gestalt view of problem solving

What is Gestalt Psychology? Theory, Principles, & Examples

Nathalia Bustamante

Harvard Graduate School of Education

Nathalia Bustamante is a Brazilian journalist at Harvard’s Graduate School of Education.

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On This Page:

Key Takeaways

• Gestalt psychology is a school of thought that seeks to understand how the human brain perceives experiences. It suggests that structures, perceived as a whole, have specific properties that are different from the sum of their individual parts.
• For instance, when reading a text, a person perceives each word and sentence as a whole with meaning, rather than seeing individual letters; and while each letterform is an independent individual unit, the greater meaning of the text depends on the arrangement of the letters into a specific configuration.
• Gestalt grew from the field of psychology in the beginning of the 19th Century. Austrian and German psychologists started researching the human mind’s tendency to try to make sense of the world around us through automatic grouping and association.
• The Gestalt Principles, or Laws of Perception, explain how this behavior of “pattern seeking” operates. They offer a powerful framework to understand human perception, and yet are simple to assimilate and implement.
• For that reason, the Gestalt Laws are appealing not only to psychologists but also to visual artists, educators and communicators.

What Does Gestalt Mean?

In a loose translation, the German word ‘Gestalt’ (pronounced “ge-shtalt”) means ‘configuration’, or ‘structure’. It makes a reference to the way individual components are structured by our perception as a psychical whole (Wulf, 1996). That structure provides a scientific explanation for why changes in spacing, organization and timing can radically transform how information is received and assimilated.

How the Gestalt Approach Formed?

Two of the main philosophical influences of Gestalt are Kantian epistemology and Husserl’s phenomenological method .

Both Kant and Husserls sought to understand human consciousness and perceptions of the world, arguing that those mental processes are not entirely mediated by rational thought (Jorge, 2010).

Similarly, the Gestalt researchers Wertheimer, Koffka and Kohler observed that the human brain tends to automatically organize and interpret visual data through grouping.

They theorized that, because of those “mental shortcuts”, the perception of the whole is different from the sum of individual elements.

This idea that the whole is different from the sum of its parts – the central tenet of Gestalt psychology – challenged the then-prevailing theory of Structuralism .

This school of thought defended that mental processes should be broken down into their basic components, to focus on them individually.

Structuralists believed that complex perceptions could be understood by identifying the primitive sensations it caused – such as the points that make a square or particular pitches in a melody.

Gestalt, on the other hand, suggests the opposite path. It argues that the whole is grasped even before the brain perceives the individual parts – like when, looking at a photograph, we see the image of a face rather than a nose, two eyes, and the shape of a chin.

Therefore, to understand the subjective nature of human perception, we should transcend the specific parts to focus on the whole.

Gestalt Psychologists

Max wertheimer.

The inaugural article of Gestalt Psychology was Max Wertheimer’s Experimental Studies of the Perception of Movement , published in 1912.

Wertheimer, then at the Institute of Psychology in Frankfurt am Main, described a visual illusion called apparent motion in this article.

Apparent motion is the perception of movement that results from viewing a rapid sequence of static images, as happens in the movies or in flip books.

Wertheimer realized that the perception of the whole (the group of figures in a sequence) was radically different from the perception of its components (each static image).

Wolfgang Köhler

Wolfgang Köhler was particularly interested in physics and natural sciences. He introduced the concept of psychophysical isomorphism – arguing that how a stimulus is received is influenced by the brain’s general state while perceiving it (Shelvock, 2016).

He believed that organic processes tend to evolve to a state of equilibrium – like soap bubbles, that start in various shapes but always change into perfect spheres because that is their minimum energy state.

In the same way, the human brain would “converge” towards a minimum energy state through a process of simplifying perception – a mechanism that he called Pragnanz (Rock & Palmer, 1990).

Kurt Koffka

Koffka contributed to expanding Gestalt applications beyond visual perception. In his major article, Principles of Gestalt psychology (1935) he detailed the application of the Gestalt Laws to topics such as motor action, learning and memory, personality and society.

He also played a key role in taking the Gestalt Theory to the United States, to where he emigrated after the rise of Nazism in Germany.

Gestalt principles

Gestalt’s principles, or Laws of Perception, were formalized by Wertheimer in a treaty published in 1923, and further elaborated by Köhler, Koffka, and Metzger.

The principles are grounded on the human natural tendency of finding order in disorder – a process that happens in the brain, not in the sensory organs such as the eye. According to Wertheimer, the mind “makes sense” of stimulus captured by the eyes following a predictable set of principles.

The brain applies these principles to enable individuals to perceive uniform forms rather than simply collections of unconnected images.

Although these principles operate in a predictable way, they are actually mental shortcuts to interpreting information. As shortcuts, they sometimes make mistakes – and that is why they can lead to incorrect perceptions.

Prägnanz (law of simplicity)

• The law of Prägnanz is also called “law of simplicity” or “law of good figure”. It states that when faced with a set of ambiguous or complex objects, the human brain seeks to make them as simple as possible.
• The “good figure” is an object or image that can easily be perceived as a whole.
• A good example of this process is our perception of the Olympic logo. We tend to see overlapping circles (the simpler version) rather than a series of curved, connected lines (Dresp-Langley, 2015).
• This law suggests that we tend to group shapes, objects or design elements that share some similarity in terms of color, shape, orientation, texture or size.
• The law of proximity states that shapes, objects or design elements located near each other tend to be perceived as a group.
• Conversely, randomly located items tend to be perceived as isolated.
• This principle can be applied to direct attention to key elements within a design: the closer visual elements are to each other, the more likely they will be perceived as related to each other, and too much negative space between elements serve to isolate them from one another.

Common Region

• This law proposes that elements that are located within the same closed region – such as inside a circle or a shape – tend to be perceived as belonging to the same group.
• Those clearly defined boundaries between the inside and the outside of a shape create a stronger connection between elements, and can even overpower the law of Proximity or of Similarity.
• This law argues that shapes, objects or design elements that are positioned in a way that suggests lines, curves or planes will be perceived as such, and not as individual elements.
• We perceptually group the elements together to form a continuous image.
• This law suggests that the human brain has a natural tendency to visually close gaps in forms, particularly when identifying familiar images.
• When information is missing, our focus goes to what is present and automatically “fills” the missing parts with familiar lines, colors or patterns.
• Once a form has been identified, even if additional gaps are introduced, we still tend to visually complete the form, in order to make them stable.
• IBM’s iconic logo is one example of applied closure – blue horizontal lines are arranged in three stacks that we “close” to form the letterforms (Graham 2008).

The classic gestalt principles have been extended in various directions. The ones above are some of the most commonly cited, but there are others, such as the symmetry principle (symmetrical components will tend to be grouped together) and the common faith principle (elements tend to be perceived as grouped together if they move together).

Applications of Gestalt

Gestalt Psychology and the Laws of Perception influenced research from a multitude of disciplines – including linguistic, design, architecture and visual communication.

Gestalt Therapy

Gestalt therapy was founded by Frederick (Fritz) and Laura Perls in the 1940s. It focuses on the phenomenological method of awareness that distinguishes perceptions, feelings and actions from their interpretations.

It believes that explanations and interpretations are less reliable than the concrete – what is directly perceived and felt. It is a therapy rooted in dialogue, in which patients and therapists discuss differences in perspectives (Yontef, G, 1993).

Design Professor and specialist Gregg Berryman pointed out, in his book Notes on Graphic Design and Visual Communication (1979), that ‘Gestalt perceptual factors build a visual frame of reference which can provide the designer with a reliable psychological basis for the spatial organization of graphic information’.

In essence, Gestalt provided a framework of understanding upon which designers can make decisions.

What made gestalt theory appealing to visual artists and designers is its attempt to explain “pattern seeking” in human behavior.

The Gestalt Laws provided scientific validation of compositional structure, and were used by designers in the mid-twentieth century to explain and improve visual work.

They are particularly useful in the creation of posters, magazines, logos and billboards in a meaningful and organized way. More recently, they have also been applied to the design of websites, user interfaces and digital experiences (Graham 2008).

Product Development

The product’s form and other perceptual attributes such as color and texture are crucial in influencing customer’s buying decisions.

Product development has adopted Gestalt Laws in approaches that consider how the target customer will perceive the final product.

By considering these perceptions, the product developer is better able to understand potential risks, ambiguities and meanings of the product he or she is working on (Cziulik & Santos 2012).

Education and Learning

In Education, Gestalt Theory was applied as a reaction to behaviorism, which reduced experiences to simple stimulus-response reflections.

Gestalt suggested that students should perceive the whole of the learning goal, and then discover the relations between parts and the whole. That meant that teachers should provide the basic framework of the lesson as an organized and meaningful structure, and then go into details.

That would help students to understand the relation between contents and the overall goal of the lesson.

Problem-based learning methodologies also arose based on Gestalt principles.

When students are exposed to the whole of a problem, they can “make sense” of it before engaging in introspective thinking to analyze the connection between elements and craft independent solutions (Çeliköz et al. 2019).

The Gestalt Principles are applied to the design of advertisement, packaging and even physical stores.

Researchers that investigated how consumers form overall impressions of consumption objects found that they usually integrate visual information with their own evaluation of specific features (Zimmer & Golden, 1988).

More recent applications also analyze how consumer perceptions apply to online shopping environments. The fundamental Gestalt Laws are thus applied to site architecture and visual impact (Demangeot, 2010).

Gestalt Legacy

Most psychologists consider that the Gestalt School, as a theoretical field of study, died with its founding fathers in the 1940s. Two main reasons may have contributed to that decline.

The first reason are institutional and personal constraints: after they left Germany, Wetheimer, Koffka and Köhler obtained positions in which they could conduct research, but could not train PhDs.

At the same time, most of the students and researchers that had remained in Germany broadened the scope of their research beyond Gestalt topics.

The second reason for the decline of Gestalt Psychology were empirical findings dismantling Köhler’s electrical field theory that sought to explain the brain’s functioning.

Neuroscience and cognitive science emerged in the 1960s as stronger frameworks for explaining the functioning of the brain.

Still, nearly all psychology students can expect to find at least one chapter dedicated to Gestalt Psychology in their textbooks.

Similarly, fundamental questions about the subjective nature of perception and awareness are still addressed in contemporary scientific research – with the perks of counting on advanced methods that were not available for the Gestaltists in the first half of the XX Century (Wagemans et al, 2012).

Berryman, G. (1979). Notes on Graphic Design and Visual Communication. Los Altos. William Kaufmann. Inc., t979.

Cziulik, C., & dos Santos, F. L. (2011). An approach to define formal requirements into product development according to Gestalt principles. Product: Management and Development, 9(2), 89-100.

Çeliköz, N., Erisen, Y., & Sahin, M. (2019). Cognitive Learning Theories with Emphasis on Latent Learning, Gestalt and Information Processing Theories. Online Submission, 9(3), 18-33.

Demangeot, C., & Broderick, A. J. (2010). Consumer perceptions of online shopping environments: A gestalt approach. Psychology & Marketing, 27(2), 117-140.

Dresp-Langley, B. (2015). Principles of perceptual grouping: Implications for image-guided surgery. Frontiers in Psychology, 6, 1565.

Graham, L. (2008). Gestalt theory in interactive media design. Journal of Humanities & Social Sciences, 2(1).

Jorge, MLM. (2010) Implicaciones epistemológicas de la noción de forma en la psicología de la Gestalt. Revista de Historia de la Psicología. vol. 31, núm. 4 (diciembre)

O”Connor, Z. (2015). Colour, contrast and gestalt theories of perception: The impact in contemporary visual communications design. Color Research & Application, 40(1), 85-92.

Rock, I., & Palmer, S. (1990). The legacy of Gestalt psychology . Scientific American, 263(6), 84-91.

Shelvock, M. T. (2016). Gestalt theory and mixing audio. Innovation in Music II, 1-14.

Wagemans, J., Elder, J. H., Kubovy, M., Palmer, S. E., Peterson, M. A., Singh, M., & von der Heydt, R. (2012). A century of Gestalt psychology in visual perception : I. Perceptual grouping and figure–ground organization. Psychological bulletin, 138(6), 1172.

Yontef, G., & Simkin, J. (1993). Gestalt therapy: An introduction. Gestalt Journal Press.

Zimmer, M. R., & Golden, L. L. (1988). Impressions of retail stores: A content analysis of consume. Journal of retailing, 64(3), 265.

Further Information

Wagemans, J., Elder, J. H., Kubovy, M., Palmer, S. E., Peterson, M. A., Singh, M., & von der Heydt, R. (2012). A century of Gestalt psychology in visual perception: I. Perceptual grouping and figure–ground organization. Psychological bulletin, 138(6), 1172.

Raffagnino, R. (2019). Gestalt Therapy Effectiveness: A Systematic Review of Empirical Evidence. Open Journal of Social Sciences, 7(6), 66-83.

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Gestalt’s perspective on insight: a recap based on recent behavioral and neuroscientific evidence.

