finding more solutions faster ( Bowden and Beeman, 1998 ; Beeman and Bowden, 2000 ).

Studies based on event-related potentials have so far been able to identify two distinct cognitive processes involved in achieving an insightful event: the breaking down of the impasse (allowing incubation/restructuring) and the formation of new associations prior to the solution ( Luo and Niki, 2003 ; Luo et al., 2011 ; Zhao et al., 2013 ; Shen et al., 2018 ; it is also described as the enlightenment stage by Wallas, 1926 ).

Associations that will result in a solution can take different routes; once strong yet incorrect associations can be overcome, weaker yet correct association can be detected ( Shen et al., 2018 ). Interestingly, the latter is facilitated by a positive emotional state ( Isen et al., 1987 ; Subramaniam et al., 2009 ; van Steenburgh et al., 2012 ). In humans, a positive emotional state at the start of testing is associated with increased activity in the anterior cingulate cortex (which is related to monitoring cognitive conflict; Carter et al., 2000 ) and an increase in insightful solutions ( Subramaniam et al., 2009 ).

While neurobiology and cognitive psychology embrace insightful solutions achieved by associations learned in the past, comparative cognition tends to exclude associative learning from its notion of insight, which is a misconception as insight can occur through distant or weak associations ( Shettleworth, 2012 ; Call, 2013 ). In comparative cognition, insight has occasionally been used as a default explanation upon failing to detect the typical gradual process of associative learning.

A candidate for explaining how we can learn non-obvious associations is latent learning ( Tolman and Honzik, 1930 ; Tolman, 1948 ). The nervous system can register associations without the need for positive reinforcement (such as those that can be acquired through random exploration). These associations remain latent and are candidates for insightful solutions ( Thorpe, 1956 ). Latent associations, being weak, can be adjusted more flexibly if required ( Call, 2013 ). In contrast, strong associations can result in functional fixedness where a previous solution prevents the innovation of a new solution (e.g., humans, Duncker, 1945 ; great apes, Ebel et al., 2020 ).

However, the path toward a solution can be achieved by other mechanisms. The free energy principle [the basis of Predictive Processing Theory (PPT), e.g., Hohwy and Seth, 2020 ; Francken et al., 2021 ] predicts that all sentient beings minimize uncertainty for energetic reasons ( Friston, 2003 ). According to PPT, all interaction with the environment involves constant amendment between perceptual input and the internal models ( Friston et al., 2016a ). When the flow of input stops during an impasse, models continue to be optimized without the agent consciously perceiving it. This has been called fact-free learning or model selection and reduction (model selection, Aragones et al., 2005 ; model reduction, Friston et al., 2016b ). In the absence of new data, the only way we can optimize our generative models is by making them simpler ( Friston et al., 2017 ).

Model reduction is a similar process to that described in the N-REM phase of sleep, where redundant connections between neurons are eliminated ( Tononi and Cirelli, 2006 ) and models are reduced in complexity in the absence of new sensory input ( Friston et al., 2017 ).

Model reduction occurs neither only during sleep, nor only in humans. Rats that move away from exploratory or spatial foraging behavior, and enter short periods of rest, have been found to have hippocampal activity similar to what we would expect in models undergoing insight-compatible changes ( Gupta et al., 2010 ; Pezzulo et al., 2014 ; Friston et al., 2017 ). Internally generated sequences (sequences of multi-neuron firing activity that do not reflect an ongoing behavioral sequence) seem to be able to restructure models, not only consolidating memory but also exploring potential solutions ( Pezzulo et al., 2014 ).

The Eureka Experience

A popular event related to insight is the so-called “aha” moment, a subjective experience of surprise and delight accompanied by sudden solutions ( Bowden et al., 2005 ; Sandkühler and Bhattacharya, 2008 ; Weisberg, 2013 ; Shen et al., 2017 ). This pleasant experience is probably one of the reasons why insight responses are associated with positive emotions versus analytical solutions that are negatively perceived ( Shen et al., 2016 , 2017 ; Webb et al., 2016 , 2019 ). This may also contribute to a better memorization and a higher success rate of insightful responses (e.g., Danek et al., 2013 ; Webb et al., 2016 ; Salvi et al., 2020 ; Stuyck et al., 2021 ).

Notably, insight does not necessarily require this “aha” experience. In verbal tests, insight lacking major emotional changes has been reported ( Kounios and Beeman, 2014 ). This may be the reason why CRAT tests do not elicit a perceivable impasse experience ( Stuyck et al., 2021 ). Nevertheless, the impasse may be an important contributing factor to the surprise element of the insight revelation as it fosters the perception of a metacognitive error in which we solve a problem faster than expected ( Dubey et al., 2021 ).

The subpersonal nature of model reduction (that is, there is no explicit inner model, hence no conscious experience of the reduction process) could explain why the agent becomes aware at the precise instance of a new association, and not before ( Metcalfe and Wiebe, 1987 ; Friston et al., 2017 ; Shen et al., 2018 ). Another proposed explanation for the relation of insight with consciousness is the asymmetrical involvement of both hemispheres and the important role of the right hemisphere in key parts of the process (see split brain perception studies, e.g., Gazzaniga, 1998 ; van Steenburgh et al., 2012 ). Furthermore, the conscious perception of the solution is plausible considering the close relationship between associative learning and consciousness ( Ginsburg and Jablonka, 2007 , 2019 ) and the essential role of consciousness for the former to occur (e.g., Baars et al., 2013 ; Meuwese et al., 2013 ; Weidemann et al., 2016 ).

Non-Human Animals, Problems, and Solutions

Comparative cognition has attempted to tackle the presence of insight in animals by rating the speed of their performance on technical problem or their ability to transfer information from one task to another ( Seed and Boogert, 2013 ).

One issue with this may be that, as mentioned earlier, there are no insight problems, only insight solutions; a problem designed to be solved by insight can also be solved by other processes ( van Steenburgh et al., 2012 ). Epstein et al. (1984) tried to highlight this issue in a popular paper which showed that pigeons solved seemingly complex problems spontaneously by “chaining” blocks of previously learned information.

Neuroscience’s results and advances have been able to compensate a lack of theoretical consistency regarding insight. Cognitive research on animal insight, on the other hand, has been limited to the creativity of experimental designs, with no apparent chance of ending long-running debates stemming from two opposing schools of thought, cognitive psychology and behaviorism, “romantics” against “killjoys” ( Shettleworth, 2010 , 2012 ; Call, 2013 ; Starzak and Gray, 2021 ). While we believe that the progress of comparative cognition feeds (as a dissipative structure) on the continued conflict between the two positions, the lack of experimental progress has kept these discussions in an impasse (e.g., Heinrich, 1995 ; Kacelnik, 2009 ; Chittka et al., 2012 ; Taylor et al., 2012 ; Emery, 2013 ; Starzak and Gray, 2021 ).

Today we know that insight is a measurable phenomenon with a physiological basis that is beginning to be revealed ( Shen et al., 2018 ). Moreover, it makes little sense to set the phenomenon apart from associative learning and experience ( Shettleworth, 2010 , 2012 ; Hanus et al., 2011 ; Call, 2013 ; Shen et al., 2018 ; Ebel et al., 2020 ). Insight does not mean developing de novo behaviors to solve a problem, but to find a solution by restructuring the problem, even if the agent reorganizes old experiences to apply them to a novel context.

Although insight involves making the nonobvious seem obvious, and even tends to correlate with a higher success rate at problem solving (higher successful rate, Salvi et al., 2016 ; Webb et al., 2016 ; but see, Stuyck et al., 2021 ), a successful restructuring does not necessarily imply a correct conceptualization of the full nature of the problem, and an answer obtained by insight need not necessarily be correct ( Kounios and Beeman, 2014 ). Just as a feeling of understanding does not equate to a true understanding of the problem, we must thus be careful in equating insight with understanding or suggesting that one predicts the other.

Insight may exist in animals outside humans and could even be relatively widespread in nature (e.g., Shettleworth, 2012 ; Pezzulo et al., 2014 ). Yet to proficiently tackle the phenomenon in non-verbal species is an unsolved problem in comparative cognition.

While rodent studies suggest that insight does not require sophisticated cognition, the role of the prefrontal cortex in important insight stages may suggest insightful solutions are more likely to emerge in species that have highly developed and functionally equivalent brain regions ( Shettleworth, 2010 , 2012 ; Call, 2013 ; Olkowicz et al., 2016 ; Shen et al., 2018 ).

Methodologies, such as the priming of different brain hemispheres, related to insight (which function similarly in non-human primates as in humans) as well as new technologies in animal eye tracking open the door to technically challenging targeted studies in species other than our own ( Krupenye et al., 2016 ; Shen et al., 2018 ; Völter et al., 2020 ; Ben-Haim et al., 2021 ).

The crucial role of subjective experience in insight, as well as the traditional reliance on verbal reports in a large number of studies, makes it tempting to conclude that the study of insight is inaccessible in non-human animals. Nonetheless, other signatures of insight do exist (e.g., Kounios and Beeman, 2014 ). Apart from EEG and fMRI studies, evidence of human insight stems also from eye tracking studies (e.g., Salvi, 2013 ; Salvi et al., 2016 ; Huang, 2017 ), grip strength ( Laukkonen et al., 2021 ), heart rate ( Hill and Kemp, 2018 ), pupil dilation, and eye movement (with pupil dilation happening only just prior to an insightful event, and an increase in microsaccade rate coinciding with analytic responses; Salvi et al., 2020 ). Moreover, it has been shown repeatably that agents do not even necessarily need to solve the problem. A promising approach could be to confront an animal with a problem and then, after a period unsuccessful interaction, to suddenly show the solution and record the response (e.g., Kizilirmak et al., 2016 ; Webb et al., 2019 ).

