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What is abstract thinking? 10 activities to improve your abstract thinking skills

Have you ever been in a meeting and proposed a unique solution to a problem? Or have you ever been faced with a difficult decision and thought about the potential consequences before making your choice?

These are examples of abstract thinking in action. Everyone uses abstract thinking in day-to-day life, but you may be wondering — what is abstract thinking?

Abstract thinking is the ability to comprehend ideas that aren't tangible or concrete. It's a crucial skill for problem-solving, creativity, and critical thinking — and the best part is that it can be developed and strengthened with practice.

In this article, we'll explore the concept of abstract thinking and offer some simple ways to become a stronger abstract thinker in everyday life. With some practice, you can become an expert problem-solver and use conceptual thinking to your advantage.

What is abstract thinking?

Abstract thinking is a cognitive process that allows us to think beyond observable information and deal with concepts, ideas, theories, and principles. By thinking outside of our existing knowledge, we can come up with solutions that aren't immediately obvious. This type of thinking is essential for problem-solving, decision-making, and critical thinking .

Abstract thinking enables us to generate new ideas, connect unrelated concepts, and look at the bigger picture. It also involves contemplating sentiments such as love, freedom, and compassion. These concepts aren’t concrete and can have different interpretations. By using abstract thinking, we can gain a deeper understanding of these concepts and their different meanings.

Abstract thinking is also crucial to creativity, innovation, and advanced problem-solving. It allows us to think beyond the surface level of a problem and come up with unique solutions. This can be especially important in fields such as science and technology, where new breakthroughs often require fresh perspectives and innovative thinking.

In addition, abstract thinking is a vital skill for personal development, enabling us to think beyond our immediate environment and beliefs and consider different perspectives. This allows individuals to make better decisions, be more receptive and open to change, and be more creative.

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Abstract vs. concrete thinking

We can best understand abstract thinking by knowing what it's not — concrete thinking. Concrete thinking is understanding and processing observable and directly experienced information. It's often associated with basic sensory and perceptual processes, such as recognizing a familiar face or identifying a physical object by its shape.

On the other hand, abstract thinking is the ability to understand and process information that isn’t directly observable or experienced. Abstract thinking is often associated with higher-level cognitive processes, such as decision making and critical thinking.

For example, if you’re asked what a chair looks like, concrete thinking would involve picturing it and what it's typically used for. By contrast, abstract thinking would involve considering what a chair could symbolize or how it could be used differently than what is traditionally accepted.

The two types of thinking aren’t mutually exclusive — instead, they complement each other in the cognitive process. We need concrete and abstract thinking skills to effectively process information and make informed decisions.

How is abstract thinking developed?

Abstract thinking is a cognitive process that develops over time, beginning in childhood and continuing into adulthood. The psychologist Jean Piaget , known for his theory of cognitive development, proposed that children go through different stages of mental growth. This begins with the sensorimotor stage, in which infants and young children learn through their senses and motor skills and develop concrete thinking skills. In their later years, they develop more advanced cognitive abilities, including abstract thinking.

During childhood, abstract thinking develops as children use the cognitive approach to learning to grasp new concepts and skills. They start to understand and manipulate abstract concepts such as numbers, time, and cause and effect. As they observe the world around them, they use what they know to make sense of what is happening and explore other possibilities.

A learning disability, mental health condition, or brain injury can, however, affect abstract thinking. Among these are psychological illnesses like schizophrenia , developmental disorders like autism, ADHD, and dyslexia, and physical illnesses like stroke, dementia, and traumatic brain injury. These individuals may have difficulty understanding and manipulating abstract concepts and require additional support to develop their abstract thinking skills.

As adults, we continue to refine our abstract thinking skills through practice. We can become adept at problem-solving and critical thinking by regularly engaging in activities that require abstract thought. These activities include brainstorming, reading, writing, playing board games, and exploring creative projects. Factors such as experience, education, and environment all play a role in the development of abstract thinking, and it's essential to continue challenging and exercising our cognitive learning skills to maintain and improve abstract thinking.

Why is it important to learn to think abstractly?

Thinking abstractly is a crucial skill that allows us to go beyond surface-level understanding and interpret the deeper meaning of concepts, ideas, and information. It enables us to see the big picture and make connections between seemingly unrelated ideas, which is a crucial thinking tool for problem solving and critical thinking. Additionally, learning to think abstractly can bring numerous benefits in our daily lives and in various fields such as science, technology, engineering, and mathematics (STEM).