1. Introduction

2. the role of perceptual experience in problem-solving cognition: was the parallelism between bistable figures and insight problem-solving warranted, 3. the holistic approach: what has recent research discovered about the idea that solutions to problems sometimes come to mind in an off-on manner.

Using Koffka ’s ( 1935, p. 176 ) words: “The whole is something else than the sum of its parts, because summing is a meaningless procedure, whereas the whole-part relationship is meaningful”. Similarly, insight problem-solving is processed in a discrete off–on manner, and when solutions to problems emerge, they do so as a “whole”, and the solver cannot retroactively report the reasoning process that led him or her to the solution.

4. The Gestalt Psychologists Assume That the Solution to Problems Comes “With Sudden Clarity.” Can We See in This Statement a Proto-Assumption That Insightful Solutions Might Be Characterized by a Perception of Higher Accuracy?

5. conclusions and future directions, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Vitello, M.; Salvi, C. Gestalt’s Perspective on Insight: A Recap Based on Recent Behavioral and Neuroscientific Evidence. J. Intell. 2023 , 11 , 224. https://doi.org/10.3390/jintelligence11120224

Vitello M, Salvi C. Gestalt’s Perspective on Insight: A Recap Based on Recent Behavioral and Neuroscientific Evidence. Journal of Intelligence . 2023; 11(12):224. https://doi.org/10.3390/jintelligence11120224

Vitello, Mary, and Carola Salvi. 2023. "Gestalt’s Perspective on Insight: A Recap Based on Recent Behavioral and Neuroscientific Evidence" Journal of Intelligence 11, no. 12: 224. https://doi.org/10.3390/jintelligence11120224

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Gestalt Theory: Understanding Perception and Organization

Gestalt theory, a psychological framework developed in the early 20th century by German psychologists Max Wertheimer, Wolfgang Köhler, and Kurt Koffka, provides valuable insights into how humans perceive and make sense of the world around them. The term “gestalt” itself translates to “form” or “whole” in German, emphasizing the theory’s focus on understanding patterns and configurations rather than isolated elements.

At its core, gestalt theory suggests that our minds naturally organize sensory information into meaningful wholes or coherent patterns. Instead of perceiving individual parts separately, we tend to perceive objects as complete entities with inherent relationships among their components. This holistic approach to perception allows us to recognize familiar objects and scenes effortlessly.

One of the fundamental principles of gestalt theory is known as “the law of proximity.” This principle states that elements that are close to each other tend to be perceived as belonging together. For example, when presented with a group of dots arranged closely in space, we will perceive them as forming a single shape or pattern rather than separate entities.

Overall, gestalt theory offers valuable insights into human perception and cognition by highlighting our innate tendency to organize sensory information into meaningful wholes. By understanding these underlying principles, we can gain a deeper appreciation for how our minds construct meaning from the world around us.

Overview of Gestalt Theory

Gestalt theory is a psychological framework that focuses on how people perceive and experience the world around them. It emphasizes that our perception is not simply a collection of individual elements, but rather, it is influenced by the way these elements are organized into meaningful patterns or “Gestalts.” In this section, we’ll delve into the key concepts and principles of Gestalt theory.

One fundamental principle of Gestalt theory is the idea that the whole is greater than the sum of its parts. This means that when we perceive something, we don’t just see individual objects or elements in isolation. Instead, our minds automatically organize these elements into cohesive wholes. For example, when looking at a painting, we don’t focus solely on each brushstroke or color patch; instead, we perceive it as a complete image with its own unique meaning and emotional impact.

Another important concept in Gestalt theory is known as “figure-ground relationship.” According to this principle, our minds naturally separate visual stimuli into distinct figures (the objects of interest) and background (the surrounding context). This separation allows us to focus our attention on specific elements while simultaneously perceiving their relation to the broader environment. For instance, when observing a tree in a forest, we can distinguish it from the other trees and appreciate its form despite being surrounded by foliage.

Gestalt psychology also highlights the role of perceptual grouping in shaping our perception. Our brains tend to group similar elements together based on various factors such as proximity (objects close to each other are seen as related), similarity (objects that share common features are grouped together), continuity (we tend to perceive smooth curves rather than abrupt changes), and closure (our tendency to fill in missing information to create complete shapes).

Additionally, Gestalt theorists emphasize that perception involves more than just visual stimuli; it encompasses all aspects of human experience including auditory, tactile, olfactory sensations, and even abstract concepts. Gestalt theory suggests that our minds naturally organize and interpret these diverse stimuli in a holistic manner, seeking patterns, meaning, and coherence.

By understanding the principles of Gestalt theory, we can gain insights into how our perception works and how we make sense of the world around us. It offers valuable perspectives for fields such as psychology, design, art, and even problem-solving. As we explore further in this article, we’ll delve into specific examples and applications of Gestalt theory to better grasp its practical implications.

Remember, this section is just the beginning of our exploration into Gestalt theory. Stay tuned for more fascinating insights and real-world examples that will deepen your understanding of this influential psychological framework.

Key Principles of Gestalt Theory

Gestalt theory, coined by German psychologists in the early 20th century, is a school of thought that emphasizes how individuals perceive and interpret the world around them. In this section, we’ll delve into the key principles of Gestalt theory that shed light on our perceptual experiences.

• The Law of Proximity: According to the law of proximity, objects that are close to each other are perceived as belonging together. This principle highlights how our brains naturally group elements based on their physical closeness. For example, imagine a series of dots scattered randomly on a page. Our minds instinctively organize them into clusters or patterns based on their proximity.
• The Law of Similarity: The law of similarity states that objects with similar features tend to be grouped together in our perception. Whether it’s shape, color, size, or texture, similarities between elements influence how we perceive and categorize them. Think about an array of differently shaped fruits displayed at a farmers’ market; we tend to group similar fruits together based on their shared characteristics.
• The Law of Closure: The law of closure suggests that our brains have a tendency to complete incomplete shapes or figures by filling in missing information. Even when presented with fragmented visual stimuli, we unconsciously connect the dots and perceive them as whole objects or forms. This principle explains why we can identify familiar symbols like logos even when they’re partially obscured.
• The Law of Figure-Ground Relationship: The law of figure-ground relationship describes how we perceive an image by differentiating between the main object (the figure) and its background (the ground). Our minds automatically separate an object from its surroundings to create distinct focal points in our perception. For instance, when looking at a photograph against a textured backdrop, we effortlessly distinguish between the subject and its environment.
• The Law of Continuity:

The law of continuity posits that our brains prefer to perceive continuous, smooth patterns rather than abrupt changes or disruptions. This principle suggests that we tend to follow the smoothest path when perceiving visual information and that our minds naturally connect elements along a common pathway. For example, when observing a winding river, we perceive it as a continuous flow rather than separate segments.

Understanding these key principles of Gestalt theory gives us insights into how our minds organize and make sense of the world. By recognizing these fundamental principles, we can better appreciate the complexities of perception and apply them in various design disciplines such as graphic design, architecture, and psychology.

Perception and Organization in Gestalt Theory

When it comes to understanding how we perceive the world around us, Gestalt theory provides valuable insights. This theory highlights that our minds have a natural inclination to organize sensory information into meaningful patterns and wholes, rather than perceiving individual elements in isolation.

One key concept in Gestalt theory is the idea of “figure-ground” perception. It suggests that we instinctively separate objects or figures from their background, allowing us to focus our attention on what stands out. For example, imagine looking at a photograph of a person standing in front of a beautiful landscape. Our mind automatically distinguishes between the person (the figure) and the background scenery (the ground), enabling us to perceive each element separately.

Another important principle within Gestalt theory is the notion of “closure.” Our brains tend to fill in missing information or gaps when presented with incomplete stimuli. This means that even if we are only given fragments or partial shapes, we can still recognize them as complete objects. For instance, if you see an image consisting of several disconnected lines forming an incomplete square, your mind will likely perceive it as a whole square.

Furthermore, Gestalt theory emphasizes how our minds naturally seek simplicity and order in visual perception. The principle of “simplicity” suggests that we tend to interpret complex stimuli by organizing them into simpler forms or patterns. By doing so, we make sense of what we see and reduce cognitive load. For instance, when presented with a scatterplot graph displaying various data points, our brain might automatically group similar points together based on proximity or shape.

Overall, understanding perception and organization through the lens of Gestalt theory sheds light on how our minds process visual information. It reveals our innate ability to form coherent perceptions by grouping elements together based on their relationships and characteristics. By grasping these principles, we can gain deeper insights into human cognition and enhance various fields such as design, psychology, and even marketing.

Gestalt Laws and Their Applications

Let’s delve into the fascinating world of Gestalt theory and explore its laws and practical applications. Understanding these principles can provide valuable insights into how we perceive and interpret the world around us.

• Law of Proximity: According to this principle, objects that are close together tend to be perceived as a group or related. For instance, imagine a group of people standing in a line. Even though they are separate individuals, our brain automatically groups them together due to their proximity.
• Law of Similarity: The law of similarity states that objects that share similar visual characteristics, such as shape, size, color, or texture, are perceived as belonging to the same group. Consider a collection of circles and squares arranged randomly on a page; we instinctively group the circles together and the squares together based on their similarity.
• Law of Closure: This principle suggests that our minds tend to fill in missing information or gaps in order to perceive whole shapes or patterns. For example, if you see an incomplete circle with a small gap at the bottom, your brain will naturally complete it as a full circle.
• Law of Continuity: The law of continuity proposes that our brains prefer smooth and continuous lines rather than abrupt changes in direction or pattern. When presented with intersecting lines or curves, we perceive them as flowing continuously rather than disjoined segments.
• Law of Figure-Ground Relationship: This principle deals with how we distinguish between an object (figure) and its background (ground). Our brains tend to focus on one element while perceiving others as less prominent or secondary. Think about how you can easily differentiate between words on a page and the blank space surrounding them.

These laws have various real-world applications across different fields:

• Graphic Design: Designers often utilize Gestalt principles to create visually appealing layouts by leveraging proximity, similarity, closure, continuity techniques.
• Advertising: Advertisers use these laws to capture viewers’ attention and create memorable visuals that communicate their message effectively.
• User Experience (UX) Design: Applying Gestalt principles in UX design helps designers create intuitive interfaces, ensuring users can easily navigate through websites or applications.
• Psychology and Perception: The study of Gestalt theory has contributed significantly to our understanding of human perception and cognitive processes.

By recognizing the power of Gestalt laws and implementing them consciously, we can enhance communication, design, and overall user experience in various aspects of our lives.

Gestalt Therapy: A Practical Approach

When it comes to therapy, there are various approaches that aim to help individuals overcome challenges and improve their well-being. One such approach is Gestalt therapy, which focuses on the here and now, emphasizing self-awareness and personal responsibility. In this section, I’ll delve into the practical aspects of Gestalt therapy and how it can be applied in real-life situations.

• Awareness in the Present Moment: Gestalt therapy places great importance on being fully present in the current moment. This means paying attention to our thoughts, feelings, bodily sensations, and behaviors as they arise. By cultivating awareness of what is happening internally and externally, individuals can gain insight into their patterns of behavior and make more conscious choices.

For example, let’s say someone is struggling with anger management issues. Through Gestalt therapy techniques like focusing on bodily sensations associated with anger or exploring the underlying emotions triggering this response, individuals can develop a greater understanding of their anger triggers. This heightened awareness empowers them to respond differently in similar situations in the future.

• Taking Responsibility for One’s Actions: Another key aspect of Gestalt therapy is the emphasis on personal responsibility for one’s actions and choices. It encourages individuals to acknowledge that they have control over how they perceive situations and how they respond to them.

For instance, consider a person who constantly blames external circumstances for their unhappiness or lack of success. In Gestalt therapy sessions, they would be encouraged to explore their role in creating these outcomes and take ownership of their choices. By recognizing their ability to make different decisions or change perspectives, individuals become active participants in shaping their own lives.

• Integration of Parts: Gestalt therapists often work with clients to help integrate different parts of themselves that may feel disconnected or conflicting. This involves exploring inner dialogue between these parts and finding ways to bring them together harmoniously.

Let’s imagine someone struggling with indecisiveness and feeling torn between different desires or values. Through Gestalt therapy techniques like the “empty chair” exercise, where individuals have a dialogue with imagined aspects of themselves, they can explore conflicting thoughts and emotions. This process facilitates self-acceptance and integration, leading to greater clarity and decision-making ability.

In summary, Gestalt therapy offers a practical approach to personal growth and healing by focusing on present awareness, taking responsibility for one’s actions, and integrating different parts of oneself. By incorporating these principles into therapeutic practice, individuals can develop a deeper understanding of themselves and work towards making positive changes in their lives.

Critiques and Controversies Surrounding Gestalt Theory

When it comes to the field of psychology, Gestalt theory has undoubtedly made its mark. However, like any prominent theory, it is not without its fair share of critiques and controversies. Let’s delve into a few key points that have sparked debate among scholars and researchers.