Even the “aha” moment itself might be accessible to study in non-verbal subjects, given the expected physiological emotional response that follows it. We know that many animals show an emotional response while learning how to solve tasks (independent from the presence of a reward; e.g., cows, Hagen and Broom, 2004 ; goats, Langbein et al., 2004 ; horses, Mengoli et al., 2014 ; dogs, McGowan et al., 2014 ; dolphins, Clark et al., 2013 ). Studying insight through the presentation of a solution would thus require both a behavioral analysis (as in traditional contrafreeloading tests or yoked experimental designs; e.g., Hagen and Broom, 2004 ; Rosenberger et al., 2020 ) as well as a physiological one. Artificially altering the transparency of the path toward the solution, and altering the time spent at an apparent impasse, may allow us to predict and modify the intensity of the respective physiological (as it would be an increased heart rate; Hill and Kemp, 2018 ) and behavioral responses (e.g., in dogs, we would predict pupil dilation, tail wagging, and increased general activity; McGowan et al., 2014 ; Webb et al., 2019 ; Salvi et al., 2020 ).

Insight is a measurable phenomenon in humans, and the mechanisms by which it occurs may well be accessible to species other than our own. Thanks to recent progress in neuroscience and human psychology, we are beginning to clarify the (in some cases subtle) differences that distinguish insight problem solving from other processes. Comparative cognition, however, has so far been limited in its approach. Performance-based setups using technical problems in both birds and mammals have produced highly interesting and suggestive, yet, ambivalent evidence on animal insight (e.g., Heinrich, 1995 ; Mendes et al., 2007 ; Bird and Emery, 2009a , b ; Laumer et al., 2017 , 2018 ; von Bayern et al., 2018 ). We are optimistic that accomplishments in neuroscience and human psychology over the past decade can be incorporated into and inspire future comparative cognition studies in their ongoing quest to learn about the capacity for insight in species other than our own.

Author Contributions

AO-M wrote the first draft. AO-M and AA finished the manuscript. All authors contributed to the article and approved the submitted version.

The authors are funded by the WWTF Project CS18-023 and START project Y 01309 by the Austrian Science Fund (FWF) to AA.

Conflict of Interest

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.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Acknowledgments

We thank Poppy J. Lambert for her helpful suggestions and language correction of the manuscript.

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Keywords: insight, comparative cognition, problem solving, neuroimaging, comparative psychology

Citation: Osuna-Mascaró AJ and Auersperg AMI (2021) Current Understanding of the “Insight” Phenomenon Across Disciplines. Front. Psychol . 12:791398. doi: 10.3389/fpsyg.2021.791398

Received: 11 October 2021; Accepted: 15 November 2021; Published: 15 December 2021.

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*Correspondence: Antonio J. Osuna-Mascaró, [email protected]

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Overview of the Problem-Solving Mental Process

Identify the Problem
Define the Problem
Form a Strategy
Organize Information
Allocate Resources
Monitor Progress
Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

Asking questions about the problem
Breaking the problem down into smaller pieces
Looking at the problem from different perspectives
Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

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You can become a better problem solving by:

Practicing brainstorming and coming up with multiple potential solutions to problems
Being open-minded and considering all possible options before making a decision
Breaking down problems into smaller, more manageable pieces
Asking for help when needed
Researching different problem-solving techniques and trying out new ones
Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors. The Psychology of Problem Solving . Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving . Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

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

What Is Insight? Definition, Psychology, And Practical Examples

The Merriam-Webster dictionary defines insight as “the act or result of apprehending the inner nature of things or of seeing intuitively.” Psychology sees insight not as a means of acquiring insightful knowledge but rather as the act of becoming aware of insightful solutions. It can be helpful to understand both definitions of insight to know how to use it to improve your mental health.

What’s the difference between insight and knowledge?

Some subjects may be taught directly, while you can learn others from observation and repetition. You might notice that some knowledge seems to appear out of thin air. Before understanding insight psychology, taking a detour to understanding knowledge can be beneficial.

What is knowledge?

Knowledge is an awareness or familiarity with objects, events, ideas, or actions learned from experience, being taught, or instinct from birth. Articulation of this concept can be found in the movie Memento (2000) when the main character, who experiences short-term memory loss, explains that, despite not being able to remember what he had completed a few moments ago, he could understand inherent knowledge. For example, he knew the sound of knocking on wood and the feeling of lifting a glass of water. He says this type of knowledge is different because it is a form of memory.

How does insight relate to knowledge?

Wolfgang Kohler and his work with the Gestalt theory led him to some interesting findings in the early 1900s. He experimented with his chimp Sultan. In his experiment, Sultan was hungry. A banana was held out of reach. The only tools Sultan could use to reach the banana were two bamboo sticks of differing lengths, neither long enough to reach the banana.

Eventually, Sultan figured out that he could fit them together by playing with the sticks to form one long rod that would reach the banana. Unlike trial and error, Sultan used reason for this solution. He had given up actively trying different ways to get the banana when he discovered the sticks could be combined. The answer came to him in what is commonly referred to as an “Aha!” moment.

The key to this insight psychology is idleness or a reduced ability to see the finish line. Like Sultan, the subject or client may give up on finding a solution. As desperation approaches, they may use creativity and insight by combining their current knowledge of events with new knowledge.

How psychologists interpret insight

Among psychologists, there are varying interpretations of how knowledge and reasoning combine to present the consciousness with a viable solution to a given task. Below are a few theories.

The nothing special view

In the “nothing special” theory, insight occurs as a natural process of the brain continually taking in information and working to make the best use of it. A solution may arrive when presented with a task or issue due to how a person processes information. In this theory, no special or esoteric significance is given to intuition.

The neo-Gestaltist view

As with Kohler and Sultan, the Gestaltist view states that insight solution problem solving is not simple. Instead, they believe it has a special quality, placing it cognitively higher than routine problem-solving.

The three process view

The three-process view posits that there are three individual types of insight, including the following:

Selective-Encoding Insight: Distinguishing relevant from irrelevant information
Selective-Comparison Insight: Renewed perception of the relationship between old information and new information
Selective-Combination Insight: Using encoded information and applying it in a novel way.

The four stages of behavioral processes

Insight is marked by four stages of behavioral processes, including impasse, fixation, incubation, and the eureka moment.

Impasse: An impasse occurs when one gives up or reaches an area they struggle to solve.
Fixation: Fixation may be a particular solution attempted that is ineffective but attempted more than once, often with an obsessive focus.
Incubation: Incubation is a gap in solution attempts allowing the mind to clear itself of irrelevant information pertaining to the solution.
Eureka: Eureka involves the appearance of a solution in the individual’s mind that suddenly becomes clear.

What does psychological research say about insight?

Insight may affect how you live your life, tackle obstacles, and practice mental health and well-being. Below are a few studies on insight.

Graham Wallas and the nine dot puzzle

When dealing with abstract concepts, reframing them into concrete examples may be helpful. For example, Graham Wallas used the nine-dot puzzle in 1926 to show how individuals can arrive at solutions by insight. The goal was to connect all nine dots with a pencil without lifting the pencil off the paper and using the fewest possible lines. At first glance, it may seem impossible to complete the task due to a narrow perception.

Because the dots appear to be in a rectangle shape, your brain may assume the solution must be derived by drawing a rectangle. Once the insight that the rectangle does not exist or limit the puzzle, the solution to “go outside the lines” may be more prominent. You may be able to solve the puzzle using triangles or a zig-zag pattern.

Responses to the nine dot puzzle and banana problem

When you apply the insight psychology definition to mental health, it is not a banana or a puzzle on a piece of paper but rather an insight into the psyche. Many symptoms of mental health conditions are challenging to treat because of a lack of insight.

Not being aware that a symptom is a symptom of a mental health condition can be detrimental to finding the correct treatment. For example, those who experience substance use disorders may struggle to see that their substance use is a problem, rationalizing it by saying they can stop when they want to. Believing they do not have a problem can be a lack of insight. In these cases, having a guiding voice like a therapist can be beneficial.

If you are struggling with substance use, contact the SAMHSA National Helpline at (800) 662-4357 to receive support and resources. Support is available 24/7.

What are a few examples of insight?

Anyone can use insight, which doesn’t necessarily relate to psychology or treating mental illness. Problem-solving comes in all different shapes and sizes. In relationships, conflict can be an area where individuals use insight. Whether in familial or romantic relationships, you may find yourself at an impasse stage, feeling you’ve exhausted all options. Conflict at an impasse can be stressful for all parties and make the relationship seem hopeless. Below are a couple of examples that showcase insight.

Relationship example

If two spouses experience a pattern of constantly arguing, with communication breaking down, there can be a tendency to want to give up on the marriage. Taking time to step back from the situation, let emotions settle, and allow reason to prevail can provide insight. Introspection psychology , an act of examining or observing thoughts, emotions, and perceptions, allows individuals to gain insight. Knowledge of oneself and time to breathe can offer a different perspective for the “Aha!” moment to occur. A relationship is often complex and unique. Applying these concepts when appropriate may help you avoid conflict and stress.