For instance, abstract thinking enables us to process information quickly and efficiently on a daily basis. It helps us understand and interpret what people are saying and what is happening around us, which can lead to better decision-making. Abstract thinking is vital in STEM fields for innovation and progress, as it encourages creative thinking and the exploration of new ideas and perspectives.

Furthermore, abstract thinking helps us understand abstract concepts such as justice, freedom, and patriotism. By using analogies and other tools, we can consider what these words stand for, their implications in our world, and how they can be applied effectively in day-to-day life. In this way, abstract thinking helps us make sense of complex ideas and concepts and enables us to navigate the world with greater insight and understanding.

10 tips to improve your abstract thinking skills

Abstract thinking is crucial for problem-solving, creativity, and critical thinking. Fortunately, there are many ways to improve these skills in your everyday life.

1. Incorporate puzzles into your life

Solving puzzles is a great way to practice abstract reasoning and exercise your brain. Whether you enjoy crosswords, Sudoku, or jigsaw puzzles, solving these types of problems improves your ability to think abstractly by requiring you to think critically and strategically to find solutions to issues that aren’t immediately obvious.

2. Learn something new

Your mind engages in the information processing cycle when learning new things. Learning something new allows you to explore different perspectives and understand how the world works. You'll gain new knowledge and practice your abstract thinking skills as you process, store, and recall what you’ve learned.

3. Explore your creativity

Creative expression is another excellent way to exercise your abstract thinking skills. Creativity engages the right side of the brain , which is responsible for abstract thinking and creative problem-solving. Through drawing, painting, writing, or photography, exploring the creative process encourages you to think outside the box and develop new ideas.

4. Practice mindfulness

Mindfulness is the practice of purposely observing the present moment without judgment or bias. Practicing mindfulness can help you improve your abstract thinking by teaching you how to observe your thoughts, feelings, and emotions objectively and without judgment. As you think more deeply and analytically about what's happening in the present moment, you will further develop your abstract thinking skills.

5. Make a habit of reading

Books and articles on various topics can help you build your understanding of complex concepts and ideas. Reading enables you to develop your ability to connect different ideas and think critically about the material. You also have to use your imagination to visualize what you're reading, which helps to improve your creative thinking abilities. Annotating your reading can step this up a notch.

6. Travel somewhere new

Traveling to new places exposes you to new cultures and ways of thinking, which can help to expand your mind and improve your abstract thinking skills. Plus, when you're in a new place, you're forced to think on your feet as you figure out how to navigate the unfamiliar landscape. This helps to build up your problem-solving skills, which are essential for developing abstract thinking abilities.

7. Get more exercise

Exercise is not only beneficial for your physical health, but it can also be beneficial for your mental health . Exercise helps to increase oxygen flow to the brain, which can improve cognitive functioning and help you think more clearly. Exercise also increases the production of endorphins, which can improve your mood and make it easier to focus on what you're doing.

8. Practice critical thinking

Critical thinking involves using your reasoning skills to evaluate information objectively. By practicing critical thinking, you can develop your abstract thinking ability by learning to analyze information, identify patterns and connections, and draw logical conclusions. Additionally, critical thinking will help you become more aware of your own biases so that you can make unbiased decisions.

9. Embrace risk-taking

Taking risks and engaging in activities that make you uncomfortable can help you practice abstract thinking. Stepping outside of your comfort zone forces you to think differently and create solutions to complex problems. It also requires you to push yourself beyond what is familiar and take a leap of faith as you learn new things .

10. Take up a new hobby

Hobbies like painting, sculpting, and photography can help you practice abstract thinking by allowing you to explore new ideas and ways of looking at the world. These activities also require you to use your imagination and creativity to devise solutions that aren’t immediately obvious. It also makes you feel accomplished when you're done, which can boost your confidence and make you more open to taking risks in other aspects of life.

Enhance your abstract thinking skills

If you've wondered, "What is abstract thinking?" now you have a better understanding. Abstract thinking skills can benefit us in many areas. From problem solving to meaningful learning to critical thinking, it's a powerful tool that can enhance our ability to navigate daily challenges.