• Reductionism: One criticism often leveled against Gestalt theory is its perceived lack of emphasis on reductionism. Some argue that the holistic approach advocated by Gestalt psychologists undermines the importance of breaking down complex psychological processes into smaller components for analysis. Critics contend that this limits our understanding of human behavior and cognition.
• Subjectivity and Interpretation: Another point of contention revolves around the subjective nature of perception in Gestalt theory. While proponents highlight how individuals actively organize sensory information into meaningful patterns, skeptics argue that interpretation plays a significant role in determining these patterns. This subjectivity raises questions about the reliability and universality of perceptual organization principles proposed by Gestalt psychologists.
• Empirical Evidence: In scientific circles, rigorous empirical evidence holds great significance when evaluating theories. Some critics claim that the experimental support for certain aspects of Gestalt theory is limited or inconclusive. They argue that more research is needed to validate some fundamental assertions put forth by this influential school of thought.
• Cultural Bias: A recurring concern within critiques surrounding many psychological theories is their potential cultural bias. Similar concerns arise with respect to Gestalt theory, as some scholars question whether its principles are applicable across diverse cultural contexts or if they are rooted in Western perspectives alone.
• Integration with Other Theories: Lastly, there are debates about how well Gestalt theory integrates with other branches of psychology and related disciplines such as neuroscience or cognitive psychology. Critics argue that despite its contributions, the gestalt framework might not fully account for all aspects of human behavior and cognition when considered alongside other theoretical frameworks.

It’s important to note that these criticisms and controversies do not negate the valuable contributions made by Gestalt theory. Rather, they serve as thought-provoking avenues for further exploration and refinement of our understanding of human perception and cognition.

In the next section, we’ll explore some real-world applications of Gestalt theory in various fields to showcase its practical relevance. Stay tuned!

Influence of Gestalt Theory on Modern Psychology

Gestalt theory, with its emphasis on the whole being greater than the sum of its parts, has had a profound influence on modern psychology. By examining how individuals perceive and interpret information, Gestalt theory has provided key insights into human cognition and behavior. Let’s delve into some examples that highlight the impact of this theory.

• Perception and Organization: Gestalt psychologists emphasized that our minds have an innate tendency to organize sensory stimuli into meaningful patterns. An example of this is the concept of figure-ground perception, where we naturally distinguish between objects (figures) and their surrounding background (ground). This understanding has greatly influenced research in visual perception, advertising design, and even user interface development.
• Problem-Solving and Insight: Gestalt theory also sheds light on problem-solving processes by emphasizing the role of insight or “aha” moments. According to this perspective, problem-solving involves restructuring our mental representation of a problem to achieve a sudden realization of the solution. This notion has informed various fields like education, cognitive psychology, and creativity studies.
• Holistic Approach in Therapy: The principles of Gestalt therapy align closely with its theoretical counterpart. Instead of focusing solely on isolated symptoms or behaviors, therapists using this approach aim to understand clients as integrated beings within their environment. The therapeutic process focuses on fostering self-awareness, personal growth, and enhancing relationships through exploring emotions in the present moment.
• Social Perception: Gestalt principles extend beyond individual perception to social contexts as well. Social psychologists have applied these ideas to explore how people form impressions about others based on fragmented information or cues they receive when encountering someone for the first time. This research highlights how our minds automatically fill in missing details to create a more coherent understanding of others’ personalities.
• Group Dynamics: Understanding group dynamics is another area significantly influenced by Gestalt theory concepts such as proximity, similarity, and closure. These principles help explain how individuals form affiliations, make group decisions, and perceive themselves as part of a larger collective. Such insights have informed fields like organizational psychology and leadership development.

Gestalt theory has left an indelible mark on modern psychology by offering novel perspectives on perception, problem-solving, therapy, social cognition, and group dynamics. Its holistic approach continues to shape our understanding of human behavior and enrich various domains within the field of psychology.

In this article, we have explored the fascinating concept of Gestalt theory and its impact on psychology and perception. Let’s summarize the key points we’ve discussed:

• Perception is more than the sum of its parts: According to Gestalt theory, our minds naturally organize sensory information into meaningful patterns and wholes. We perceive objects as unified entities rather than a collection of individual elements.
• The principles of Gestalt theory: We have examined several fundamental principles that govern how we perceive visual stimuli, including figure-ground relationship, proximity, similarity, closure, and continuity. These principles help us make sense of the world around us and facilitate efficient processing of visual information.
• Applications in various fields: Gestalt theory has found applications in many domains beyond psychology. It has influenced art, design, advertising, user experience (UX) design, and even problem-solving techniques. Understanding how people perceive and interpret visual information can greatly enhance communication and effectiveness in these areas.
• Limitations and criticisms: While Gestalt theory offers valuable insights into perception, it also faces criticism for oversimplifying complex cognitive processes. Some argue that it neglects other factors such as attention and memory that influence perception.
• Ongoing research: Despite being introduced over a century ago, researchers continue to explore the intricacies of Gestalt theory and its implications today. Advancements in neuroscience allow us to delve deeper into understanding how our brains process visual stimuli.

In conclusion,

Gestalt theory provides a framework for understanding how our minds organize sensory information to create meaningful perceptions of the world around us. By studying these perceptual principles, we gain insights into human cognition that can be applied across various disciplines.

Remembering that perception is not simply about individual elements but about the whole picture helps designers create visually appealing graphics or interfaces while advertisers use this knowledge to engage their target audience effectively.

As technology advances further and our understanding grows deeper through ongoing research efforts, we can expect to uncover even more about the intricacies of perception and its implications for our daily lives.

So, next time you marvel at a beautiful painting or get captivated by an engaging advertisement, remember that Gestalt theory plays a significant role in shaping your perception.

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Gestalt Psychology

Seeing the Mind and Behavior as a Whole

Gestalt psychology is a  school of thought  that looks at the human mind and behavior as a whole. Gestalt psychology suggests that humans don't focus on separate components but instead tend to perceive objects as elements of more complex systems.

Emily Roberts / Verywell

A core belief in Gestalt psychology is holism —that the whole is greater than the sum of its parts. The approach has played a major role in the study of human sensation and perception .

Gestalt Meaning

Gestalt is a German word that roughly means "configuration" or the way things are put together to form a whole.

The History of Gestalt Psychology

Originating in the work of Max Wertheimer , Gestalt psychology formed in part as a response to the structuralism of  Wilhelm Wundt .

Whereas followers of structuralism were interested in breaking psychological matters down into their smallest possible parts, Gestalt psychologists wanted to look at the totality of the mind and behavior. Guided by the principle of holism, Wertheimer and his followers identified instances where perception was based on seeing things as a complete whole, not as separate components.

A number of thinkers influenced the development of Gestalt psychology, including Immanuel Kant, Ernst Mach, and Johann Wolfgang von Goethe.

Wertheimer developed Gestalt psychology after observing what he called the phi phenomenon while watching alternating lights on a railway signal. The phi phenomenon is an optical illusion where two stationary objects seem to move if they are shown appearing and disappearing in rapid succession. In other words, we perceive movement where there is none.

Based on his observations of the phi phenomenon, Wertheimer concluded that we perceive things by seeing the whole perception, not by understanding individual parts. In the example of blinking lights at a train station, the whole we perceive is that one light appears to move quickly between two points. The reality is that two separate lights are blinking rapidly without moving at all.

Influential Gestalt Psychologists

Wertheimer's observations of the phi phenomenon are widely credited as the beginning of Gestalt psychology and he went on to publicize the core principles of the field. Other psychologists also had an influence on this school of psychology.

Wolfgang Köhler : Köhler connected Gestalt psychology to the natural sciences, arguing that organic phenomena are examples of holism at work. He also studied hearing and looked at problem-solving abilities in chimpanzees.

Kurt Koffka : Together with Wertheimer and Köhler, Koffka is considered a founder of the field. He applied the concept of Gestalt to child psychology , arguing that infants first understand things holistically before learning to differentiate them into parts. Koffka played a key role in bringing Gestalt principles to the United States.

Principles of Gestalt Psychology

Gestalt psychology helped introduce the idea that human perception is not just about seeing what is actually present in the world around us. It is also heavily influenced by our motivations and expectations .

Wertheimer created principles to explain how Gestalt perception functions. Some of the most important principles of Gestalt theory are:

• Prägnanz : This foundational principle states that we naturally perceive things in their simplest form or organization.
• Similarity : This Gestalt principle suggests that we naturally group similar items together based on elements like color, size, and orientation. An example would be grouping dogs based on whether they are small or large, or if they are big or small.
• Proximity : The principle of proximity states that objects near each other tend to be viewed as a group.
• Continuity : According to this Gestalt principle, we perceive elements arranged on a line or curve as related to each other, while elements that are not on the line or curve are seen as separate.
• Closure : This suggests that elements that form a closed object will be perceived as a group. We will even fill in missing information to create closure and make sense of an object. An example of this Gestalt psychology principle is using negative space to give the illusion that a particular shape exists when it doesn't.
• Common region : This Gestalt psychology principle states that we tend to group objects together if they're located in the same bounded area. (For example, objects inside a box tend to be considered a group.)

Uses of Gestalt Psychology

Gestalt psychology is useful in many areas, including therapy, design, product development, and learning.

Gestalt Therapy

Gestalt therapy is based on the idea that overall perception depends on the interaction between many factors. Among these factors are our past experiences, current environment, thoughts, feelings, and needs. Gestalt therapy involves key concepts such as awareness , unfinished business, and personal responsibility.

The main goal of Gestalt therapy is to help us focus on the present . While past context is important for viewing yourself as a whole, a Gestalt therapist will encourage you to keep your focus on your present experience.

Research suggests that Gestalt therapy is effective at treating symptoms of depression and anxiety , and it may help people gain confidence and increase feelings of self-efficacy and self-kindness. It is often a helpful way to structure group therapy .

The therapeutic process is reliant on the relationship between the client and therapist . As a client, you must feel comfortable enough to develop a close partnership with your therapist, and they must be able to create an unbiased environment where you can discuss your thoughts and experiences.

Beginning in the 1920s, designers began incorporating Gestalt principles in their work. Gestalt psychology led these designers to believe that we all share certain characteristics in the way we perceive visual objects and that we all have a natural ability to see "good" design.

Designers embraced Gestalt concepts, using our perception of contrast, color, symmetry, repetition, and proportion to create their work. Gestalt psychology influenced other design concepts, such as:

• Figure-ground relationship : This describes the contrast between a focal object (like a word, phrase, or image) and the negative space around it. Designers often use this to create impact.
• Visual hierarchy : Designers use the way we perceive and group visual objects to establish a visual hierarchy, ensuring that the most important word or image attracts our attention first.
• Associativity : This concept involves the principle of proximity. Designers often use this to determine where to place important objects, including text elements such as headlines, captions, and lists.

Product Development

Product designers use Gestalt psychology to inform their decisions during the development process. Consumers tend to like products that follow Gestalt principles.

This influence can be seen in the appearance of the products themselves and in their packaging and advertising. We can also see Gestalt principles at work in apps and digital products. Concepts like proximity, similarity, and continuity have become standards of our expected user experience.

Learning and Education

The Gestalt Theory of Learning relies on the law of simplicity. In simple terms, it states that each learning stimulus is perceived in its simplest form.

The psychology behind this learning theory states that we use our senses and previous experiences to gain knowledge about the world around us. It also suggests that we learn from the methods by which we are taught, in addition to being impacted by classroom environments and the academic culture.

Impact of Gestalt Psychology

Gestalt psychology has largely been subsumed by other types of psychology, but it had an enormous influence on the field. Researchers like Kurt Lewin and Kurt Goldstein were influenced by Gestalt concepts before going on to make important contributions to psychology.

Gestalt theory is also important in that the idea of the whole being different than its parts has influenced our understanding of the brain and social behavior. Gestalt theory still impacts how we understand vision and the ways that context, visual illusions, and information processing impact our perception.

The Takeaway

Gestalt therapy continues as an effective tool for psychologists today. Its emphasis on a holistic approach plays an important role in cognitive psychology , perception, and social psychology , among other fields.

Frequently Asked Questions

Gestalt psychology was founded by Max Wertheimer, a Czechoslovakian psychologist who also developed a lie detection device to objectively study courtroom testimony. ]Wolfgang Köhler and Kurt Koffka are also considered co-founders of the Gestalt theory.

Most of the foundational principles of Gestalt psychology explain how we group things, such as by similarity, proximity, continuity, closure, and common reason. Prägnanz is another Gestalt principle and says that we tend to perceive complex things in their most simple form. Prägnanz is sometimes referred to as the law of simplicity, a concept that was first presented in 1914.

Gestalt psychology has influenced how we study perception and sensation. It also increases our understanding of how our cognitive processes influence the way we behave socially.

Some therapists use Gestalt psychology to help patients focus on the present over the past. Designers and product developers also use Gestalt theory to make their creations more appealing or to draw focus to certain elements over others. Educators may also use Gestalt principles to help their students learn.

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

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Gestalt psychology

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Gestalt psychology , school of psychology founded in the 20th century that provided the foundation for the modern study of perception . Gestalt theory emphasizes that the whole of anything is greater than its parts. That is, the attributes of the whole are not deducible from analysis of the parts in isolation. The word Gestalt is used in modern German to mean the way a thing has been “placed,” or “put together.” There is no exact equivalent in English. “Form” and “shape” are the usual translations; in psychology the word is often interpreted as “pattern” or “configuration.”