Therapy example

Insight can also be helpful in a therapeutic session. For example, clients with social anxiety can shift their paradigm from fear of social situations to learning to manage their symptoms from within. Someone who pushes people away but craves intimacy can benefit from the insight that their actions may stem from a fear of abandonment. Many people may experience “Aha!” moments of eureka in therapy.

What to expect from insight psychology therapy

While it can be empowering to become aware of the above processes and apply them in your personal life, it can be overwhelming to wade through the ideas in your mind alone. In therapy, you can discuss these concerns with your therapist while maintaining an open, trusting relationship. If this is not your experience or you find in-person therapy inaccessible due to finances, location, or accessibility, you might try online therapy through a platform like BetterHelp.

Some methods of therapy have been aligned to elicit insight. For example, researchers have developed metacognitive insight and reflection therapy (MERIT) to help individuals recover from psychosis. Following a three-month trial, a 2020 study found significantly improved metacognition and other benefits from administering MERIT.

These insights were particularly pronounced among those who did not understand or believe that they had a problem, a common effect of psychosis. MERIT is increasingly available to psychologists around the US, as well as those who practice online. A recent survey revealed that nearly a third of respondents would not seek in-person counseling but would do so if online therapy were available. Online therapy continues to gain popularity, with four out of ten Americans using it since 2021.

Therapy is insight: Learn more about insight and insight therapy

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If you need a crisis hotline or want more insight into therapy, please see below:

RAINN (Rape, Abuse, and Incest National Network) - 1-800-656-4673
The National Suicide Prevention Lifeline - 1-800-273-8255
National Domestic Violence Hotline - 1-800-799-7233
NAMI Helpline (National Alliance on Mental Illness) - 1-800-950-6264

For more insight on mental health, please see:

SAMHSA (Substance Abuse and Mental Health Services Administration) SAMHSA Facebook , SAMHSA Twitter , SAMHSA LinkedIn
Mental Health America, MHA Twitter , MHA Facebook , MHA Instagram , MHA Pinterest , MHA LinkedIn
WebMD, WebMD Facebook , WebMD Twitter , WebMD Pinterest , WebMD LinkedIn
NIMH (National Institute of Mental Health), NIMH Facebook , NIMH Twitter, NIMH YouTube , NIMH LinkedIn
APA (American Psychiatric Association), APA Twitter , APA Facebook , APA LinkedIn , APA Instagram

Get help and insight now:

Emergency: 911
National Domestic Violence Hotline: 1- 800-799-7233
National Suicide Prevention Lifeline: 1-800-273-TALK (8255)
National Hopeline Network: 1-800-SUICIDE (784-2433)
Crisis Text Line: Text “DESERVE” TO 741-741
Lifeline Crisis Chat (Online live messaging): https://suicidepreventionlifeline.org/chat/
Theory Of Mind Medically reviewed by April Justice , LICSW
Consolidation Theory Of Forgetting Medically reviewed by Laura Angers Maddox , NCC, LPC
Psychologists
Relationships and Relations

Testimonials

Insight: Creative Problem Solving

In the business world, there is more and more pressure for creative problem solving for developing new products, streamlining delivery systems, optimizing managerial structure, and dealing with personnel and clients. Constant innovation is the game. But what do we do when we’re faced with a problem that we don’t know how to solve? In fact, what we know may actually get in the way of a new solution: Our brain’s electrical activity may inhibit other circuits, and other ideas. We tend to think of creativity in terms of art and music. We recognize that artists and musicians are creative people, but what about the rest of us? Does that mean we’re not at all creative or that creativity is not useful in our lives?

Key Takeaway

Insight is the sudden solution to a long-vexing problem, a sudden recognition of a new idea, or a sudden understanding of a complex situation, an Aha! moment. Solutions found through insight are often more accurate than those found through step-by-step analysis. In the several seconds before people have an insight, or an Aha! moment, brain activity slows down, attention becomes more diffuse and less focused on the problem. To encourage insight, this means that we need to step back and let our minds wander or sleep on the problem. Insight cannot happen when our minds are constantly engaged.

One form of creativity is insight. It’s the sudden solution to a long-vexing problem, a sudden recognition of a new idea, or a sudden understanding of a complex situation, an Aha! moment. Einstein once described how he achieved his insights by making “a great speculative leap” to a conclusion and then tracing back the connections to verify the idea.

Insight may also be an important agent of change for helping people change their habits and way of thinking because of the enhanced and perhaps distinctive way in which people remember ideas achieved through insight. And we can all get closer to that magical spark of insight thanks to what we’ve learned from the neuroscience of insight.

Some people are "insight machines"

Enter John Kounios and Mark Beeman, two researchers who have studied the neuroscience of insight extensively. They have found that, in the several seconds before people have an insight, or an Aha! moment, their brain activity slows down ! Their attention becomes more diffuse, less focused on the problem. At the moment of insight, their brain activity spikes. Mark Beeman has seen this so often, that he can tell by people’s brain activity who will solve the problem analytically, in a step by step fashion, and who will solve the problem using insight: He calls such people “insight machines”.

Solutions found through insight are often more accurate than solutions using analytical thinking. But, not all solutions reached through insight are accurate. So after you have a moment of insight, it's important to evaluate your solution.

Solutions found through insight are often more accurate than solutions using analytical thinking. That’s because insight is an all-or-nothing phenomenon while analytic solving is incremental. Incremental, step-by-step analytic solving produces partial information on which you can base a guess, and guessing increases the likelihood of being wrong. Insightful, all-or-none solving does not yield intermediate results and people will not offer a solution unless they “know” it is right. Nevertheless, not all solutions reached through insight are accurate. So after you have a moment of insight, it’s important to evaluate your solution.

Insight can't be forced. To increase your insight potential, cultivate a quiet mind, daydream, or sleep on the problem. Insight cannot happen with a cluttered mind.

What can you do to increase your insight potential? Insight can’t be forced, but there are things you can do to foster it. Engage in activities that encourage an open mind. Gather a wide base of knowledge, ask how you could do this differently, engage in a new hobby that uses completely different skills, or just generally relax and let your mind wander. Sleeping on the problem, meditating, or stepping away from it and concentrating on something else may help your unconscious mind to cultivate a creative solution. Insight cannot happen with a cluttered mind. This is why insight, or Aha! moments, can happen in the shower or when you’re daydreaming, when your mind isn’t focused on anything in particular.

Thank you Irena,

I am not sure why I am responding and hoping I will understand by the time I finish.

I think it may be that I have discovered who I am rather that what I do, as I identify with this model closely. In some ways I have felt pressure from the world to get on this sequential train with a definite end position. Rather than an Insightful approach which I feel is more of a parrallel thought mechanism, that can take you anywhere and everywhere.

I am often criticised because I think slow and talk slow, but I am frustrated because people don’t see far and don’t look at possibilities. I now know I am not slow, just thinking about a whole lot more.

I feel that this insightful way of looking at things (parallel thinking) is my right-hand and the analytical process (sequential thinking) is my left-hand. I am a capable analytical thinker but but clumsy and very deliberate.

When I gain insight and analyse the solution, I tend to make it complex and the task of moving ahead becomes huge. I am beginning to learn to start the solution phase and work out the details as I go, so long as others are not involved.

However, when I look at the world I see people who I call solution fitters, these are people, who have gained insight and are trying to fit the problem to the insight.

I think it is like many things, there is a process that must followed, insight is good, but we need to go back to first principal thinking, what is it that we want to create, a solution or art and what is true.

Art in my view is simply an open communication that inspires others to think about something from a fresh point of view or through a new medium. (Purist may well put me straight on this point). So there is giving insight and receiving insight and the pleasure is always in the giving.

Solving a problem with insight and creativity is self satisfy and may benefit us in many ways, but I think the real satisfaction comes from being useful to others, even if we are paid for it.

So why did I respond to this article; – Above all we should value peoples strengths and not be afraid of the opposites (Analytical thinkers and insightful thinkers) and know they have a place in The Process. – This article and my responce has provided clarity for myself and I feel happy with who I am. – I question if we can be good at both ways of thinking, it is a bit like being lefthanded and righthanded, it is possible to be good with both but it is rare. – I am greatful that you took the time to write this article, it has given me insight how I think and may move forward in the future. – Many other thoughts beyond this article have sprung up from writing this response, so I shall finish and hope that my input may trigger others and provide them with similar insight and clarity about themselves.

Good Luck and happy thinking David

Thank you David for you thoughtful comment. I agree that we all prefer one way of thinking over the other. But, both kinds of thinking are valuable. That doesn’t mean that we shouldn’t explore ways of thinking that don’t come easily to us. Insightful thinkers must analyze their insights because they’re not always the best solution. And analytical thinkers would benefit from expanding their world. Like you, I’m an analytical thinker and quite slow too, and it’s because we analyze everything. Insight happens in an instant, which is one reason why insightful thinkers tend to be faster.

Even if our preferred way of thinking is analytical, we can still benefit from insight. Haven’t you slept on a problem overnight and woken up to a solution? That’s insight! This happens to me all the time as I’m writing or preparing a Masterclass: When I get stuck, I know to let it go and when I come back to it later in the day or the next morning, I have a way to move forward! We just need to let our minds wander.

Happy thinking to you too David.

Great insight… Excuse the pun! Thanks Irena

You’re welcome, Alan.