By incorporating activities that promote the abstract thinking process into our daily routine, we can improve our ability to grasp abstract ideas, improve our decision-making skills, and see the bigger picture. With practice and dedication, we can master the art of abstract thinking and unlock its full potential.

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What is Abstract Thinking? Understanding the Power of Creative Thought

When we think about thinking, we usually imagine it as a straightforward process of weighing options and making decisions. However, there is a more complex and abstract thinking type. Abstract thinking involves understanding and thinking about complex concepts not tied to concrete experiences, objects, people, or situations.

Abstract thinking is a type of higher-order thinking that usually deals with ideas and principles that are often symbolic or hypothetical. It is the ability to think about things that are not physically present and to look at the broader significance of ideas and information rather than the concrete details. Abstract thinkers are interested in the deeper meaning of things and the bigger picture. They can see patterns and connections between seemingly unrelated concepts and ideas. For example, when we listen to a piece of music, we may feel a range of emotions that are not directly related to the lyrics or melody. Abstract thinkers can understand and appreciate the complex interplay of elements that create this emotional response.

Understanding Abstract Thinking

Humans can think about concepts and ideas that are not physically present. This is known as abstract thinking. It is a type of higher-order thinking that involves processing often symbolic or hypothetical information.

Defining Abstract Thinking

Abstract thinking is a cognitive skill that allows us to understand complex ideas, make connections between seemingly unrelated concepts, and solve problems creatively. It is a way of thinking not tied to specific examples or situations. Instead, it involves thinking about the broader significance of ideas and information.

Abstract thinking differs from concrete thinking, which focuses on memorizing and recalling information and facts. Concrete thinking is vital for understanding the world, but abstract thinking is essential for problem-solving, creativity, and critical thinking.

Origins of Abstract Thinking

The origins of abstract thinking are partially clear, but it is believed to be a uniquely human ability. Some researchers believe that abstract thinking results from language and symbolic thought development. Others believe that it results from our ability to imagine and visualize concepts and ideas.

Abstract thinking is an essential skill that can be developed and strengthened with practice regardless of its origins. By learning to think abstractly, we can expand our understanding of the world and develop new solutions to complex problems.

Abstract thinking is a higher-order cognitive skill that allows us to think about concepts and ideas that are not physically present. We can improve our problem-solving, creativity, and critical thinking skills by developing our abstract thinking ability.

Importance of Abstract Thinking

Abstract thinking is a crucial skill that significantly impacts our daily lives. It allows us to understand complex concepts and think beyond what we see or touch. This section will discuss the benefits of abstract thinking in our daily lives and its role in problem-solving.

Benefits in Daily Life

Abstract thinking is essential for our personal growth and development. It enables us to think critically and creatively, which is necessary for making informed decisions. When we think abstractly, we can understand complex ideas and concepts, which helps us communicate more effectively with others.

Abstract thinking also helps us to be more adaptable and flexible in different situations. We can see things from different perspectives and find innovative solutions to problems. This skill is beneficial in today’s fast-paced world, where change is constant, and we need to adapt quickly.

Role in Problem Solving

Abstract thinking plays a crucial role in problem-solving. It allows us to approach problems from different angles and find creative solutions. When we can think abstractly, we can see the bigger picture and understand the underlying causes of a problem.

By using abstract thinking, we can also identify patterns and connections that may not be immediately apparent. This helps us to find solutions that are not only effective but also efficient. For example, a business owner who can think abstractly can identify the root cause of a problem and develop a solution that addresses it rather than just treating the symptoms.

Abstract thinking is a valuable skill with many benefits in our daily lives. It allows us to think critically and creatively, be more adaptable and flexible, and find innovative solutions to problems. By developing our abstract thinking skills, we can improve our personal and professional lives and positively impact the world around us.

Abstract Thinking Vs. Concrete Thinking

When it comes to thinking, we all have different approaches. Some of us tend to think more abstractly, while others tend to think more concretely. Abstract thinking and concrete thinking are two different styles of thought that can influence how we perceive and interact with the world around us.

Key Differences

The key difference between abstract and concrete thinking is the level of specificity involved in each style. Concrete thinking focuses on a situation’s immediate and tangible aspects, whereas abstract thinking is more concerned with the big picture and underlying concepts.