Gestalt theory originated in Austria and Germany as a reaction against the associationist and structural schools’ atomistic orientation (an approach which fragmented experience into distinct and unrelated elements). Gestalt studies made use instead of phenomenology . This method, with a tradition going back to Johann Wolfgang von Goethe , involves nothing more than the description of direct psychological experience, with no restrictions on what is permissible in the description. Gestalt psychology was in part an attempt to add a humanistic dimension to what was considered a sterile approach to the scientific study of mental life. Gestalt psychology further sought to encompass the qualities of form, meaning, and value that prevailing psychologists had either ignored or presumed to fall outside the boundaries of science .

The publication of Czech-born psychologist Max Wertheimer ’s “Experimentelle Studien über das Sehen von Bewegung” (“Experimental Studies of the Perception of Movement”) in 1912 marks the founding of the Gestalt school. In it Wertheimer reported the result of a study on apparent movement conducted in Frankfurt am Main , Germany, with psychologists Wolfgang Köhler and Kurt Koffka . Together, these three formed the core of the Gestalt school for the next few decades. (By the mid-1930s all had become professors in the United States.)

The earliest Gestalt work concerned perception , with particular emphasis on visual perceptual organization as explained by the phenomenon of illusion . In 1912 Wertheimer discovered the phi phenomenon , an optical illusion in which stationary objects shown in rapid succession, transcending the threshold at which they can be perceived separately, appear to move. The explanation of this phenomenon—also known as persistence of vision and experienced when viewing motion pictures —provided strong support for Gestalt principles.

Under the old assumption that sensations of perceptual experience stand in one-to-one relation to physical stimuli , the effect of the phi phenomenon was apparently inexplicable. However, Wertheimer understood that the perceived motion is an emergent experience, not present in the stimuli in isolation but dependent upon the relational characteristics of the stimuli. As the motion is perceived, the observer’s nervous system and experience do not passively register the physical input in a piecemeal way. Rather, the neural organization as well as the perceptual experience springs immediately into existence as an entire field with differentiated parts. In later writings this principle was stated as the law of Prägnanz , meaning that the neural and perceptual organization of any set of stimuli will form as good a Gestalt, or whole, as the prevailing conditions will allow.

Major elaborations of the new formulation occurred within the next decades. Wertheimer, Köhler, Koffka, and their students extended the Gestalt approach to problems in other areas of perception, problem solving , learning , and thinking . The Gestalt principles were later applied to motivation, social psychology , and personality (particularly by Kurt Lewin ) and to aesthetics and economic behaviour. Wertheimer demonstrated that Gestalt concepts could also be used to shed light on problems in ethics , political behaviour, and the nature of truth. Gestalt psychology’s traditions continued in the perceptual investigations undertaken by Rudolf Arnheim and Hans Wallach in the United States .

Health, Brain and Neuroscience

Mental, physical health and neuroscience, gestalt theory: what is it, characteristics, its laws and main applications.

What is Gestalt Theory? Discover here one of the most important trends in psychology. We will tell you about their characteristics, main authors, contributions, and applications. Also a bonus on how these contribute in a personal level.

Table of Contents

What is the Gestalt Theory?

Gestalt is a decisive trend in psychology history. It was born in Germany at the beginning of the 20th century. It was Christian von Ehrenfels, an Austrian philosopher, who gave this movement its name in The Attributes of Form, his most important work. There is no perfect English translation of the term “gestalt”. But we can interpret it as “totality”,”figure”,”structure”,”configuration” or “organized unity”.

“The whole is more than the sum of its parts” is its maximum. The main authors of Gestalt proposed alternatives to the dominant psychological paradigms and made great contributions to cognitive psychology .

This particular focus was a breath of fresh air and allowed people who did not feel represented by the main currents of psychology to find an alternative.

Gestalt Theory: Characteristics

• Its main predecessors of gestalt theory are philosophers: Thinkers such as Kant, Descartes or Husserl developed the theoretic basis on which this school developed. The psychologists belonging to this current were able to take their ideas to the laboratory and obtain amazing results.
• We must treat people as a whole: We cannot explore the different dimensions that shape us in isolation. A holistic approach is needed when speaking about mental health. The complexity of the human mind cannot be reduced. Gestalt theory explores the dynamic relationships that connect the various elements of reality. Gestalt theory does not conceive separating processes such as learning from memory.
• We are active in understanding reality: We do not all perceive reality, in the same way, we have our own vision. Each one structures the information they receive according to their previous experiences. Our mental representations do not correspond completely with those that exist in reality, we construct them ourselves. We are also able to adapt our mental processes and contents as new situations arise.
• They opposed the predominant schools in their time: Gestalt theory psychologists did not agree with approaches such as behaviorism , which limits human behavior to associations between stigmas and responses. This perspective leaves mental processes aside and does not contemplate the potential of human intelligence. On the other hand, they did not adhere to psychoanalysts either, seeing people as passive agents without willpower .
• Gestalt theory’s main study area is perception: Gestalt theorist focused especially on seeking simple and natural explanations that could be adapted to our natural way of perceiving reality. Through perception , we are able to acquire knowledge of the world, interact with it and connect with others.

Our senses and mental processes interact to allow us to perform tasks as varied as removing the hand from a burning surface or notice that the person speaking to us is upset by their frowning. Gestalt theory focuses on visual perception. However, their ideas have been adapted to fields such as music.

Gestalt Theory: Main contributions

Gestalt psychologists are known for their contributions to the study of the learning process and problem-solving. However, their most relevant contribution, which was stated by Wertheimer, is the elaboration of some basic laws that govern our perception.

Gestalt Theory Laws

We can see a host of examples of these principles around us. In addition, they are fully applicable to our daily life.

1. Law of Prägnanz

Perception tends to organize the elements in the simplest possible way. Our brain prefers harmonious compositions. Mental processes are not infinite, we cannot dedicate time and resources to everything around us. Therefore, we simplify what we perceive and prefer simplicity. In this picture, we don’t need any more data to know that we are looking at a cup.

2. Figure-ground law

We have all seen Rubin’s glass at one time or another, it is the best-known example of this phenomenon. We will have realized that it is impossible to perceive the faces and the cup at the same time.

3. Law of proximity

The elements closest to each other tend to form a group as if they were one set. If you look at three piles of candy, you’ll notice three groups instead of seeing all the candy separately. In this example, we perceive the objects in each box as a single block.

4. Law of similarity

Similar figures seem to have the same shape. Their similarity may be due to the fact that they have a similar color, shape or any other characteristic that allows us to draw a parallel between them. We know that each tree has its own characteristics; not all trees have exactly the same height and color. However, from this point of view, they seem to us to be practically the same because of their similarity.

5. Common Fate law

Elements that seem to move together towards a certain orientation are perceived as a whole. If we see some children running to an ice cream stand, we will look at them as a whole. However, we can also look at them one by one if we are interested. In this case, we perceive the group in a homogeneous way.

6: Law of Closure

We tend to mentally close the contours to simplify reality. If we see a slightly curved curve that is practically closed, we will notice a circumference. It is also possible to apply this law to verbal messages.

For example, advertisers release suggestive phrases for their audience to complete. This technique requires a little effort on the part of the public to be effective. However, it maintains its interest and can achieve greater involvement.

This photograph leads us to imagine a closed line that unites all people. We see that they are separate, but our brain reduces the information.

7. Law of Good Continuity

We prefer to ignore the abrupt changes in an image we are seeing. Generally speaking, we pay more attention to the characteristics of a stimulus that allow us to perceive a smooth continuity.

One example is that if we are walking around and notice on a poster an A covered in half by a street lamp, we will continue to know that the letter is A and read the text without difficulties. In this example, we can see the continuity of the branches.

Gestalt Theory: Applications

Basic research.

The study of basic psychological processes such as attention or perception has been influenced by Gestalt theory. Their research is fundamental for other authors to apply their discoveries to practice.

For example, advances in the field of perception make it possible for us to carry out programmes to improve road signs and avoid accidents. Their ideas continue to be reviewed and modified by experts to help us better understand how we work.

Problem solving

Gestalt psychologists believed that the circumstances are composed of several components that interact with each other. If we want to solve a problem we have to reorganize its components to discover a new solution. This idea can be extrapolated to all areas of our life. What do we have to do every day to solve a problem?

Wertheimer proposed the difference between productive thinking , which consists in carrying out creative reorganizations of the elements of the problems in order to solve them, and reproductive thinking , which is limited to applying the previous knowledge in a mechanical way.

Gestalt theory insists on using productive thinking, which will help us to reach insight. This term refers to the eureka moment, which takes place when we suddenly realize what the answer to our difficulties is.

Students should be more than just data recorders and learn to look for ways to solve their difficulties on their own. Practically all the contributions of the Gestalt can be integrated into the field of education. From their insights into mental processes to their ideas about therapy, they enable students to progress both academically and personally.

Communication

People linked to the world of communication and creativity, such as artists, designers or publicists, must know Gestalt Theory very well in order to attract the attention of their audience. Knowing how we interpret images is essential for them to be able to create works that allow them to transmit their messages and establish an effective dialogue with their audience.

When we see a poster saturated with visual elements and plagued with different typographies on a billboard, we are likely to ignore it directly. These laws allow us to understand that “less is more”.

If we want to compose memorable images that come directly to our recipients, we must select what? is the most important part of our message. We have to put it as clearly as possible. All the attention must be focused on the essentials without irrelevant distractions.

Gestalt Theory: Therapy

This therapy is approached from a humanistic approach , which considers people active beings and independent. It analyzes the human mind from its most transcendental side, explores its functioning from a holistic point of view and focuses on the positive aspects of life.

Gestalt theory therapy adopts the Kantian idea that we cannot know how things are in reality, but if we experience them. Each person presents his/her own thoughts, experiences, desires and other complexities. Our variability involves that each individual is considered individually. This therapy also has similarities with Buddhism, as it focuses on developing attention and awareness.

Gestalt theory therapy began to be developed by Fritz Perls in the 1940’s. For this author, each one of us has their own truth and he focused on the creative potential of each person. Perls emphasized that perception is the key to reality and we are responsible for changing it. He composed a sentence summarizing his thoughts:

I do what I do and you do what you do. I am not in this world to meet your expectations, nor are you in this world to meet my expectations. You are you, and I am I, and if by chance we meet, it will be wonderful. If not, nothing can be done – Fritz Perls

Gestalt therapy wants us to live “here and now” without pretending to be something that we are not. The intention is for us to grow personally and have a clear identity. Therapist and patient collaborate in this process without establishing hierarchies, they are two people with a common objective.

What can Gestalt Theory give us?

We can apply everything we have read in this article to our daily life. The great advantages of Gestalt’s theory are its application to everyday fields and the simplicity of its approaches.

Your ideas help us to better understand how we process and interpret reality. For example, they explain some optical illusions or our behavior when we go down the street and group the various elements together instead of paying attention to each one.

In addition, Gestalt can help us in daily challenges as common as problem-solving, encouraging us to be more creative and organized . On the other hand, we can follow some of the indications of Gestalt therapy to promote our personal growth.

Criticism of Gestalt Theory

Their ideas are still successful, but they are not spared from critics. Some experts consider their perceptual organizational approaches to be vague and ambiguous. In addition, other professionals claim that their experiments were not scientific enough.

On the other hand, Gestalt therapy is blamed for its individualism. They propose that each person finds his or her own path in isolation rather than deepening his or her social side. This can lead to selfish behavior. However, its followers claim that we need to discover ourselves first in order to connect with others afterward.

There are different approaches to psychology and we cannot determine who is right. Even so, it is possible to combine different perspectives in order to elaborate more complete and integrative explanations.

Gestalt Theory: Fundamental Authors

These psychologists were the most important representatives of Gestalt Theory. Their ideas continue to be revised and inspire new theories today.

1. Wolfgang K ö hler

Founded this movement with Koffka and Wertheimer. His main contribution was learning by discovery and maintains that this process is active and dynamic.

He showed that chimpanzees try to solve problems by trial and error. After several failures in tasks such as reaching for food, the primates with whom he experimented seemed to reflect on the solution until they found it. In fact, they were then able to extrapolate it to similar new situations.

2. Max Wertheimer

The phenomena phi or apparent movement is its most revolutionary discovery. It consists in the perceiving movement from the succession of different fragmented images. For example, it happens when we perceive the succession of film frames as if it were a real movement.

3. Kurt Koffka

His contributions were elementary in several fields. He studied memory, learning, perception and also applied Gestalt to fields such as child psychology.

It emphasized the need to consider mental processes from a holistic point of view. He also helped Wertheimer in his research on the apparent movement by becoming involved as a subject.

4. Kurt Lewin

He was not one of the founders of Gestalt Theory. However, he was a prominent social psychologist who brought the ideas of Gestalt to this area. His study was more focused on motivation and psychosocial intervention using Gestalt.

These four psychologists were forced to emigrate to the United States after feeling threatened by Nazism.