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PMC10219327

Tracing Cognitive Processes in Insight Problem Solving: Using GAMs and Change Point Analysis to Uncover Restructuring

1 Institute of Psychology, University of Klagenfurt, 9020 Klagenfurt, Austria

Amory H. Danek

2 Department of Psychology, Heidelberg University, 69117 Heidelberg, Germany

Nemanja Vaci

3 Department of Psychology, Sheffield University, Sheffield S10 2BP, UK

Merim Bilalić

4 Department of Psychology, University of Northumbria at Newcastle, Newcastle upon Tyne NE1 8ST, UK

Associated Data

Technical details, such as data and code for the analysis, is available at https://osf.io/pwuhs/?view_only=7c52bda4e6fa481e826e5d7570b6ef34 (accessed on 25 April 2023).

Insight problems are likely to trigger an initial, incorrect mental representation, which needs to be restructured in order to find the solution. Despite the widespread theoretical assumption that this restructuring process happens suddenly, leading to the typical “Aha!” experience, the evidence is inconclusive. Among the reasons for this lack of clarity is that many measures of insight rely solely on the solvers’ subjective experience of the solution process. In our previous paper, we used matchstick arithmetic problems to demonstrate that it is possible to objectively trace problem-solving processes by combining eye movements with new analytical and statistical approaches. Specifically, we divided the problem-solving process into ten (relative) temporal phases to better capture possible small changes in problem representation. Here, we go a step further to demonstrate that classical statistical procedures, such as ANOVA, cannot capture sudden representational change processes, which are typical for insight problems. Only nonlinear statistical models, such as generalized additive (mixed) models (GAMs) and change points analysis, correctly identified the abrupt representational change. Additionally, we demonstrate that explicit hints reorient participants’ focus in a qualitatively different manner, changing the dynamics of restructuring in insight problem solving. While insight problems may indeed require a sudden restructuring of the initial mental representation, more sophisticated analytical and statistical approaches are necessary to uncover their true nature.

1. Introduction

In cognitive science, the temporal dynamics of problem-solving processes have always been an important topic of investigation. Most problems are assumed to be solved gradually, by piecing together information in order to arrive at a solution ( Newell and Simon 1972 ). To investigate these problems, several tools have been developed, which allow for the observation of each step of the problem-solving process (e.g., Tower of Hanoi, Hobbits and Orcs problem). In the case of “insight problems”, the solution often comes seemingly out of nowhere ( Duncker 1945 ), despite the problem appearing unsolvable just a moment earlier. To be solved, insight problems are thought to require a fundamental, sudden change in the way the problem is perceived, a process referred to as restructuring or representational change ( Ohlsson 1992 ; Wertheimer 1925 ). The restructuring from the initial, incorrect mental representation to the correct one is the key component in modern theories such as representational change theory (RCT) ( Knoblich et al. 1999 ; Ohlsson 1984 , 1992 , 2011 ).

Although the sudden nature of the underlying restructuring process is a main theoretical assumption about insight, the evidence for this claim is inconclusive. Ohlsson ( 1992 ) even hypothesized that “the sudden appearance of the complete solution in consciousness is an illusion caused by our lack of introspective access to our cognitive processes (...)” (p. 17). To truly understand the temporal nature of insight, the cognitive component of insight (restructuring) must be examined with appropriate tools. Observing changes in solvers’ mental problem representation is a methodological and statistical challenge, which is addressed in the present work. Among the reasons for this lack of clarity is that many measures of insight rely solely on the solvers’ subjective experience of the solution process. Using matchstick arithmetic problems, we demonstrate that it is possible to objectively trace problem-solving processes.

We first review the research on representational change, focusing on the experimental designs. After that, we describe a novel analytical approach that improves upon previous attempts. Finally, and arguably most importantly, we show that this analytical approach needs to be combined with appropriate statistical tools in order to work properly. We demonstrate the feasibility of this approach by re-analyzing eye-tracking data from an already published study ( Bilalić et al. 2019 ). The paper is accompanied by an online supplement , with technical details, such as data and code for the analysis, which is freely available at https://osf.io/pwuhs/?view_only=7c52bda4e6fa481e826e5d7570b6ef3 (accessed on 25 April 2023).

1.1. Temporal Dynamics of the Restructuring Process

In 1994, Durso and colleagues conducted an early study on the temporal dynamics of insight problem solving. They asked participants to rate the relatedness of word pairs in a word puzzle and found that, on average, solution-relevant pairs were rated as increasingly similar as participants approached a solution. The authors concluded that “[l]ike dynamite, the insightful solution explodes on the solver’s cognitive landscape with breathtaking suddenness, but if one looks closely, a long fuse warns of the impending reorganization” ( Durso et al. 1994, p. 98 ). Novick and Sherman ( 2003 ; Experiment 2) provided similar evidence. They asked participants to indicate within a short time window (250 ms after stimulus offset) whether presented anagrams were solvable. They found that, although participants could not find the solution within the allotted time, they were increasingly better at differentiating between solvable and unsolvable anagrams as the presentation time of the anagrams increased. The authors concluded that solvers gradually accumulate information relevant for solving the anagrams.

Several studies have focused on the concept of restructuring in insight problem solving, but have typically not measured the dynamics of the solving process (e.g., Ash et al. 2012 ; Ash and Wiley 2006 , 2008 ; Fleck and Weisberg 2013 ; MacGregor and Cunningham 2009 ). However, a number of studies have attempted to measure the temporal dynamics of restructuring, using different methods to acquire trace data. Some used repeated ratings of problem elements, either regarding their similarity ( Durso et al. 1994 ) or with regard to their relevance for the solution ( Cushen and Wiley 2012 ; Danek et al. 2020 ). Others recorded eye movements ( Ellis et al. 2011 ; Knoblich et al. 2001 ; Bilalić et al. 2019 ; Tseng et al. 2014 ) or employed solvability judgments ( Novick and Sherman 2003 ). In some of these studies, both incremental and sudden solution patterns were found ( Cushen and Wiley 2012 ; Danek et al. 2020 ; Novick and Sherman 2003 ), whereas other studies found only incremental patterns ( Durso et al. 1994 ).

1.2. Eye Movements and Matchstick Arithmetic Problems

Here, we will take a closer look at using eye movement recordings to measure the temporal dynamics of restructuring in insight problems (for a comprehensive overview on eye movements, please see Holmqvist et al. 2011 ). In general, eye movements provide an objective measure of cognitive processes, as they are closely linked to attention (e.g., Just and Carpenter 1976 ; Rayner 1995 ; Reingold et al. 2001 ). Specifically, eye fixations reveal when people pay attention to certain features of a problem and for how long. More importantly, eye tracking is particularly useful when participants might not remember or even concurrently report that they are paying attention to these elements ( Bilalić and McLeod 2014 ; Bilalić et al. 2008 , 2010 ; Kuhn and Land 2006 ; Kuhn et al. 2009 ). This is particularly relevant in the case of insight problems, where it is possible that people are not aware of the dynamics of their solution process.

We use the matchstick arithmetic problems introduced by Knoblich et al. ( 1999 ). Matchstick arithmetic problems are suitable for investigation with eye tracking, as was powerfully demonstrated by the seminal study of Knoblich et al. ( 2001 ). A matchstick arithmetic problem consists of a false arithmetic statement written using Roman numerals, arithmetic operators, and equal signs, all formed using matchsticks ( Knoblich et al. 1999 , 2001 ; see also Figure 1 below). The task is to transform the false arithmetic statement into a true statement by moving only a single stick. Four types of matchstick arithmetic problems have been defined with varying levels of difficulty, depending on the constraints that need to be relaxed and the tightness of the chunks that need to be decomposed. These problem types were theoretically derived from the representational change theory ( Ohlsson 1992 ) and have been empirically confirmed ( Knoblich et al. 1999 ; Öllinger et al. 2006 , 2008 ). The use of matchstick arithmetic problems enables us to build on a well-researched task domain. It is known which problem type should elicit the restructuring process ( Knoblich et al. 1999 ; Öllinger et al. 2006 , 2008 ), and it is possible to contrast it with a type which requires no restructuring. Additionally, based on Knoblich’s study (2001), predictions about eye movement patterns can be made. Furthermore, the matchstick arithmetic domain is well suited for eye tracking because each problem consists of individual matchsticks that do not overlap, allowing for precise differentiation of fixations. In other words, we can determine at any point in time which aspect of the problem is attended to.

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Matchstick arithmetic problem. Participants are required to transform the false arithmetic statement to a true statement by moving a single matchstick. This problem requires restructuring, because the initial assumption that only the matchsticks from values can be manipulated needs to be changed. In this case, the operator “+” can be decomposed and its vertical matchstick moved to make another “=” sign (VI = VI = VI). The “+” sign is the critical element that needs to be changed for solution.

Knoblich et al. ( 2001 ) investigated constraint relaxation type problems, which are considered to require restructuring; see Figure 1 for an example. They found that for this problem (constraint relaxation type), both solvers and non-solvers examined the values in the beginning and spent most of their time doing so. This can be seen as an indication that participants were using an initial incorrect problem representation, triggered by previous knowledge, where only values can be changed. Only in the final third of the problem- solving period did later solvers change their mental representation, as demonstrated by their eye movements. Solvers started to pay attention more to the operators and less to the values. In contrast, non-solvers remained stuck in their initial representation, as they continued to attend to values rather than to operators. Similar results for the same problem were found by another eye-tracking study ( Tseng et al. 2014 ).