Concrete thinking is often associated with literal interpretations of information, while abstract thinking relates to symbolic and metaphorical interpretations. For example, if we describe a tree, someone who thinks concretely might describe its physical appearance and characteristics. In contrast, someone who thinks abstractly might explain its symbolic significance in nature.

The transition from Concrete to Abstract

While some people may naturally lean towards one style of thinking over the other, it is possible to transition from concrete to abstract thinking. This can be particularly useful in problem-solving and critical-thinking situations, where a more abstract approach may be needed to find a solution.

One way to make this transition is to focus on a situation’s underlying concepts and principles rather than just the immediate details. This can involve asking questions that explore the broader implications of a situation or looking for patterns and connections between seemingly unrelated pieces of information.

Abstract and concrete thinking are two different styles of thought that can influence how we perceive and interact with the world around us. While both styles have their strengths and weaknesses, transitioning between them can be valuable in many areas of life.

Development of Abstract Thinking

As we grow and learn, our ability to think abstractly develops. Age and education are two major factors that influence the development of abstract thinking.

Influence of Age

As we age, our ability to think abstractly improves. This is due to the development of our brain and cognitive abilities. According to Piaget’s theory of cognitive development , children progress through four stages of cognitive development, with the final stage being the formal operational stage. This stage is characterized by the ability to think abstractly and logically about hypothetical situations and concepts.

Role of Education

Education also plays a significant role in the development of abstract thinking. Through education, we are exposed to new ideas, concepts, and theories that challenge our existing knowledge and encourage us to think abstractly. Education also gives us the tools and skills to analyze and evaluate complex information and ideas.

In addition to traditional education, engaging in activities promoting abstract thinking can be beneficial. For example, participating in debates, solving puzzles, and playing strategy games can all help improve our abstract thinking skills.

The development of abstract thinking is a complex process influenced by age and education. By continually challenging ourselves to think abstractly and engaging in activities that promote abstract thinking, we can continue to improve our cognitive abilities and expand our knowledge and understanding of the world around us.

Challenges in Abstract Thinking

Abstract thinking can be a challenging cognitive process, especially for those not used to it. Here are some common misunderstandings and difficulties people may encounter when thinking abstractly.

Common Misunderstandings

One common misunderstanding about abstract thinking is that it is the same as creative thinking. While creativity can certainly involve abstract thinking, the two are not interchangeable. Abstract thinking consists of understanding and thinking about complex concepts not tied to concrete experiences, objects, people, or situations. Creative thinking, on the other hand, involves coming up with new and innovative ideas.

Another common misunderstanding is that abstract thinking is only helpful for people in certain fields, such as science or philosophy. Abstract thinking can benefit many different areas of life, from problem-solving at work to understanding complex social issues.

Overcoming Difficulties

One difficulty people may encounter when thinking abstractly is a lack of concrete examples or experiences to draw from. To overcome this, finding real-world examples of the concepts you are trying to understand can be helpful. For example, if you are trying to understand the concept of justice, you might look for examples of situations where justice was served or not served.

Another challenge people may encounter is focusing too much on details and needing more on the bigger picture. To overcome this, try to step back and look at the broader significance of the ideas and information you are working with. This can involve asking yourself questions like “What is the main point here?” or “How does this fit into the larger context?”

Abstract thinking can be a challenging but valuable cognitive process. By understanding common misunderstandings and overcoming difficulties, we can develop our ability to think abstractly and apply it in various aspects of our lives.

Frequently Asked Questions

How does abstract thinking differ from concrete thinking.

Abstract thinking is a type of thinking that involves the ability to think about concepts, ideas, and principles that are not necessarily tied to physical objects or experiences. Concrete thinking, on the other hand, is focused on the here and now, and is more concerned with the physical world and immediate experiences.

What are some examples of abstract thinking?

Examples of abstract thinking include the ability to understand complex ideas, to think creatively, to solve problems, to think critically, and to engage in philosophical discussions.

What is the significance of abstract thinking in psychiatry?

Abstract thinking is an important component of mental health and well-being. It allows individuals to think beyond the present moment and to consider different possibilities and outcomes. In psychiatry, the ability to engage in abstract thinking is often used as an indicator of cognitive functioning and overall mental health.

At what age does abstract thinking typically develop?