Thank you so much for reading this article. We hope that the Gestalt Theory has been inspiring to you. If you have any questions or would like to make a contribution, please do not hesitate to comment.

This post is originally in Spanish written by Ainhoa Arranz, translated by Alejandra Salazar. 

Alejandra is a clinical and health psychologist. She is a child specialist with a diploma in evaluation and intervention in autism. She has worked in different schools with young children and private practice for over 6 years. She is interested in early childhood intervention, emotional intelligence, and attachment styles. As a brain and human behavior enthusiast, she is more than happy to answer your questions and share her experience.

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Home » Learning Theories » Gestalt Theory (Wertheimer)

Gestalt Theory (Wertheimer)

Along with Kohler and Koffka, Max Wertheimer was one of the principal proponents of Gestalt theory which emphasized higher-order cognitive processes in the midst of behaviorism. The focus of Gestalt theory was the idea of “grouping”, i.e., characteristics of stimuli cause us to structure or interpret a visual field or problem in a certain way (Wertheimer, 1922). The primary factors that determine grouping were: (1) proximity – elements tend to be grouped together according to their nearness, (2) similarity – items similar in some respect tend to be grouped together, (3) closure – items are grouped together if they tend to complete some entity, and (4) simplicity – items will be organized into simple figures according to symmetry, regularity, and smoothness. These factors were called the laws of organization and were explained in the context of perception and problem-solving.

Wertheimer was especially concerned with problem-solving. Werthiemer (1959) provides a Gestalt interpretation of problem-solving episodes of famous scientists (e.g., Galileo, Einstein) as well as children presented with mathematical problems. The essence of successful problem-solving behavior according to Wertheimer is being able to see the overall structure of the problem: “A certain region in the field becomes crucial, is focused; but it does not become isolated. A new, deeper structural view of the situation develops, involving changes in functional meaning, the grouping, etc. of the items. Directed by what is required by the structure of a situation for a crucial region, one is led to a reasonable prediction, which like the other parts of the structure, calls for verification, direct or indirect. Two directions are involved: getting a whole consistent picture, and seeing what the structure of the whole requires for the parts.” (p 212).

Application

Gestalt theory applies to all aspects of human learning, although it applies most directly to perception and problem-solving. The work of  Gibson  was strongly influenced by Gestalt theory.

The classic example of Gestalt principles provided by Wertheimer is children finding the area of parallelograms. As long as the parallelograms are regular figures, a standard procedure can be applied (making lines perpendicular from the corners of the base). However, if a parallelogram with a novel shape or orientation is provided, the standard procedure will not work and children are forced to solve the problem by understanding the true structure of a parallelogram (i.e., the figure can be bisected anywhere if the ends are joined).

• The learner should be encouraged to discover the underlying nature of a topic or problem (i.e., the relationship among the elements).
• Gaps, incongruities, or disturbances are an important stimulus for learning
• Instruction should be based upon the laws of organization: proximity, closure, similarity and simplicity.
• Ellis, W.D. (1938). A Source Book of Gestalt Psychology. New York: Harcourt, Brace & World.
• Wertheimer, M. (1923). Laws of organization in perceptual forms. First published as Untersuchungen zur Lehre von der Gestalt II, in  Psycologische Forschung ,  4 , 301-350. Translation published in Ellis, W. (1938).  A source book of Gestalt psychology  (pp. 71-88). London: Routledge & Kegan Paul.
• Wertheimer, M. (1959). Productive Thinking (Enlarged Ed.). New York:Harper & Row.

NOTE : Thanks to Gerhard Stemberger ([email protected]) for his help with this page.

Creativity in problem solving: integrating two different views of insight

• Original Paper
• Open access
• Published: 02 September 2021
• Volume 54 , pages 83–96, ( 2022 )

Cite this article

You have full access to this open access article

• Per Øystein Haavold   ORCID: orcid.org/0000-0002-6786-9400 1 &
• Bharath Sriraman 2  

Even after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the first view argue that insight is the consequence of analytic thinking and a sequence of conscious and stepwise steps. The second view suggests that insight is the result of unconscious processes that come about only after an impasse has occurred. Extant models of problem solving within mathematics education tend to highlight the first view of insight, while Gestalt inspired creativity research tends to emphasize the second view of insight. In this study, we explore how the two views of insight—and the corresponding set of models—can describe and explain different aspects of the problem solving process. Our aim is to integrate the two different views on insight, and demonstrate how they complement each other, each highlighting different, but important, aspects of the problem solving process. We pursue this aim by studying how expert and novice mathematics students worked on two ill-defined mathematical problems. We apply both a problem solving model and a creativity model in analyzing students’ work on the two problems, in order to compare and contrast aspects of insight during the students’ work. The results of this study indicate that sudden and unconscious insight seems to be crucial to the problem solving process, and the occurrence of such insight cannot be fully explained by problem solving models and analytic views of insight. We therefore propose that extant problem solving models should adopt aspects of the Gestalt inspired views of insight.

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1 Introduction

Most mathematics educators would probably agree that the development of students’ problem solving abilities is an important objective of instruction. Thus there has been a considerable amount of research on problem solving in the last several decades (Lester, 2013 ). In general, researchers into problem solving have usually defined the term problem as tasks or questions that an individual or group of individuals do not immediately know how to answer (Lester, 2013 ). However, this definition says very little about how to teach individuals to become better problem solvers (Lester, 2013 ). Several models of problem solving have therefore been developed to describe and explain factors and processes involved in problem solving—most of which have drawn heavily on Pólya’s ( 1949 ) famous four-stage model of problem solving. Nevertheless, problem solving instruction is still considered ineffective. There are many reasons for this perception, but one key issue is the lack of concern for the complexity and the many factors involved in problem solving processes (Lester, 2013 ).

The focus of this paper is one of the more subtle yet essential factors involved in problem solving. Ever since the Gestaltists first began studying problem solving nearly 100 years ago, insight in problem solving has been of interest to psychologists (Hadamard, 1945 ; Ohlsson, 2011 ; Poincaré, 1948 ; Weisberg, 2015 ). Here, it is important to note that insight ( Einsicht ) within the Gestalt approach, and much of the literature on insight and problem solving, have a broader meaning than the standard definition in English. According to the Gestaltists, an individual’s comprehension of a problem cannot be reduced to a collection of individual perceptual features. Instead, the individual perceives a particular Gestalt of the problem, which can be interpreted as the totality of the relations between its parts. Insight, to the Gestaltists, was therefore considered a mental restructuring of the problem into a more productive Gestalt (Ohlsson, 2011 ; Wertheimer, 1959 ). In this study, we draw on the Gestalt view and consider insight as a perceptual and conceptual restructuring of a problem in a more productive manner. This view of insight has also been described as mentally crossing a ‘logical gap’, and it has often been referred to as a sudden and unexpected feeling of comprehension during an attempt at solving a problem (Ohlsson, 2011 ; Sternberg & Davidson, 1995 ).

Currently there are two main views on the source of insight during problem solving. Proponents of the first view argue that insight is the consequence of analytic thinking in which the problem is matched with information in memory. The solution typically unfolds in a sequence of conscious steps, and the individual has a feeling of steady incremental progress. Insight is gained gradually and consciously. The Gestaltists called this reproductive thinking (Weisberg, 2015 ). The second view, termed productive thinking by the Gestaltists, suggests that insight is the result of a particular set of processes distinct from conscious analytical thinking. Here, insight is the result of unconscious processes that come about only after an impasse has occurred. Furthermore, insight is gained quickly, often spontaneously, and as a result of mental restructuring of the problem (Weisberg, 2015 ). Extant models of problem solving within mathematics education tend to highlight the first view of insight. Lester and Kehle ( 2003 ), for example, characterizes successful problem solving as “coordinating previous experiences, knowledge, familiar representations and patterns of inference, and intuition…” (p. 510). Although unconscious processes such as intuition are sometimes mentioned, they are usually not explained or elaborated in problem solving models, and the emphasis is on analytic and conscious cognitive processes. On the other hand, within the field of creativity research and theoretical models of creativity—in particular Gestaltist inspired research—analytic thinking is considered unable to produce novelty. Highly inspired by the Gestaltists, the focus has therefore often been on more spontaneous processes that can result in a new interpretation of the problem (Weisberg, 2015 ).

In this study, we investigated how the two views of insight—a and corresponding set of models—can describe and explain different aspects of the problem solving process. The aim of our study was to integrate the two different views on insight, and demonstrate how they complement each other, each highlighting different, but important aspects of the problem solving process. We pursued this aim by studying how expert and novice mathematics students at a large research university in Norway approached and worked on two ambiguous and ill-defined mathematical problems. We then applied both a problem solving model and a creativity model in our analysis of students’ work on the two problems, in order to compare and contrast aspects of insight during the students’ work. More specifically, we set out to answer the following research question:

How do expert and novice students approach and attempt to gain insight into ill-defined mathematical problems?

To work towards our aim, we made use of a novice-expert comparison, which has proven to be useful within cognitive research (National Research Council, 2000 ). Expertise has commonly been described as 10 years of intense preparation in some field (Ericsson & Lehmann, 1996 ), or “proficiency taken to its highest level” (Glaser, 1987 ). However, expertise has also been defined in terms of cognitive development and knowledge structures (Hoffman, 1998 ), and described as a continuum or multiple stages rather than a dichotomy between experts and novices (e.g. Dreyfus & Dreyfus, 2005 ). In this study, we therefore differentiated between expert and novice students according to educational background and mathematical attainment. The main rationale for this choice was to contrast mathematical performance with two different theoretical perspectives of insight during problem solving.

We also made use of ill-defined problems , which are those problems for which there are conflicting assumptions, evidence, and opinions that may lead to different solution (e.g., Kitchener, 1983 ; Krutetskii, 1976 ). They force the problem solver to deal with uncertainty, and facilitate multiple possible approaches by looking at the problem in new and productive ways. Ill-defined problems are therefore particularly useful for facilitating perceptual restructuring and insight during the problem solving process (Webb et al., 2016 ).

1.1 Problem solving models

Problem solving has long been of interest to mathematics education researchers. At the root of this research, and most problem-solving frameworks, lies the work of the eminent mathematician George Polya (Schoenfeld, 1985a ). In his work How to Solve It , Pólya ( 1949 ) presented a four-step model of problem solving which consisted of the four steps understanding , planning , implementing , and looking back . The model outlines problem solving as a systematic and gradual process that facilitates insight primarily by building on prior knowledge and conscious evaluation. Because of the structured and pedagogical approach to problem solving and the explicit focus on prior knowledge, Polya’s four step model has become the most popular approach to teaching and learning problem solving (Liljedahl et al., 2016 ).

One of the shortcomings of Polya’s model is that research generated under its umbrella focused almost entirely on heuristics, or rules of thumb for making progress on difficult problems, while ignoring “managerial skills necessary to regulate one’s activity (metacognitive skills)” (Lester, 1985 , p. 62). Lester ( 1985 ) and Schoenfeld ( 1985a ) suggested that metacognitive activity (knowledge of one’s thought processes or self-regulation) underlies the application of heuristics and algorithms. As a result, Polya’s model was modified (Lester, 1985 ; Schoenfeld, 1985a ) to include a cognitive component and a metacognitive component. In the cognitive component, the four phases of understanding, planning, implementing, and looking back are labeled as orientation , organization , execution , and verification respectively. The metacognitive component consists of three classes of variables attributed to Flavell and Wellman ( 1977 ). This model purports to describe the four cognitive categories in terms of ‘points’ where metacognitive actions occur during problem-solving (see Fig.  1 ).

The cognitive-metacognitive model (Lester, 1985 )

The cognitive component Orientation refers to strategic behavior to assess and understand a problem. It includes comprehension strategies, analysis of information, initial and subsequent representation, and assessment of familiarity and chance of success. Organization refers to identification of goals, global planning, and local planning. The category of execution refers to regulation of behavior to conform to plans. It includes performance of local actions, monitoring progress and consistency of local plans, and trade-off decisions (speed vs. accuracy). Finally, verification consists of evaluating decisions made and evaluating the outcomes of the executed plans. It includes evaluation of actions carried out in the orientation, organization, and execution categories. The metacognitive component of the model is comprised of three classes of variables, namely person variables, task variables, and strategy variables. Person variables refer to an individual’s belief system and affective characteristics that may influence performance. Task variables refer to features of a task, such as the content, context, structure, syntax and process. An individual’s awareness of features of a task influences performance. Finally, strategy variables are those that refer to an individual’s awareness of strategies that help in comprehension, organizing, executing plans, and checking and evaluation.

The main purpose of this model is to show that metacognitive actions can influence cognitive behavior at all phases of problem solving (Lester, 1985 ; Schoenfeld, 1985a ). The introduction of metacognitive actions is an important modification of Polya’s model (Liljedahl et al., 2016 ). In contrast to Polya’s non-specific heuristics, the introduction of metacognitive components is an acknowledgment that problem solving is an emergent process that depends on the individual’s prior knowledge and internal dialogue. Unlike Pólya ( 1949 ), who prescribed heuristics applicable to all problems and problem solvers, Schoenfeld ( 1985a ) and Lester ( 1985 ) portray problem solving heuristics as personal objects that are limited to the individual’s existing knowledge and understanding of the problem (Liljedahl et al., 2016 ).