The Knoblich et al. ( 2001 ) study provides strong evidence for the claim that in problems that require constraint relaxation, a restructuring of the problem representation took place. However, it did not answer the question of whether this change was a sudden or a gradual one. In the final third of the allotted time, solvers paid attention to the important but previously ignored features, which could be interpreted as a result of sudden restructuring. It is nevertheless not that clear, since the final period may have lasted minutes, given that they took around five minutes to solve the problem. Thus, the restructuring might have been a continuous process over time. On the other hand, an eye-tracking study on anagrams by Ellis et al. ( 2011 ; see also Ellis and Reingold 2014 ) found that participants started disregarding the irrelevant problem elements several seconds before they came up with the solution. The viewing times on that problem elements were decreasing gradually. Most intriguingly, both participant groups, those who experienced pop-out insight-like solutions and those who did not, displayed the same gradual accumulation of solution knowledge.

1.3. Metacognitive Processes and Insight Problems

There is evidence that the problem-solving process benefits from hints (e.g., Bowden 1997 ; Bilalić et al. 2019 ; Ammalainen and Moroshkina 2021 ; Becker et al. 2021 ; Korovkin and Savinova 2021 ; Spiridonov et al. 2021 ). This is the case even when hints were unreportable; that is, hints even work when presented briefly below the threshold of consciousness. Ammalainen and Moroshkina ( 2021 ) found evidence that hints can influence the problem-solving ability, which can be both, positive and negative. In a positive way, hints which are helpful to find the solution increase solution rates. On the other hand, misleading hints can negatively affect solution rates by distracting problem solvers and leading to a decrease in their success rate. In our paper ( Bilalić et al. 2019 ), we also provided hints when participants were unable to find the correct solution after a certain time.

These hints serve two purposes: a practical and a theoretical one. On a practical level, they provide an additional check on the main assumption behind the restructuring process. On a theoretical level, they serve as explicit clues that tap into metacognitive processes ( Takeuchi et al. 2019 ; Metcalfe and Shimamura 1994 ). Hints make participants aware of important aspects in the problem, drawing their attention towards elements that may have been neglected. They also change participants’ knowledge about the problem, potentially affecting the way they solve insight problems ( Bowden 1997 ; Bilalić et al. 2019 ; Korovkin and Savinova 2021 ).

The present work is a re-analysis of our paper ( Bilalić et al. 2019 ). In our paper, we also combined solving of insight and non-insight problems with eye tracking. We presented first a non-insight matchstick problem and then the matchstick insight problem depicted here (see Figure 1 ) to 61 participants (5 male; M age = 22.8; SD age = 6.5). The study was designed to take into account the methodological issue discussed in the previous section. It built upon previous attempts that utilized more time periods and sometimes presented the last 5 or 10 s separately (see also Bilalić et al. 2008 , 2010 , 2014 ). In the 2019 study, we provided a more fine-grained temporal analysis of the solution process by using ten time periods of equal length for our eye movement analysis 1 (for more information, please refer to Bilalić et al. 2019 ). We demonstrated that the restructuring is a gradual process on the insight problem as the solvers started paying attention to the important aspects of the problem long before they found the solution. Here, we provide another set of data where the jump is sudden; that is, the solvers started paying attention to the important aspects immediately before they found the solution (as reported by Knoblich et al. 2001 ). This is done to illustrate (1) how classical ways of analyzing data, such as ANOVA, are inappropriate for discovering the sudden changes, and (2) how other non-linear approaches are required.

We expected that all participants would initially focus on the values. Solvers would shift their attention towards the critical element (the “+” operator), while non-solvers would remain fixated on the values. The first question of interest is whether the representational shift in eventual solvers will be sudden or rather incremental. The second question of interest is whether the explicit cue, that is, the hint, will produce a sudden rearrangement of attention towards the critical elements (here “+”, but also “=” because “=” is also an operator). In our design, we included hints for participants who had not solved the problem within five minutes. The hint provided at this point was ‘You can change the operators, too.’ We were interested in whether the hints change the dynamics of problem solving, specifically whether the solution process remains sudden even after receiving an explicit cue.

The problem proved difficult as only 34% found the solution. After the hint was provided, an additional 11% of participants were able to find the solution. We present the eye data analysis below, with a particular focus on the critical element of the problem, the plus sign (+). Additionally, when analyzing the impact of hints, we also focused on the equal sign (=) as the hints should also affect the attention drawn to this operator through metacognitive control. For analysis of other problem elements, please refer to the supplementary materials .

3.1. Is Insight Sudden or Incremental? (Solvers vs. Non-Solvers: First 5 Min Analysis)

In Figure 2 , raw data and means for each bin of the critical element for the first five minutes are presented. 2 The solving pattern follows the typical sudden pattern, where there is not much difference between eventual solvers and non-solvers with regard to the time spent on the critical element (+) until the end of the first five minutes. Solvers suddenly increase their dwell time just before announcing the solution, while non-solvers continue to observe the critical element sporadically until the end of the solving period.

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Raw data and means for each bin of the critical element (+). The raw data represents every data point of each participant over the entire problem-solving period. The problem-solving period was divided in 10 proportional bins, each representing 10% of the total problem-solving time. The error bars represent the 68% confidence interval. This figure illustrates a nonlinear increase in the amount of time that solvers spend on the critical element. In the case of solvers, the 100% bin means the participant provided a solution.

The crucial question is how to analyze the temporal changes presented in Figure 2 . The traditional method, which we had chosen in our previous paper ( Bilalić et al. 2019 ), is to use an analysis of variance (ANOVA) where the bins and groups are factors that predict the amount of time spent on the critical element. However, ANOVA not only requires a completely balanced dataset, but it also ignores the clustered nature of data ( van Rij et al. 2020 ). Furthermore, it is based on linear regression, which is not suitable for capturing sudden attentional shifts, which are nonlinear in nature. In order to capture the sudden shift as depicted in Figure 2 (the 100% bin for the solvers), ANOVA would need to adjust the linear trend throughout the whole problem-solving period. In other words, a sudden trend may appear as an incremental one as ANOVA adjusts by increasing previous periods (see Figure 3 , left panel).

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Estimated model means based on ( a ) ANOVA with linear term; ( b ) ANOVA with both linear and quadratic terms. Y-Axis: Time on the problem element (%). Please refer to supplementary material for the detailed analysis.

ANOVA can be expressed as linear regression, where an additional quadratic polynomial term is included next to the linear one, in an attempt to capture the shift. However, even in this case, the predicted shift by the ANOVA model would begin earlier, namely at the 80% bin, than it does in the raw data (see Figure 3 , right panel). The general limitation of linear regression, with or without polynomial terms, is that it heavily relies on previous trends. If the change is sudden, the previous time periods will also be adjusted accordingly.

One way around this problem is generalized additive (mixed) modeling (GAM). These models are specifically designed to handle nonlinear relationships, as they are data-driven and use non-linear mixed-effects regression ( van Rij et al. 2020 ). A key benefit of GAMs is that they do not require the user to specify the shape of the nonlinear regression line, as the model determines this based on the data. However, while GAMs have a high level of flexibility in modeling nonlinear changes in time series data, they only allow for the exploration of changes in the function and do not provide parametric estimates such as standard error of estimate or its impact on predictive accuracy of the model. More specifically, GAMs do not provide parametric estimates, which means that they do not give us a set of parameters that describe the shape of the nonlinear function. However, the present work intends to demonstrate the advantages and downsides of the available analysis tools in question, which is why GAMs are included here.

Arguably the most reliable way of checking the assumption of suddenness is the use of change point analysis, which looks for significant deviance from previous trends ( Raftery and Akman 1986 ). Unlike the standard regression analysis (ANOVA) and nonlinear GAMs, change point regression estimates the moment of the function inflection. In other words, it includes the possibility to estimate additional parameters, such as intercept and slope of regression, time point when the function changes, and how the intercept and/or slope of regression changes (see the figures of the MCP analysis for illustrations). This makes the technique particularly valuable in detecting increasing patterns as one would expect several points of change in the attentional pattern on the way towards the solution. In this instance, we use the one implemented in the Multiple Change Points package (MCP; Lindeløv 2020 ).

Below, we address the three main questions using both GAM and MCP analysis. In the supplemental material , we provide the model-estimated values for each case, which include the results and, in the case of the MCPs, how well the model fits the data and which model was used. We begin with the GAM analysis of solvers and non-solvers for the first five minutes to determine whether the insight is sudden or incremental. Figure 4 provides the estimated trend lines for both solvers and non-solvers, as well as the time periods (shaded in orange) where the difference between the two is statistically significant. The model estimates closely follow the raw data (see Figure 2 ), and the difference between solvers and non-solvers is indeed significant at the beginning of the solving phase, as well as at the 90% bin and the 100% bin.

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GAM: the difference between two estimated trend lines for solvers and non-solvers of the critical element (+). This figure illustrates that the GAM also found a nonlinear increase in the amount of time that non-solvers spend on the critical element. The orange area determines where the differences between solvers and non-solvers were significant.

Figure 5 shows the results of the MCP analysis for the same data as the GAM above. Similarly to the GAM, the MCP analysis identified a change point around the 90% bin for the solvers, which captures an attentional shift they made. While some non-solvers also shifted their attention towards the “+” sign at the end, it was not as clear as in the case of the solvers.