Abstract thinking typically develops during adolescence, around the age of 12 or 13. However, the ability to engage in abstract thinking can continue to develop throughout adulthood, with continued practice and exposure to new ideas and experiences.

What are the stages of abstract thought according to Piaget?

According to Piaget, there are four stages of abstract thought: the sensorimotor stage (birth to 2 years), the preoperational stage (2 to 7 years), the concrete operational stage (7 to 12 years), and the formal operational stage (12 years and up). During the formal operational stage, individuals are able to engage in abstract thinking and to think about hypothetical situations and possibilities.

What are some exercises to improve abstract thinking skills?

Some exercises that can help improve abstract thinking skills include engaging in philosophical discussions, solving puzzles and brain teasers, playing strategy games, and engaging in creative activities such as writing or painting. Additionally, exposing oneself to new ideas and experiences can help broaden one’s perspective and improve abstract thinking abilities.

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What is abstract thinking? How it works & more

• Abstract thinking, essential in various aspects of life, enables us to tackle problems ranging from calculus to navigating busy highways, showcasing its broad applicability.
• Applied on a daily basis, abstract thinking is a universal skill, transcending professions and daily routines, highlighting its pervasive nature.
• Abstract thinking involves thought processes that deviate from everyday rhythms, habits, and routines, providing a framework for simple to complex problem-solving scenarios.
• Delving into the concept of abstract thinking, it encompasses the ability to engage in unconventional thought processes, fostering creativity and strategic thinking.

From completing calculus problems to enabling us to strategize to successfully navigating a busy highway, abstract thinking allows us to accomplish a lot. Abstract thinking is applied daily, no matter what your profession or daily routines and habits are. 

But what exactly is abstract thinking? And how can it be used? Learn more about abstract thinking below, including examples and comparisons between abstract and concrete thoughts.

What Is Meant By “Abstract Thinking?”

Abstract thinking typically refers to thinking and thought processes that often diverge from the ordinary rhythms, habits , and routines of daily life. Abstract thinking allows us to engage in simple to complex problem-solving.

Abstract thinking can be used to make decisions in split seconds or even ones that take days to consider. This form of thinking involves:

• Predictions
• Prior knowledge
• Past experiences 

Often, abstract thinking patterns are not rooted in tangible, visible things but are rooted in concepts.

What Is an Example of Abstract Thinking?

A simple example of abstract thinking is solving a math problem; you might look at the problem and begin to use prior knowledge and logic to strategize on how to solve the problem before you begin. 

A more psychologically-rooted example of abstract thinking can include character strengths, for example, such as wisdom and strength. In order to be able to define, discuss, and recognize wisdom and strength as concepts, you must first be able to think abstractly as to what they are, for you cannot see them physically or tangibly as items. 

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What Are the 4 Stages of Abstract Thinking?

Abstract thinking and thought patterns tend to follow the four stages below:

• Non-objective fragmentation (birth months) : This stage is characterized by the developmental task of the infant building their understanding of the world through the use of their senses and being able to identify objects.
• Deconstruction ( 2-6 months ) :  As children in this stage continue to develop relationships with objects and their senses, they can begin to understand routines and cause-and-effect patterns.
• Two-dimensionalization (6-12 months) : This is an exciting stage, as object permanence begins to develop; that is, being able to understand the abstract concept that an object can still exist even when you can’t physically see it.
• Non-figurative (12-18 months) : As sensorimotor and object permanence continue to develop, children begin to understand and develop memories for abstract concepts and ideas.

These four stages are based on the four stages of development posited by the developmental psychologist, Piaget . The four stages described above are developmental experiences that Piaget discovered that all children go through in their journey toward beginning to develop abstract thinking. 

Though the four stages tend to end at approximately 18 months, as you can guess, the development of abstract concepts and thought processes is a lifelong process and continues to develop well past 18 months; the start of this secondary process occurs at 18 months. The stages above are described as the “sensorimotor stage” of development. 

What Are Abstract Thinkers Good at?

Abstract thinkers tend to be very well-adjusted and well-adapted at handling difficult, unpredictable, and complex situations. They are often good at bringing original ideas to the table and this enables them to effectively solve complex problems as they can think critically and creatively , using flexible thought processes and patterns of thinking that are abstract, allowing them to be generative in their thinking.