Nevertheless, both the original model by Pólya ( 1949 ) and the revised model (Lester, 1985 ; Schoenfeld, 1985a ) lay out problem solving as a conscious and incremental process in which the problem solver gains insight primarily through past experience and conscious evaluation. Generally, the first step in the process, after gaining an initial understanding of the problem, would entail attempts at matching the problem with prior knowledge and evaluating whether a solution method could be transferred to the new problem. If this attempt is unsuccessful, the problem solver would then move on to applying heuristic methods. Through the use of heuristics, the problem solver attempts to modify the present state of the problem so that he/she can advance towards the final goal (Weisberg, 2015 ). Of course, the process is not nearly this simple or linear, but it provides a general overview of the analytic approach to problem solving. Insight, or restructuring of the problem in a new and more productive manner, is gradually gained through a stepwise and conscious process.

However, within most of creativity research, which leans heavily on the Gestalt view of insight, this view of gradually gaining insight is rejected (Weisberg, 2015 ). Problem solving models, and similar reproductive approaches to insight in problem solving, do not explain how existing knowledge and analytic thinking can produce novel ideas, which are usually necessary for solving problems that require some form of insight. The argument is essentially that a logical system can only produce information that is already present, at least implicitly, in the premises, and that is therefore not novel (Weisberg, 2015 ). Therefore, insight has to be the result of some kind of special cognitive process different from the conscious and evaluative approach that characterizes analytic thinking (Ohlsson, 2011 ).

1.2 Creativity models

From the perspective of creativity research then, when one tries to solve a problem the individual will first try solutions based on similarities with other problems and consciously evaluate the progress. However, those attempts will often fail as problems that require some form of novelty will not be solved by transferring methods from similar problems. The problem solver will eventually reach an impasse. It is at this point that the person may suddenly and unconsciously gain insight through a mental restructuring of the problem and come up with a solution. This notion of insight as a result of sudden and unconscious illumination is usually attributed to the Gestalt psychologists, and it is currently the dominant view of creative thinking (Ohlsson, 2011 ).

According to the Gestaltists, creative thinking and insight follow a sequence of four stages, namely, preparation - incubation - illumination , and verification (Wallas, 1926 ; Hadamard, 1945 ; Poincaré, 1948 ). The first stage consists of working hard to understand the problem at hand. Poincaré calls this the preliminary period of conscious work. The second stage occurs when the problem is put aside for a period of time and the mind is occupied with other things. The third stage is where the solution suddenly appears while the individual is perhaps engaged in other unrelated activities. "This appearance of sudden illumination is a manifest sign of long, unconscious prior work." (Poincaré, 1948 , p. 16). However, the creative process does not end here. There is a fourth and final stage, namely verification, which includes expressing the results by language or writing. At this stage one verifies the result, makes it precise, and looks for possible extensions through utilization of the result.

More recently, Ohlsson ( 2011 ) reformulated the four step Gestalt model of creativity as the insight sequence in an effort to draw a clear distinction between problem solving through analytic thinking and problem solving through sudden insight. Furthermore, while the Gestaltists were concerned with insight and creative thought on timescales of months and years, proponents of more recent Gestalt inspired research that uses the insight sequence, consider aspects of insight and creativity also on much shorter timescales (Beghetto & Karwowski, 2019 ; Ohlsson, 2011 ). The insight sequence describes successful problem solving as a chain consisting of the following events: attempted solution \(\to\) consistent failure \(\to\) impasse \(\to\) restructuring \(\to\) insight \(\to\) Solution. Unlike problem solving models that describe insight as something gained gradually through analytic and conscious thinking, the insight sequence emphasizes impasse and sudden (and unconscious) cognitive restructuring as the basis for insight (Weisberg, 2015 ). Presently, this restructuring is thought to occur by an impasse that causes an altered balance in a lower layer of cognitive processing systems, which leads to a new, and possibly more productive, representation in a higher and more conscious layer (Ohlsson, 2011 ).

An important idea in the setting of perceptual restructuring is cognitive flexibility . Cognitive flexibility refers to our ability to switch between different mental sets, tasks and strategies in light of uncertainty and impasse (Ionescu, 2012 ). According to Nijstad et al. ( 2010 ), cognitive flexibility is a key element for achieving creative insights, problem solutions, or ideas through the use of flexible switching among categories, approaches, and sets, and through the use of remote (rather than close) associations. Cognitive fixation , on the other hand, is the counterpart to flexibility. The notion of people struggling to come up with creative solutions because they fixate, or fail to abandon non-productive strategies, has its roots a long way back in psychological literature and features particularly in the writings of the Gestalt school (Haylock, 1987 ).

Although cognitive flexibility seems to relate to the intuitive concept, we still lack a clear definition and comprehension of the phenomenon (Ionescu, 2012 ). For example, in a review of the literature, Ionescu ( 2012 ) identified several behaviors that are considered flexible, as follows: switching between tasks or multitasking; changing behavior in light of a new rule; finding a new solution to a problem; and creating new knowledge or tools. In this paper, we consider flexibility as the ability to break away from inappropriate approaches, i.e., particular methods and strategies, within a single problem (Haylock, 1987 ). Regarding cognitive fixation, Haylock ( 1987 ) concluded that there are two particularly important types of fixation in mathematical problem solving: algorithmic fixation and content universe fixation . Algorithmic fixation is closely related to the Einstellung effect , and it refers to individuals continuing to use an initially successful algorithm or method learnt beforehand or developed through the sequence of tasks themselves. The other type of fixation, content universe fixation, refers to situations where students’ thinking about mathematical problems is restricted unnecessarily to an insufficient range of elements that may be used or related to the problem (Haylock, 1987 ). The overcoming of these kinds of fixations, and thus allowing the mind to range over a wider set of possibilities than might first come to one’s conscious awareness, is an important aspect of successful problem solving.

1.3 Expert and novice problem solvers

Besides the use of metacognition to describe phases of problem-solving performance, another widespread approach within the problem solving research paradigm has been to describe in detail solutions used by ‘expert’ problem solvers and compare this to solutions of ‘novices’ (Simon & Simon, 1978 ). The rationale behind this genre of research was to identify strategies used by experts, and develop prescriptive models to teach students how to problem solve like experts. The main findings of studies in the ‘expert-novice’ genre were that experts and novices differed in their problem solving strategies because of the following:

Knowledge for understanding and representing problems (Orientation).

Strategic knowledge (Organization).

Repertoires of known procedures and familiar patterns (Execution and Verification).

Experts are adept at creating a representation of the problem, and understanding it in terms of fundamental principles. While experts tend to focus on structural properties of problems, novices place a greater emphasis on surface properties. Furthermore, novices are often not able to construct problem representations that are helpful in achieving solutions. This description fits into the orientation category of Lester’s ( 1985 ) cognitive-metacognitive model. Experts also solve problems by using a process of successful refinements. Global planning and qualitative analysis characterize their strategies, before generating specific equations to solve the problems. Novices, on the other hand, tend to go directly from the problem text in search of equations that could be used. This behavior fits into the organization category of Lester’s model. Finally, experts have developed a repertoire of problem types and solution methods besides having an extensive knowledge of basic principles. Novices are lacking much of this knowledge and experience. This observation fits into the execution and verification categories of Lester’s model.

Expert and novice differences have also been studied within creativity research. In general, it is believed that the more knowledge we have in a domain, the more flexible problem solvers we are in that domain (Ionescu, 2012 ). The most common explanation for this aspect is that experts have acquired, over many years of practice, a vast knowledge base of techniques, methods, strategies, etc., when solving problems. This large knowledge base enables the expert often to solve novel problems by small modifications to what they already know, which in turn requires relatively minor cognitive effort (Ohlsson, 2011 ). However, it has also been argued that expertise could lead to less flexibility and more cognitive fixations. Expertise is generally considered to be domain specific, as skills tend to go from higher levels of generality to greater specificity as a result of practice (Ohlsson, 2011 ). As a result, it is conceivable that expertise can lead to less flexibility and a greater fixation on a narrow pattern of previous experiences. Others have found non-linear relationships between expertise and flexibility. In a series of clever studies on the relationship between expertise and flexibility among chess experts, Bilalic et al. ( 2008 ) found a clear difference between ordinary (3 SDs above average performance) and super experts (5 SDs above average performance). While ordinary chess experts demonstrated cognitive fixation, possibly caused by knowledge specificity, the super experts demonstrated cognitive flexibility and not fixations induced by previous mental sets. Somewhat similarly, Elgrably and Leikin ( 2021 ) recently investigated the relationship between different types of mathematical expertise and creativity. Two groups of students—expert problem solvers in mathematics and mathematics majors in university—were given a problem-posing-through investigation-task. The results showed that the expert problem solvers posed three times as many problems, with more flexible and original properties, than the mathematics majors. These findings are in line with much of the literature that indicates a clear, yet somewhat nuanced relationship between mathematical knowledge and flexibility (e.g., Haavold et al., 2020 ).

2.1 Data collection and materials

To answer our research question and work towards the aim of the study, we investigated how expert and novice mathematics students approached and attempted to gain insight into two ill-defined mathematical problems. We report here on data from task-based interviews with small (3–4) groups of students. Each session lasted for about 60 min, in which the students worked on two ill-defined mathematical problems. During the interview, the interviewer answered clarification questions, but deflected more task specific and content related questions back to the students. We opted to make use of group based protocols as they are particularly appropriate for observing decision-making and students’ real social cognitive behavior (Schoenfeld, 1985b ).

The participants in the study consisted of two different groups of students aged 22–24 years, both of which are in their fifth and final year of their study programmes. All participants volunteered and were recruited by the first author of this paper via postings on the university’s learning management system (Canvas). The first group (novice group) consisted of 12 students, divided into four groups of three, enrolled in a 5 year pre-service teacher education programme specifically aimed at teaching in primary school and lower secondary school. The students in the novice group were not mathematics specialists, and had studied only 1 year of mathematics after upper secondary school. The mathematical content in their previous mathematics studies was focused on elementary mathematical topics such as geometry, algebra, and numeracy—with a particular didactical emphasis. The expert group consisted of four master’s students who excelled at graduate level mathematics. We classified this group as experts as they all were, at the time, working on their master’s degree in mathematics and had demonstrated proficiency (i.e., high grades—85th percentile) in advanced mathematics courses in calculus, number theory, algebra, and statistics.

Two ill-defined problems were given to the students. Each of them provided different types of misdirection and extensions of the problem space for the problem solvers.

Problem 1: the Roman inheritance problem The first problem comes from The Moscow Puzzles and is usually referred to as the Roman problem:

A dying Roman knowing his wife was pregnant, left a will saying that if she had a son, he would inherit two-thirds of the estate and the widow one-third, but if she had a daughter, the daughter would get one-third and the widow two-thirds. Soon after his death, his widow had twins- a boy and a girl, a possibility the will had not foreseen. What division of the estate keeps as closely as possible to the terms of the will?

There isn’t a single right answer to this problem as the constraints are not fully exhaustive. This presents the students with a problem that can be repeatedly restructured and facilitate many approaches, and insight is predicated on recognizing this ambiguity. The Roman jurist, Salvian Julian, proposed for instance that the father’s intent is that the daughter should receive half as much as her mother, and the son twice as much. The inheritance should be divided into seven parts, and the mother should get two parts, the son four parts, and the daughter one part. However, an opposing view is that the father wished the mother to inherit at least 1/3 of the estate, but Salvian Julian would give her only 2/7. Therefore, give instead the mother 1/3 and divide the rest between son and daughter according to the intended ratio of four to one. The solution of the problem depends on which of the constraints the line of reasoning is based on.

Problem 2: wrong arithmetic, but correct result The second problem was based on the idea of mathematical pathologies, which refer to examples that are specifically designed to violate properties that are perceived as valid (Sriraman & Dickman, 2017 ):

Sometimes the wrong method gives us the right answer. When does this method work?

This example is ‘cooked up’ knowingly to violate common properties of fraction multiplication. To gain insight into this problem, the students need to accept the counterintuitive properties as a premise and break away from established mental sets related to arithmetic. So when does this method work? One possible approach is to use algebra to identify the constraints of each digit:

which boils down to

and finally

As ten is on the left side, there are now four cases that can be investigated further: \(b-a=5, b-a=-5, c=5, and d=5.\) For each of these cases, new constraints can be imposed and the situation further investigated.

2.2 Data analysis

Ill-defined problems contain conflicting or incomplete constraints, and they necessitate restructuring of the problem in a new and more productive manner—which is how we define insight in this paper. To identify how the students attempted to gain insight into the two ill-defined problems, we carried out a three-step analysis (e.g., Simon, 2019 ) in which the interviews and students’ written work were analyzed retrospectively using approaches from qualitative content analysis (Mayring, 2015 ).