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MCP analysis of the critical element (+) for non-solvers and solvers. This figure illustrates every data point of each participant over the problem-solving period. Lines at the bottom of the figure illustrate the posterior density (estimated likelihood) of the change point for each MCMC chain. There is a nonlinear increase in the amount of time that solvers spend on the critical element.

3.2. Do Explicit Cues Rearrange Attentional Distribution? (An Immediate Change after the Hint)

Figure 6 illustrates the impact of providing an explicit hint to the non-solvers from the first five minutes (presented here as a single group; solvers from the first five minutes are not included in this graph). The attentional shift from values towards operators, “+” and “=”, is substantial immediately after the hint. The operator “=” is attended to twice as much immediately after the hint than before. The change for “+” is slightly less dramatic at first (only 4%), but by the 20% bin, the dwell time has doubled in comparison to before the hint was provided. Note that only non-solvers are shown here, since solvers did not receive any hints.

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Raw data and means for each bin of the operators (“+” upper panel; “=” lower panel) in the period before and after the hint. The raw data represents every data point of each participant (non-solvers only) over the problem-solving periods. Each of both problem-solving periods (before and after the hint was provided) were divided in 10 proportional bins, each representing 10% of the total problem-solving time. It is necessary to view the problem-solving periods as distinct periods; therefore, each period is labeled from beginning to end (10% to 100%) to differentiate them. The error bars represent the 68% confidence interval. This figure illustrates the attentional shifts from values (mostly attended to before the hint) towards operators (attended to after the hint was given).

The GAM analysis effectively captures the attentional shift, as depicted in Figure 7 . However, it predicts that the change occurs prior to the hint being provided, starting already at the 90% bin, which is not a correct reflection of the actual data. While GAM is considerably more flexible than regressions with polynomial terms, the same problem of interdependence of neighboring phases remains. The shift caused by the explicit cue is so drastic that the GAM needs to adjust the increase to begin earlier in order to account for it.

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GAM: estimated trend line for non-solvers of the critical element (+; upper panel) and the other operator (=; lower panel). This figure illustrates that the GAM also found a nonlinear increase in the amount of time that non-solvers spend on the critical element after receiving a hint. The orange area indicates where there is a significant shift in attention.

In contrast, the switch points of the MCP analysis correctly capture where the change in attention allocation happens (see Figure 8 ).

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MCP analysis of the critical element (+; upper panel) and the other operator (=; lower panel). This figure illustrates that the switch points of the MCP analysis correctly captures where the shift in attention happens.

3.3. Does Metacognition Influence Insight Problem Solving? (Solvers vs. Non-Solvers after the Hint)

The final question we aimed to address was whether the explicit cue, and the additional knowledge about the problem associated with it, would alter the way the problem was solved. Figure 9 indicates that both solvers and non-solvers maintain the level of attention on the critical aspects throughout the problem-solving period, which is a direct consequence of the explicit cue. However, this was not sufficient for finding the solution. The eventual solvers initially shifted their attention to “=” around the 30% bin, but starting from the 50% bin, they increasingly focused on “+”. This means that at this point in time, the solvers may have realized that the “+” symbol was the critical element they needed to solve the problem. Consequently, they gathered more information about the symbol by attending to it more closely.

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Object name is jintelligence-11-00086-g009.jpg

Raw data and means for each bin of the critical element (+; upper panel) and the other operator (=; lower panel) after the hint was provided. The raw data represent every data point of each participant over the remaining problem-solving period after the hint was given. The error bars represent the 68% confidence interval. This figure illustrates a nonlinear increase or decrease in the time solvers spend on the critical element.

This incremental pattern of solving is well captured by GAMs, as Figure 10 illustrates. While the non-solvers attended to the critical “+” operator consistently over the entire problem-solving period, but on a rather low level of 25% of their time, solvers gradually increased their attention towards it. Significant differences were found in the middle and the end of the problem-solving period. This was also the case for the other operator (=). Non-solvers attended to “=” in a consistent manner throughout the problem-solving period, while the solvers attended to “=” more in the middle of the problem-solving period and less at the very end of it, probably because they were then already focusing more on the “+” sign which needs to be changed for a solution.

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GAM: the difference between two estimated trend lines for solvers and non-solvers of the critical element (+; upper panel) and the other operator (=; lower panel). This figure illustrates that the GAM also found a nonlinear increase in the time solvers spend on that particular element. The orange area in the figure indicates regions where there are statistically significant differences between the attention patterns of solvers and non-solvers.

Figure 11 illustrates that the attentional shifts after receiving a hint are effectively captured by the MCP analysis. Again, non-solvers attended to the “+” operator on a consistently low level throughout the entire problem-solving process, while solvers attended to the “+” operator more and more. The same trend is observed for the “=” operator. Non-solvers attended to it less, while solvers shifted their attention to it in the middle of the problem-solving process. Towards the end of the problem-solving process, the data suggest that solvers became aware that the “=” operator was not as important for solving the problem and began to focus more on the “+” operator.

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Object name is jintelligence-11-00086-g011.jpg

MCP analysis of the critical element after the hint (+; upper panel) and the other operator (=; lower panel) for non-solvers and solvers. This figure demonstrates that the switch points of the MCP analysis correctly captures the incremental pattern of solving for the critical element (+). It also demonstrates that after the hint, the non-solvers attended to the noncritical element (=) more in the beginning but not the critical element (+). As the GAMs showed already, the non-solvers attended to the critical element (+) in the same way throughout the whole problem-solving period.

4. Discussion

We have demonstrated that recording eye movements is a valuable method for gaining insight into complex cognitive processes, including mental restructuring in insight problems. It is also an adequate tool for investigating attentional shifts after receiving hints. However, it is important to use eye movement recording with appropriate analytical approaches. Our results show that it is necessary to conduct a more fine-grained analysis of the eye movement data to capture the temporal dynamics of the problem-solving process. This is particularly relevant for insight problems such as the one used here, which are believed to feature a sudden change in eye movement patterns reflecting a change in mental representation.

We were able to identify the point at which solvers and non-solvers start to differ in their attentional patterns by dividing the problem-solving period into ten equal bins. The temporal resolution of the problem-solving period is one aspect, but it is also important to choose an appropriate statistical procedure. We have demonstrated that nonlinear statistical models, such as GAM and MCP, can effectively capture the sudden change that is a hallmark of insight problem solving. The GAM analysis can effectively capture the attentional shift; however, it predicts that the change occurs prior to the correct reflection of the actual data. While GAM is considerably more flexible than regressions with polynomial terms, the same problem of interdependence of neighboring phases remains. The shift caused by the explicit cue is so drastic that the GAM needs to adjust the increase to begin earlier to account for it. In contrast, the change points of the MCP analysis correctly capture where the change in attention allocation happens. A change point is a time point where the statistical properties of a time series change abruptly. However, in contrast to GAMs, one needs a priori knowledge about the number of change points and the form of the segments in between ( Lindeløv 2020 ). Therefore, one might decide from case to case which statistical procedure is appropriate.

Our example illustrates the importance of considering theoretical assumptions when choosing analytical and statistical procedures. The restructuring of mental representations is a key concept in theories of insight ( Knoblich et al. 1999 ; Ohlsson 1984 , 1992 , 2011 ). It is a nonlinear process in essence, which can be operationalized as a sudden burst of attention to the relevant aspects of a problem ( Bilalić et al. 2019 ). The shift inevitably deviates significantly from participants’ previous problem solving. Seen as a part of the overall problem-solving continuum, the sudden shift is difficult to capture with linear statistical procedures. Only truly nonlinear statistical procedures can appropriately capture the sudden nature of representational change.

Providing explicit hints typically alters the dynamics of problem solving. It is obvious that the given hints were effective, as participants’ patterns of attention show a drastic change, which is very well captured by both GAM and MCP. However, it is important to note that the eventual solvers, after receiving the hint, exhibit a gradual, incremental shift, with increasing attention to the main elements during the problem-solving period. In contrast, non-solvers display an immediate burst of refocusing following the hint, but subsequently, their attention to the important aspects diminishes.

Both the analytical procedure for capturing the temporal resolution and the nonlinear statistical procedures can be easily extended beyond eye movements to other tracing methods. For example, “importance-to-solution” ratings of individual problem elements that are made repeatedly during the solving process ( Durso et al. 1994 ; Cushen and Wiley 2012 ; Danek et al. 2020 ; Danek and Wiley 2020 ) often reveal patterns of sudden change which could be effectively captured by GAMs and MCPs. Similarly, “Feelings-of-Warmth” that are used to assess metacognitive knowledge about solution progress ( Kizilirmak et al. 2018 ; Hedne et al. 2016 ; Pétervári and Danek 2020 ) are another suitable candidate for nonlinear modeling with GAMs. Other tracing methods, such as mouse-tracing data ( Loesche et al. 2018 ; van Rij et al. 2020 ), think-aloud protocols ( Gilhooly et al. 2010 ; Schooler et al. 1993 ; Blech et al. 2020 ), or even self-reports ( Fedor et al. 2015 ), are also better modeled with GAMs than with commonly applied linear methods, even if they are more appropriate than the classical ANOVA.