In the first step, we investigated the students’ work on each problem through an inductive analysis. The goal was to isolate and identify each individual solution that the students attempted. We refer to this step as approaches as it includes students’ solution attempts at solving the particular task, the type of strategies and reasoning employed by the students, and explicit assumptions made by the students. As we mentioned earlier, insight is predicated on some form of mental restructuring that allows the problem solver to view the problem a new and more productive manner. Although we cannot observe the cognitive processes directly, we can observe and identify the individuals’ approaches, in the form of actions and utterances, which indicate how they conceive the problem’s starting and goal state, constraints and operators. In other words, each approach indicates a particular mental structuring or restructuring of the problem (Weisberg, 2015 ).

In the second step, we made use of a mixed content analysis (Mayring, 2015 ) and looked more closely at the students’ approaches from both creativity and problem solving perspectives. More specifically, from a problem solving perspective, we first imposed the four stages of orientation, organization, execution, and verification (Lester, 1985 ) on to the previously identified approaches, and examined how the students moved between approaches. This step was accomplished by further categorizing all the observed behavior, i.e., utterances and actions, for each of the identified approaches. All behavior related to assessing or understanding the problem was coded as orientation. We then coded all behavior related to organizing and execution as a common category, as it can be very difficult to distinguish planning and execution of plans (Schoenfeld, 1985a ). The last category, verification, referred to all behavior related to evaluation of decisions made and the outcome of the executed plans. After the deductive coding, we made use of inductive coding with two goals in mind, as follows: (1) identify common characteristics of each phase across both problems for both groups of students respectively, and (2) identify how the groups of students moved between problem solving phases during the problem solving process.

To investigate the students’ work from a creativity perspective, we made use of a creativity model based on the Gestalt view of insight in the second step of our analysis. As mentioned earlier, the Gestaltists viewed insight as dependent on sudden and cognitive restructuring (Weisberg, 2015 ). Although cognitive flexibility can refer to various categories and sets, in this study we considered the identified approaches as a particular mental structuring, or restructuring, of the problem. Cognitive flexibility then, in this context, becomes the ability to switch between different approaches to the ill-defined problems. Furthermore, and as Nijstad et al. ( 2010 ) point out, the use of remote associations is a particular characteristic of cognitive flexibility. Thus, we looked more closely at (1) how many different approaches the students’ in each group made use of, (2) to what extent and in what way each approach differed from previous approaches in terms of strategies used and assumptions made, and 3) to what extent and in what way impasses during the problem solving process occurred—indicating the occurrence of fixations. Here, it is important to point out that we did not consider the success of each approach. It is often necessary to produce several attempts at solving an ill-defined problem in the absence of a priori knowledge of a valid solution, before finally solving it. Failed attempts are therefore often crucial to the creative process, as creative products are generated in the course of a dynamic process of exploration and assessment across both failed and successful attempts (Corazza, 2016 ).

In the third and final step, we attempted to develop explanatory inferences and work towards the aim of the paper. Here we compare and contrast how the two models—and corresponding views of insight—can describe and explain different aspects of the problem solving process. More specifically, we attempted to identify how and to what extent each of the two different models can describe and explain how the two groups of students gained, or failed to gain, insight into the ill-defined problems.

3.1 Problem 1: the Roman inheritance problem

Expert students The expert group approached the problem in two ways. At the start of the first approach, the students read the problem several times, first individually and then aloud, and discussed what they were “supposed to actually find out” as one student said. Simultaneously, they wrote down some of the constraints that they had identified in the problem: the wife should get more than the daughter, but less than the son. They then quickly reasoned what the wife’s proportion of the will would be if the total sum were halved. As one student said, “the wife should get exactly half of one third plus two third”. They concluded the wife should get half, and the rest be split between the daughter and the son. However, they quickly concluded that this was incorrect as this would either leave the son with less than the wife, or an inheritance exceeding the upper limit.

After rejecting the first approach, the expert students made a second attempt at solving the problem. They went back to talking about the information and conditions of the problem. They then decided to set up an equation, as this would “impose the all the necessary conditions on to the problem and we can solve it” as one student said. The right side of the equation had to be 1, as this represented the entire inheritance. The mother’s share was set as x, the son as y and the daughter z. They then substituted the variables and solved the equation (see Fig.  2 ).

Experts’ equation solution to the Roman problem

The students concluded that this was the right result. One of the students said: “The wife gets \(\frac{2}{7}\) , the daughter gets \(\frac{1}{7}\) , and the son gets \(\frac{4}{7}\) . This is the right result I guess”. However, this solution takes into account only the ratio between the wife, son and daughter, and not the share of the inheritance each person was promised. The students in the expert group mentioned this inconsistency a few times, but as one of the students said: “this is a bit weird, but I guess this is how you solve the problem”.

Novice students We identified three approaches for the novice groups.

As did the experts, all four novice groups first read the problem several times. However, unlike the experts, none of the novice groups discussed the information or constraints in the problem. Instead, they immediately started proposing possible solution strategies. The first approach all four novice groups attempted was some form of fraction expansion, followed by an empirically test to see if a more fine grained partition could make the inheritance division correct. The students would first set up a preliminary model, for instance imposing the constraints that the son would get more than the wife, and the wife would get more than the daughter. Then, they would adjust the model according to the results using bar charts, matrices or other heuristic approaches, and compare them to the conditions of the task. All four groups of students came up with at least three different partitions, before concluding that they were not able to build a model that satisfied all conditions of the task (see Fig. 3 ).

Example of novices’ model solution for the Roman problem

After concluding that the first approach did not satisfy all the conditions of the problem, all four novice groups immediately moved on to what we identified as a second approach. In the second approach, the novice students would use one of the son, the wife or daughter as a starting point based on the information in the task, and then quantify what share of the inheritance the others would get. For instance, if the son would receive \(\frac{2}{3}\) of the inheritance, then the wife would get \(\frac{2}{9}\) and the daughter would get \(\frac{1}{9}\) . The students would then use the daughter or the wife as the starting point, respectively, and quantify how much the others would get. However, after trying different starting points, all four novice groups concluded that this approach would not provide a correct solution.

The third approach we observed for all four novice groups was similar to the expert group’s second approach. The students wrote down and identified the ratios between the wife, the son and the daughter as the key constraints of the task. This approach was observed immediately after the novice students concluded their second approach was inappropriate, and it was also clear that this approach was inspired by the second approach. As one student said: “We have to take into account all constraints. At the same time. Not one by one. The son should get twice as much as the wife, and the wife should get twice as much as the daughter.” However, unlike the expert students, the novice students did not explicitly formulate equations that represented the conditions of the problem. Instead, they reasoned more informally. As one student said: “the wife should get twice as much as the daughter, and the son should get twice as much as the wife. The daughter then gets one part, the wife two parts, and the son four parts. That gives us seven parts in total”. All three novice groups concluded that this was the solution closest to the intentions of the will, but still not a satisfactory solution. After the third approach, three of the novice groups discussed the overall intentions of the will and which of their approaches was most in line with the wishes of the dying Roman. All three novice groups concluded that it was impossible to find a solution that was in full accordance with the will. However, all three groups also concluded that the main intention of the will was that the son should get more than the wife, and the wife should get more than the daughter.

3.2 Problem 2: wrong arithmetic, but correct result

Expert students The expert students approached the problem in two ways. First, the expert students read the problem, first individually and then out aloud. The experts then spent a few minutes talking about how “weird the expression was”, while verifying that both sides of the equation were equal, and the proposed method was correct. The students quickly agreed on both the meaning and goal of the problem. As one student said: “oh, they’ve just placed the digits together, and we need to find out when fraction multiplication gives this kind of product.” After verifying that the expression was indeed correct, the students proposed a hypothesis for which type of numbers this method was correct based on the example given. The students quickly mentioned that the sums of the digits in both the numerators and denominators were nine, and that nine was also a common factor of both 18 and 45. However, this hypothesis was not pursued further. Instead, the students quickly rejected the first approach and decided to represent the problem algebraically, which we have identified as their second approach.

After setting up the algebraic expression seen in Fig.  4 , the students repeatedly stated that this expression wasn’t appropriate. As one student said: “you can’t use correct algebra on something that is incorrect. The left side is ok, but the right side is completely wrong”. One of the students mentioned that they could have further identified constraints on each of the four “unknowns”, but he quickly decided that such a pursuit was pointless as it was “not correct mathematics”. The students then concluded that they couldn’t find any other solutions, as it couldn’t be solved algebraically and it was difficult to generalize any sort of pattern from just one case.

Experts’ algebraic solution for the Wrong arithmetic, but right result problem

Novice students Each of the four novice groups approached the problem in two ways. As with the Roman inheritance problem, all four novice groups first read the problem both individually and out loud. However, unlike the experts, the novice students did not explicitly discuss and agree on the meaning and goal of the problem. Instead, they seemed to spend a few minutes on their own trying to understand the problem. This period of apparent uncertainty was then interrupted by one of the students in the group proposing a particular solution strategy. For all four novice groups this involved a proposed hypothesis regarding the relationship between the numbers, which they refined empirically without considering the mathematical structure of the problem. For instance, the students explored commutativity and tried \(\frac{8}{5}\times \frac{1}{4}=\frac{81}{54}\) , they added the same numbers to denominators and numerators, and attempted to work with more or less randomly chosen fractions that, according to one student, were “in the same ballpark” as the fractions in the task. Common to all these hypotheses were that they were inferred from the specific numerical example in the problem text, and they were not based on any systematic investigation of the structural properties of the expression. One student, for example, evaluated the hypothesis according to “how close they came to giving an equal left and right side”. The students switched back and forth between several different hypotheses, but did not explicitly consider how the right side of the expression was constructed mathematically. Eventually, all four novice groups concluded that this approach was not “fruitful”, as one student said.

Eventually, all four novice groups rejected the first approach. Although there were some variations between the four groups, it seemed the second approach was an informal line of reasoning similar in structure to the novice students’ third approach on the Roman inheritance problem. Furthermore, the second approach seemed to evolve out of the seemingly superficial hypotheses proposed in the first approach. As one student said, “We need to make things easier… we’re just looking for connections between the numbers here, but there can so many of them.” In the second approach, the novice students seemed to look for specific examples that would satisfy the conditions of the problem and thus identify possible structural relationships. For instance, three of the novice groups realized eventually that they could just “turn the fractions upside down and maintain the same ratio between them” as one student said. Two of the groups also listed several trivial solutions that satisfied the criterion 1 × 1 = 1. The main difference between the novices’ first and second approaches, was that the first approach seemed to focus on identifying properties in the numbers given in the task, while the second approach seemed to focus on finding other examples that also satisfied the proposed method (see Fig. 5 ).

Example of novices’ empirical model solution to the Wrong arithmetic, but right result problem

3.3 Problem solving model

During the orientation phase of both tasks, both the experts and novices first read the task instructions individually and aloud. Both groups of students seemed to prefer to read the problem first and gain an initial understanding of it before talking about it to the other students. However, after reading the problem carefully, either quietly or aloud, the rest of the orientation phase was different for the experts and novices. While the experts wrote down and discussed the goals and conditions of the problems, seemingly to make sure everyone had the same understanding of the problem and its goal, the novices immediately began working on a solution strategy proposed by one of the students. Furthermore, after rejecting their first more informal approach, the experts went back to the orientation phase to make sure they all understood the problem correctly and had identified all the relevant conditions of the problem. There were also similarities and differences between the experts and novices in the organization and execution phases. For both problems, the experts first quickly proposed and rejected a hypothesis that seemed to be based on surface properties and incomplete constraints of the problems. For example, regarding problem two, there seemed to be no deeper analysis of the problem behind the first approach other than trying to identify common properties of the numbers on both sides of the equation sign. Similarly, the novices also first proposed hypotheses that seemed to be based on surface properties and incomplete constraints of the two problems. However, after rejecting the first approach, the experts then quickly sought a generalized and formalized solution, by representing and applying algebraic expressions and equations. The novices, on the other hand, continued to formulate hypotheses that they tested empirically, or they looked for numerical examples that satisfied given constraints of the problems. Finally, during the verification phase, there were also some noticeable differences between the two groups of students. The expert students quickly concluded, without any form of justification, that their first approach, for both problems, was incorrect. The students then similarly concluded quickly that their second approach was either correct or that the problem couldn’t be solved, for problem 1 and problem 2 respectively. Unlike the expert students, who evaluated each approach quickly and conclusively after the organization and execution phase, the novices seemed to evaluate the approach continuously and gradually come to a conclusion regarding its correctness.

These observations are in line with much of the existing literature on expert vs. novice problem solvers (Lester & Kehle, 2003 ; Schoenfeld, 1985a ). The experts placed a greater focus on understanding the problem, global planning, and creating representations that captured the structural properties of the problems. The novices, on the other hand, tended to go directly from the problem text in search of solution strategies that could be productive. Furthermore, the novices tended to create representations of the problems that were either incomplete or focused on surface properties. We also noticed that the experts quickly determined whether or not a particular approach was correct, while the novices seemed to explore each approach to a much greater extent before assessing its validity. This could be a result of a more extensive knowledge base. How the two groups of students moved between the different problem solving phases is also similar to results in the literature regarding expert and novice problem solving. Schoenfeld ( 1985a ) found, for example, that novices tend to spend much time on what he called the explore phase, which can be said to be an unstructured exploration of the problem analogous to orientation and organization. Experts, on the other hand, tend to display greater control and monitoring as they cycle more purposefully between the different problem solving phases. In this study, the experts’ problem solving behavior seemed to consist of repeating cycles of orientation → organizing/execution → verification. The novices, on the other hand, seemed to stick to cycling back and forth between the organizing/execution phase and the verification phase, after a single and initial orientation phase.

3.4 Creativity model

For the experts, we identified two approaches for each of the two problems. For the novices, we identified three approaches for the first problem and two approaches for the second problem. Immediately, a purely quantitative analysis would seem to indicate that the novices displayed greater cognitive flexibility during the problem solving process. However, a more detailed analysis reveals a more nuanced picture. For both problems, the experts’ first approach seemed to be unstructured exploration based on either surface or an incomplete set of properties of the problem. The second approach, on the other hand, for both problems, was a more general and structured approach, where all the relational properties of the problem were represented using algebraic equations. For example, the experts’ first approach to the Roman inheritance problem seemed to conclude that the wife’s part of the inheritance would simply be the midpoint of the two different situations described in the will. The second approach, on the other hand, was an equation that seemingly covered all the relational properties described in the problem. The experts’ work on both problems indicates a prominent mental shift between the first and the second approaches. It seems they were able to quickly break away from an inappropriate approach and instead pursue a more appropriate approach. Furthermore, the second approach is vastly different from the first approach in terms of both assumptions and strategies. As Nijstad et al. ( 2010 ) pointed out, sudden switching between remote mental sets—such as assumptions and strategies within a particular approach—is a key feature of cognitive flexibility. The novices, on the other hand, seemed to switch between approaches that were related to each other. For example, the novices’ two approaches on the Wrong arithmetic, but correct result problem were both based on unstructured exploration around arithmetic properties. This pattern indicates that although the novices were able to break away from unproductive approaches, the closely related approaches indicate less cognitive flexibility than that shown by the experts. This interpretation is in line with much of the relevant literature which concludes that extensive knowledge is positively associated with flexible problem solving (Ionescu, 2012 ).

Turning to the issue of cognitive fixation, we observed several incidents of ostensible impasses from which the experts and novices were unable to break. For both problems, the novices stuck to empirical investigations of hypotheses and informal reasoning. Although the novices shifted fluidly between different assumptions and strategies for both problems, the fact that they stuck to a particular set of approaches, indicates to some extent the presence of algorithmic fixation (Haylock, 1987 ). Although algorithmic fixation primarily refers to the inappropriate continued use of a particular algorithm, this kind of fixation also includes a more general predisposition to solve a problem in a specific manner even though better or more appropriate methods of solving the problem exist. Creating, for example, algebraic representations for both problems, in particular the second problem, would have helped the novices determine the relevant structural properties. The experts also experienced incidents of prolonged impasse that could indicate cognitive fixations. However, unlike the novices who displayed tendencies of algorithmic fixation, the experts seemed to primarily display tendencies of content universe fixation (Haylock, 1987 ). Working on the first problem, the experts concluded quickly that their second approach was “the correct solution”, as one student said, even though the constraints of the problem were not fully exhaustive and the ill-defined nature of the problem allowed multiple interpretations. For the second problem, the experts repeatedly stated that the algebraic expression (see Fig.  4 ) they had created was not appropriate, as they believe you could not apply “correct algebra on something that is incorrect”, as one student said. However, within the context of the problem, creating an equation that captures all the relevant structural properties is perfectly appropriate. In fact, analyzing the algebraic expression would have help the students’ identify the constraints of each digit. Overall though, the findings in the context of creativity is also in line with much of the literature. Both the experts and the novices displayed both flexibility and fixation during the problem solving process—although somewhat differently.

3.5 How students gained insight

Immediately, it would appear that the findings in this study are in line with much of the literature on expert and novice problem solving. Furthermore, both the experts’ and the novices’ work seemed to progress largely in a stepwise manner, as described and explained both by the problem solving model utilized in this study (Lester, 1985 ) and the analytic view of insight (Weisberg, 2015 ). One instance of this aspect can be seen in the novices’ work on the first problem. While their second approach was premised only on a single constraint of the problem, their third approach took into account all the relational properties between the wife, the daughter and the son simultaneously. In this instance, the novice students’ clearly modified their approach in a gradual and stepwise manner and further insight was gained as a result. A second important instance can be found in the experts’ work. For both problems, the experts returned to the orientation phase after their first approach, and then produced a new and more effective approach. This chain of events indicates that the experts’ first ineffective approach and return to the orientation phase somehow led to a productive mental restructuring of the problem—or greater insight in other words—which in turn resulted in a more effective approach.

However, a more finely-grained scrutiny of the students’ work reveals several limitations of the problem solving model. One such discrepancy is the emphasis on past experiences during problem solving (Liljedahl et al., 2016 ). Problem solving models (Lester, 1985 ; Pólya, 1949 ; Schoenfeld, 1985a ), and the analytic view of insight (Weisberg, 2015 ), highlight the importance of past experiences during problem solving and argue that insight is a consequence of matching the problem with information in memory. In this study, we did not observe a single incident in which either group explicitly referenced past experiences or compared the problem to other problems. It could be argued that the ill-defined structure of the problems themselves was unfamiliar, but it is still noticeable that neither group of students performed any sort overt assessment of familiarity with the task (Lester, 1985 ).

Another ostensible discrepancy can be found in the novices’ many approaches to the problems. Although the novices did not move between the different problem solving phases to the same extent as the experts, they did not stick to one particular approach “come hell or high water”—as Schoenfeld ( 1985a ) observed to be common among novice problem solvers. Instead, the novices moved seemingly effortlessly between different approaches, constantly adapting to the ambiguity of the ill-defined problems. This behavior is a clear indication of cognitive flexibility (Ionescu, 2012 ). Furthermore, each of these apparent mental restructurings of the problems seemed to follow small impasses in the problem solving process—as predicted by the Gestaltists (Weisberg, 2015 ).

Insight as a consequence of impasses and sudden mental restructuring, as opposed to a stepwise and conscious process, was even more prominent in the experts’ work. The experts’ work on both problems indicates a significant mental shift between the first and the second approach. After trying and concluding that their first and more informal approach was inappropriate, the experts quickly decided to pursue a completely different and more structured approach. Although this behavior can be projected on to the four phases of the problem solving model (Lester, 1985 ), as seen earlier, the model itself cannot qualitatively explain the drastic shift in terms of assumptions and strategies. The experts’ second approach was in no way a further refinement of their first approach, and they did not explicitly reference past experiences. Instead, it seemed the second approach appeared suddenly, unconsciously and as a response to the failure of the first approach. This chain of events is similar to what Ohlsson ( 2011 ) refers to as the insight sequence , which describes insight as something gained after an attempted solution fails and a sudden and meaningful mental restructuring is required. After an impasse has occurred, insight is gained after dealing with the problem from a completely novel perspective.

Finally, our analyses also indicate occurrences in which both groups of students failed to gain insight. For example, while the novices applied mostly empirical and informal reasoning, the experts sought generalized and formalized solutions. Although much of the literature explains this as a consequence of the experts’ more extensive knowledge base (Lester & Kehle, 2003 ; Schoenfeld, 1985a ), neither problem used in this study required advanced mathematics. The algebraic representations that the experts made use of were fairly simple and seemingly within the grasp of individuals who have taken at least upper secondary algebra. An alternative explanation can therefore be cognitive fixation (Haylock, 1987 ), in which individuals fail to abandon ineffective approaches and move beyond impasses. This was perhaps seen most clearly in the experts’ work on the second problem. After creating an algebraic representation of the structural properties of the problem, the experts quickly rejected, in unison, the approach as inappropriate. We propose that this is a clear example of an unnecessary restriction to an insufficient range of elements (Haylock, 1987 ). In other words, the experts imposed an unnecessary set of restrictions on to the problem solving process based on their conceptions of the situation, rather than the properties of the problem itself. Now, it can be argued that this fixation can be linked to the experts’ past experiences. However, the problem solving model, and the analytic view of insight, do not explain or describe how the problem solver can break away from established mental sets. In fact, the problem solving model, and the analytic view of insight, emphasize the use of prior knowledge and reliance on past experiences when first attacking a problem (Liljedahl, 2016). When facing a new problem, in particular an ill-defined problem such as those made use of in this study, the focus on past experiences could actually be a hindrance to making progress (Weisberg, 2015 ).

4 Final thoughts

In this study, we aimed to integrate two different views on insight during problem solving, and explore how they each highlight different aspects of the problem solving process. Looking back, applying both problem solving and creativity models on to the experts’ and novices’ work reveals and explains different aspects of the students’ problem solving processes. While the problem solving model helps us analyze and understand parts of the problem solving process, there are crucial aspects of the students’ work that it does not explain. In this study, we observed what we claim to be the occurrence of cognitive flexibility, cognitive fixation, and more importantly, sudden, and seemingly unconscious, insight during the problem solving process—for both experts and novices. The results of this study therefore dovetail with what the Gestaltists said all along: Sudden and unconscious insight seems to be crucial to the problem solving process, and the occurrence of such insight cannot be fully explained by standardized problem solving models and an analytic view of insight. Current researchers inspired by the Gestaltists have dubbed this understanding of insight as the special process view of insight (Ohlsson, 2011 ; Weisberg, 2015 ), as it asserts that the thought processes underlying insight are distinctly different from those thought processes underlying analytic thinking.

We suggest, based on the results of this study and the review of the relevant literature, that research into problem solving within mathematics education would benefit from adopting aspects of Gestalt inspired views of insight. Although we do not go as far as some who claim that adherence to any sort of heuristics can be a hindrance to the problem solving process, we do agree that there are no prescriptive heuristics for some of the more unconscious, yet highly important, cognitive aspects of problem solving (Liljedahl et al., 2016 ). So, what happens during the moment of insight or subconscious work? What is the source of creative thought? Although we do not fully understand mental restructuring and creative thought, Ohlsson ( 2011 ) has proposed redistribution theory as a Gestalt-inspired response. Here, the problem solver first creates an initial inappropriate representation of the problem. This particular interpretation activates one or more incorrect solutions, which the problem solver then works through. At some point, after working through the incorrect solutions, the problem solver reaches an impasse. It is at this point that the initial, and inappropriate, representation of the problem could be inhibited. This inhibition of the original representation of the problem might then result in a new representation of the problem, which causes the problem solver to realize that the problem can be thought of in a different way—in other words, a mental restructuring has occurred. Somewhat ironically, the Gestalt inspired method of problem solving can therefore also be said to rely heavily on past experience. What is entailed is not to match the problem with past experiences to find an appropriate solution, but rather to relax unnecessary constraints and inhibit knowledge that is not necessary. We propose that this line of reasoning can add to extant problem solving models in at least two ways, as follows: 1) Most problem solving models highlight the importance of assessing the familiarity of the problem (Lester, 1985 ; Liljedahl et al., 2016 ; Pólya, 1949 ; Schoenfeld, 1985a ). However, the heuristic emphasis seems to be on identifying similarities between the problem at hand and past experiences. We suggest that identifying divergences between the problem at hand and past experiences is also important, as it may help the problem solver recognize unnecessary constraints. 2) Working through numerous incorrect approaches and solutions can be helpful to the overall problem solving process, as it may lead to an impasse and a subsequent more appropriate restructuring of the problem. We suggest that problem solving models should also emphasize the value of working hard on problems for an extended period of time, and even failed attempts.

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Haavold, P.Ø., Sriraman, B. Creativity in problem solving: integrating two different views of insight. ZDM Mathematics Education 54 , 83–96 (2022). https://doi.org/10.1007/s11858-021-01304-8

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On the nature of insight solutions: evidence from skill differences in anagram solution

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• 1 Department of Psychology and Human Development, Vanderbilt University, Nashville, TN 37203, USA. [email protected]
• PMID: 12613568
• DOI: 10.1080/02724980244000288

According to the Gestalt psychologists, problem solutions that pop into mind suddenly with no awareness of the process by which they were generated are objectively as well as subjectively sudden. Thus, such pop-out solutions are qualitatively different from search solutions, which are constructed incrementally. The authors tested this claim in the domain of anagram solution. Experiment 1 documented that anagrams yield pop-out solutions, especially among highly skilled solvers. The results of Experiment 2 indicated that both pop-out and search solutions depended on the gradual accumulation of partial information, contrary to the Gestalt view of problem solving. Nevertheless, some aspects of the Experiment 2 results, as well as new analyses of an anagram study reported elsewhere, suggest that there may in fact be a qualitative difference between pop-out and search solutions. In particular, pop-out solutions may result from parallel processing of the constraints on the rearranged order of the anagram letters, whereas search solutions may result from a serial hypothesis-testing procedure. Like 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, Rea, & Dayton, 1994, p. 98)

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