5. Conclusions

Our results indicate that for insight problems, the restructuring process leaves a discernible trace of suddenness. Eye movements suggest that just prior to solving the problems, participants shift their focus from elements that constituted the initial problem representation to those crucial for the solution. Our results also demonstrate that receiving hints leads to attentional shifts towards critical aspects, which in turn facilitates the generation of a correct solution. However, in order to accurately capture the sudden shift in attention, a combination of the appropriate methodological approach and statistical procedure is necessary. These nonlinear processes are best captured by nonlinear statistical procedures, such as GAMs and MCPs.

Acknowledgments

The help and cooperation from participants is greatly appreciated, as is Matthew Bladen’s contribution in preparing the text.

Supplementary Materials

The following supporting information can be downloaded at: https://osf.io/pwuhs/?view_only=7c52bda4e6fa481e826e5d7570b6ef34 .

Funding Statement

This research was funded by Talent Austria der OeAD-GmbH, finanziert aus Mitteln des österreichischen Bundesministeriums für Wissenschaft, Forschung und Wirtschaft (BMWFW), grant number ICM-2017-07423 given to the first author.

Author Contributions

Conceptualization, M.B. and M.G.; methodology, M.B. and M.G.; software, M.G.; validation, M.B., N.V., A.H.D., and M.G.; formal analysis, M.G. and N.V.; investigation, M.G.; data curation, M.G.; writing—original draft preparation, M.G.; writing—review and editing, M.B., A.H.D., N.V., and M.G.; visualization, M.G., N.V., and M.B.; project administration, M.G. and M.B.; funding acquisition, M.G. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Since this is a re-analysis of our paper ( Bilalić et al. 2019 ), please refer to the original paper for the Institutional Review Board Statement.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

Conflicts of interest.

The authors declare no conflict of interest.

1 The length of time taken to solve (or not solve) a problem is different from person to person, meaning that one cannot compare the eye tracking data directly between people. For example, some may need only 45 s to solve the problem, whereas others need four minutes to find a solution. In consequence, the data must be transformed in order to be able to compare the data between people properly. While the problem-solving period can be extended by adding more time phases, it is important to note that the duration should not be prolonged beyond a certain point. Utilizing too many time frames may leave too little data (e.g., a 10-second trial should not be divided into 100 bins, as each bin will have the duration of only 100 ms). This can lead to distorted eye movement patterns, masking the underlying effects present before the data were binned. On the other hand, choosing too few bins may not capture the full temporal dynamics of the problem-solving process. In either case, ANOVA is not suitable for analyzing a large number of problem-solving periods, unlike GAM and multiple change point analysis, which can easily accommodate a large number of time frames. MCP analysis is another adequate tool for this type of analysis as it can capture the shift of attention. However, in contrast to GAMs, one needs a priori knowledge about the number of change points and the form of the segments in between ( Lindeløv 2020 ).

2 Please note that the data presented here are simulated to represent a sudden shift, which is difficult to capture by classical analyses. The original data in Bilalić et al. ( 2019 ) indicate a gradual shift.

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4 Main problem-solving strategies

In Psychology, you get to read about a ton of therapies. It’s mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches.

Yet, you can’t deny the kernel of truth that’s there in all of them. All therapies, despite being different, have one thing in common- they all aim to solve people’s problems. They all aim to equip people with problem-solving strategies to help them deal with their life problems.

Problem-solving is really at the core of everything we do. Throughout our lives, we’re constantly trying to solve one problem or another. When we can’t, all sorts of psychological problems take hold. Getting good at solving problems is a fundamental life skill.

Problem-solving stages

What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists.

To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are:

Initial state

The problem itself can either be well-defined or ill-defined. A well-defined problem is one where you can clearly see where you are (A), where you want to go (B), and what you need to do to get there (engaging the right operators).

For example, feeling hungry and wanting to eat can be seen as a problem, albeit a simple one for many. Your initial state is hunger (A) and your final state is satisfaction or no hunger (B). Going to the kitchen and finding something to eat is using the right operator.

In contrast, ill-defined or complex problems are those where one or more of the three problem solving stages aren’t clear. For example, if your goal is to bring about world peace, what is it exactly that you want to do?

It’s been rightly said that a problem well-defined is a problem half-solved. Whenever you face an ill-defined problem, the first thing you need to do is get clear about all the three stages.

Often, people will have a decent idea of where they are (A) and where they want to be (B). What they usually get stuck on is finding the right operators.

Initial theory in problem-solving

When people first attempt to solve a problem, i.e. when they first engage their operators, they often have an initial theory of solving the problem. As I mentioned in my article on overcoming challenges for complex problems, this initial theory is often wrong.

But, at the time, it’s usually the result of the best information the individual can gather about the problem. When this initial theory fails, the problem-solver gets more data, and he refines the theory. Eventually, he finds an actual theory i.e. a theory that works. This finally allows him to engage the right operators to move from A to B.

Problem-solving strategies

These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are:

Trial and error

1. Algorithms

When you follow a step-by-step procedure to solve a problem or reach a goal, you’re using an algorithm. If you follow the steps exactly, you’re guaranteed to find the solution. The drawback of this strategy is that it can get cumbersome and time-consuming for large problems.

Say I hand you a 200-page book and ask you to read out to me what’s written on page 100. If you start from page 1 and keep turning the pages, you’ll eventually reach page 100. There’s no question about it. But the process is time-consuming. So instead you use what’s called a heuristic.

2. Heuristics

Heuristics are rules of thumb that people use to simplify problems. They’re often based on memories from past experiences. They cut down the number of steps needed to solve a problem, but they don’t always guarantee a solution. Heuristics save us time and effort if they work.

You know that page 100 lies in the middle of the book. Instead of starting from page one, you try to open the book in the middle. Of course, you may not hit page 100, but you can get really close with just a couple of tries.

If you open page 90, for instance, you can then algorithmically move from 90 to 100. Thus, you can use a combination of heuristics and algorithms to solve the problem. In real life, we often solve problems like this.

When police are looking for suspects in an investigation, they try to narrow down the problem similarly. Knowing the suspect is 6 feet tall isn’t enough, as there could be thousands of people out there with that height.

Knowing the suspect is 6 feet tall, male, wears glasses, and has blond hair narrows down the problem significantly.

3. Trial and error

When you have an initial theory to solve a problem, you try it out. If you fail, you refine or change your theory and try again. This is the trial-and-error process of solving problems. Behavioral and cognitive trial and error often go hand in hand, but for many problems, we start with behavioural trial and error until we’re forced to think.

Say you’re in a maze, trying to find your way out. You try one route without giving it much thought and you find it leads to nowhere. Then you try another route and fail again. This is behavioural trial and error because you aren’t putting any thought into your trials. You’re just throwing things at the wall to see what sticks.

This isn’t an ideal strategy but can be useful in situations where it’s impossible to get any information about the problem without doing some trials.

Then, when you have enough information about the problem, you shuffle that information in your mind to find a solution. This is cognitive trial and error or analytical thinking. Behavioral trial and error can take a lot of time, so using cognitive trial and error as much as possible is advisable. You got to sharpen your axe before you cut the tree.

When solving complex problems, people get frustrated after having tried several operators that didn’t work. They abandon their problem and go on with their routine activities. Suddenly, they get a flash of insight that makes them confident they can now solve the problem.

I’ve done an entire article on the underlying mechanics of insight . Long story short, when you take a step back from your problem, it helps you see things in a new light. You make use of associations that were previously unavailable to you.

You get more puzzle pieces to work with and this increases the odds of you finding a path from A to B, i.e. finding operators that work.

Pilot problem-solving

No matter what problem-solving strategy you employ, it’s all about finding out what works. Your actual theory tells you what operators will take you from A to B. Complex problems don’t reveal their actual theories easily solely because they are complex.

Therefore, the first step to solving a complex problem is getting as clear as you can about what you’re trying to accomplish- collecting as much information as you can about the problem.

This gives you enough raw materials to formulate an initial theory. We want our initial theory to be as close to an actual theory as possible. This saves time and resources.

Solving a complex problem can mean investing a lot of resources. Therefore, it is recommended you verify your initial theory if you can. I call this pilot problem-solving.

Before businesses invest in making a product, they sometimes distribute free versions to a small sample of potential customers to ensure their target audience will be receptive to the product.

Before making a series of TV episodes, TV show producers often release pilot episodes to figure out whether the show can take off.

Before conducting a large study, researchers do a pilot study to survey a small sample of the population to determine if the study is worth carrying out.

The same ‘testing the waters’ approach needs to be applied to solving any complex problem you might be facing. Is your problem worth investing a lot of resources in? In management, we’re constantly taught about Return On Investment (ROI). The ROI should justify the investment.

If the answer is yes, go ahead and formulate your initial theory based on extensive research. Find a way to verify your initial theory. You need this reassurance that you’re going in the right direction, especially for complex problems that take a long time to solve.

Getting your causal thinking right

Problem solving boils down to getting your causal thinking right. Finding solutions is all about finding out what works, i.e. finding operators that take you from A to B. To succeed, you need to be confident in your initial theory (If I do X and Y, they’ll lead me to B). You need to be sure that doing X and Y will lead you to B- doing X and Y will cause B.

All obstacles to problem-solving or goal-accomplishing are rooted in faulty causal thinking leading to not engaging the right operators. When your causal thinking is on point, you’ll have no problem engaging the right operators.

As you can imagine, for complex problems, getting our causal thinking right isn’t easy. That’s why we need to formulate an initial theory and refine it over time.

I like to think of problem-solving as the ability to project the present into the past or into the future. When you’re solving problems, you’re basically looking at your present situation and asking yourself two questions:

“What caused this?” (Projecting present into the past)

“What will this cause?” (Projecting present into the future)

The first question is more relevant to problem-solving and the second to goal-accomplishing.

If you find yourself in a mess , you need to answer the “What caused this?” question correctly. For the operators you’re currently engaging to reach your goal, ask yourself, “What will this cause?” If you think they cannot cause B, it’s time to refine your initial theory.

Hi, I’m Hanan Parvez (MA Psychology). I’ve published over 500 articles and authored one book. My work has been featured in Forbes , Business Insider , Reader’s Digest , and Entrepreneur .

7.3 Problem-Solving

Learning objectives.

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.

PROBLEM-SOLVING STRATEGIES

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.


Method	Description	Example
Trial and error	Continue trying different solutions until problem is solved	Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning
Algorithm	Step-by-step problem-solving formula	Instruction manual for installing new software on your computer
Heuristic	General problem-solving framework	Working backwards; breaking a task into steps

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 :

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).

Solving puzzles.

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.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

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.


Bias	Description
Anchoring	Tendency to focus on one particular piece of information when making decisions or problem-solving
Confirmation	Focuses on information that confirms existing beliefs
Hindsight	Belief that the event just experienced was predictable
Representative	Unintentional stereotyping of someone or something
Availability	Decision is based upon either an available precedent or an example that may be faulty

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.

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

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.

References:

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

Review Questions:

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

d. experiment

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?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

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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COMMENTS

Insight Learning (Definition+ 4 Stages
From his observations of how chimpanzees solve complex problems, he concluded that the learning process went through the following 4 stages: Preparation: Learners encounter the problem and begin to survey all relevant information and materials. They process stimuli and begin to make connections.
Insight Learning Theory: Definition, Stages, and Examples
Unlike gradual problem-solving methods, insight learning involves sudden and profound understanding. Individuals may be stuck on a problem for a while, but then, seemingly out of nowhere, the solution becomes clear. ... Gestalt psychology, which influenced insight learning theory, proposes that learning and problem-solving involve the ...
Problem-Solving Strategies: Definition and 5 Techniques to Try
In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness. 4. Working backward. Working backward is a problem-solving approach often ...
Problem-Solving Strategies and Obstacles
Problem-solving involves taking certain steps and using psychological strategies. Learn problem-solving techniques and how to overcome obstacles to solving problems. ... In cognitive psychology, the term 'problem-solving' refers to the mental process that people go through to discover, ... Insight can occur when the problem in front of you is ...
Restructuring processes and Aha! experiences in insight problem solving
There are two main approaches to studying insight problem-solving. According to one approach, the abrupt shift in representation or sudden restructuring is a defining feature of insightful ...
Frontiers
Other Gestalt psychologists adapted Köhler's problem solving methodology to study insight in humans. Duncker (1945), for example, designed situations in which everyday objects had to be used in unusual ways to solve a task (e.g., the candle problem, see Figure 1; Duncker, 1945).Notably, if he asked the subjects to use these objects in their usual way before the test, the success rate was ...
Psychological Research on Insight Problem Solving
Weisberg, R.W. (1992): Metacognition and insight during problem solving: Comment on Metcalfe. Journal of Experimental Psychology: Learning, Memory, and Cognition 18, 426-431. Article Google Scholar Weisberg, R W. (1995): Prolegomena to theories of insight in problem solving: A taxonomy of problems.
Restructuring insight: An integrative review of insight in problem
Insight in problem-solving has traditionally been studied with specific tasks or "insight problems" which are designed to elicit insight solutions (see Table 1 for a list of most common insight tasks). After solving the task, the participant is often asked to make a retrospective forced choice about whether or not they solved the task with insight (e.g., Jung-Beeman et al., 2004), or rate ...
PDF The Psychology of Problem Solving
The Psychology of Problem Solving is divided into four parts. Fol-lowing an introduction that reviews the nature of problems and the ... solving, including the roles that insight and metacognitive skills play in problem solving. Robert J. Sternberg is IBM Professor of Psychology and Education at
Insight is not in the problem: Investigating insight in problem solving
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 ...
Intuition and Insight: Two Processes That Build on Each Other or
Here, response patterns of both triad types (i.e., coherent vs. incoherent) are compared to each other. In recent research on insight problem solving, Bowden et al. (2005) presented a novel framework and a new class of problems in order to probe insight problem solving. The authors equate subjectively reported aha-experiences with insight.
The Problem-Solving Process
Learn about problem-solving, a mental process that involves discovering and analyzing a problem and then coming up with the best possible solution. ... Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight. ... The Psychology of Problem Solving. Cambridge University Press; 2003. doi:10.1017 ...
Current Understanding of the "Insight" Phenomenon Across Disciplines
Despite countless anecdotes and the historical significance of insight as a problem solving mechanism, its nature has long remained elusive. ... Wolfgang Köhler, one of the pioneers of Gestalt psychology, introduced the term insight into comparative psychology (although this way of problem solving was already described before him in non-human ...
PDF Psychological Research on Insight Problem Solving
Psychological Research on Insight Problem Solving Michael Ollinger¨ 1 and Gun¨ ther Knoblich2 1 Parmenides Center for the Study of Thinking, 80333 Munc¨ hen, Germany, [email protected] 2 Rutgers University, Psychology Department, Newark, NJ 07102, USA, [email protected]
Insight Psychology
Through therapeutic theories of insight psychology or insight therapy, solutions to problems can arise out of the ideas and memories you hold. Wolfgang Kohler and his work with the Gestalt theory led him to some interesting findings in the early 1900s. He experimented with his chimp Sultan. In his experiment, Sultan was hungry.
Insight Problem Solving: A Critical Examination of the Possibility of
Insight Problem Solving: The Possibility of Formal Theory 65. •volume 5, no. 1 (Fall 2012) the daughters. The oldest gets ½ of the horses, which is 9; the middle daughter gets 6 horses which is 1/3rdof the horses, and the youngest gets 2 horses, 1/9thof the lot. That's 17 horses, so the lawyer gets on his own horse and rides off with a ...
Insight: Creative Problem Solving
Insight cannot happen with a cluttered mind. This is why insight, or Aha! moments, can happen in the shower or when you're daydreaming, when your mind isn't focused on anything in particular. There is growing pressure for creative problem solving in business. Insight is a form of creativity that is often more accurate. It requires a quite mind.
Tracing Cognitive Processes in Insight Problem Solving: Using GAMs and
Several studies have focused on the concept of restructuring in insight problem solving, but have typically not measured the dynamics of the solving ... Paving the way to eureka—Introducing "dira" as an experimental paradigm to observe the process of creative problem solving. Frontiers in Psychology. 2018; 9:1773. doi: 10.3389/fpsyg.2018 ...
4 Main problem-solving strategies
In Psychology, you get to read about a ton of therapies. It's mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches. ... Insight. When solving complex problems, people get frustrated after having tried several operators that didn't ...
Problem solving and insight
If problem solving is a process of search that can call upon existing knowledge in memory, then it might be expected that "feeling-of-knowing" judgments would just as readily be produced for insight problems and noninsight problems. In one study 3 participants were asked to give "ratings of warmth" (i.e. estimated closeness to solution) every ...
7.3 Problem-Solving
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 ...

Insight Learning (Definition+ 4 Stages + Examples)

What Is Insight Learning?

Is Insight Learning Only Observed In Humans?

Four Stages of Insight Learning

Preparation

Verification

Examples of Insight Learning

Where Is the Best Place to Have an Epiphany?

The Three B’s of Creativity

Sleep

Meditation

Laugh!

Insight Vs. Other Types Of Learning.

Insight Vs. Trial And Error Learning

Insight Vs. Learning Through Observation, Imitation, And Repetition

Can Major Scientific Breakthroughs be made through observation and experiment alone?

The Historical Development Of The Theory of Insight Learning

Kohler’s 4 Stage Model Of Insight Learning

Applying Insight Learning To The Classroom

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About The Author

Psychology Resources

Psychology Tests

Insight Learning Theory: Definition, Stages, and Examples

What Is Insight Learning?

Three Components of Insight Learning Theory

1. Sudden Realization

2. Restructuring of Problem-Solving Strategies

3. Aha Moments

Four Stages of Insight Learning Theory

1. Problem Recognition

2. Incubation

3. Illumination

4. Verification

Famous Examples of Insight Learning

Archimedes’ Principle

Köhler’s Chimpanzee Experiments

Eureka Moments in Science

Everyday Examples of Insight Learning Theory

Exploring the Uses of Insight Learning

Problem-Solving

Learning New Skills

Overcoming Challenges

Alternatives to Insight Learning Theory

Behaviorism

Cognitive Learning Theory

Gestalt Psychology

Information Processing Theory

Restructuring processes and Aha! experiences in insight problem solving

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Going beyond the AHA! moment: insight discovery for transdisciplinary research and learning

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Irrelevant insights make worldviews ring true

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MINI REVIEW article

Introduction

Insight As a Global Phenomenon

Scientific Insight

First Scientific Approximations To Insight

Our Current Understanding of Insight

Convergent Insight Process Theories

Fixation and Impasse

Incubation/Restructuring and Illumination

The Eureka Experience

Non-Human Animals, Problems, and Solutions

Author Contributions

Conflict of Interest

Publisher’s Note

A Word From Verywell