Abstract thinkers are also great at context; they can typically use this generative way of thinking to make more informed decisions.

How Can You Tell if Someone Is an Abstract Thinker?

One of the best ways that you can tell if someone is an abstract thinker is to watch or have them describe ways that they solve problems. If they typically solve problems quickly and with few options or solutions, they are not typically an abstract thinker.

 Abstract thinkers tend to involve many different types of cognitive inputs from various sources (past knowledge/experiences, current life experience, knowledge of certain concepts, etc.) to formulate many different solutions. Abstract thinkers are generative and typically offer a more structured, thorough thought process and multiple different solutions to one problem instead of formulating/focusing on one solution only.

What Does Abstract vs Concrete Thinking Mean?

The term “ abstract vs. concrete thinking ” simply refers to the description of two different philosophies or schools of thought. In other words, it identifies that there are two separate, distinct thought processes and ways of thinking that humans use to problem-solve and navigate their world and environment daily. 

Humans will tend to demonstrate one type of problem-solving over the other due to predispositions, learned behaviors, past experiences, current environmental influences, and the type of problem or challenge they face.

What Is the Difference Between Abstract Thinking and Concrete Thinking?

There are many differences between abstract and concrete thinking styles . One of the most recognizable differences is that abstract thinking patterns involve uses of logic, and non-tangible ideals such as predictions, and typically cannot be fully tangibly measured whereas concrete thinking patterns typically involve constructs that can be fully measured from start to finish (think facts, numbers, statistics, etc). 

Abstract thinking requires flexibility to be able to develop a solution(s) that fit the outcome and are usually highly individualized. Concrete thinking patterns tend to focus on simply solving the problem at hand using faster, non-flexible thought patterns and do not tend to include any measures of prediction or future-oriented thinking.

Am I an Abstract or Concrete Thinker?

One of the best ways to identify if you are an abstract or a concrete thinker is to test yourself. Give yourself a problem that needs to be solved and write down or record yourself speaking as you engage in the thought process.

Explore how you make your decisions:

• Was your decision-making process quick and did you settle on just one decision? 
• What sources did you consider and how many did you consider as you pursued solutions for your decision? 

Concrete thinkers also tend to gravitate towards tangible, measurable facts-based items to make decisions such as statistics. On the other hand, an abstract thinker might base their solution-making process on not only facts/statistics but also theories, philosophies, and other “abstract” thought patterns.

Published Nov 15, 2023

Features 2 cited research articles.

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We are dedicated to providing you with valuable resources that educate and empower you to live better. First, our content is authored by the experts — our editorial team co-writes our content with mental health professionals at Thriveworks, including therapists, psychiatric nurse practitioners, and more.

We also enforce a tiered review process in which at least three individuals — two or more being licensed clinical experts — review, edit, and approve each piece of content before it is published. Finally, we frequently update old content to reflect the most up-to-date information.

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Dumontheil, I. (2014). Development of abstract thinking during childhood and adolescence: The role of rostrolateral prefrontal cortex . ScienceDirect. https://www.sciencedirect.com/science/article/pii/S1878929314000516

Malik, F., & Marwaha, R. (2023, April 23). Cognitive development – StatPearls – NCBI bookshelf . National Center for Biotechnology Information. https://www.ncbi.nlm.nih.gov/books/NBK537095/

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What is Abstract Thinking? How it Works & More

Welcome to the fascinating world of abstract thinking! Imagine your mind as a superpower beyond ordinary thinking – it's like having a secret key to creativity, problem-solving, and big ideas.

So, what is abstract thinking in psychology ? It's all about thinking beyond what you can see and touch. It's the kind of thinking that lets you come up with cool ideas, be creative, and solve tricky problems in new ways.

In this journey, we're going to explore what abstract thinking really means and why it's super important for how our brains work. We'll dig into how our minds develop this awesome skill and how it helps us solve puzzles and create amazing things. Let's uncover the secrets of abstract thinking and discover why it's like having a superpower for your brain!

Understanding Abstract Thinking

Abstract thinking refers to the ability to think about concepts, ideas, and situations that are not necessarily tangible or concrete. It involves the capacity to consider possibilities, imagine scenarios, and make connections beyond what is immediately visible or evident. Abstract thinking allows individuals to engage in creative problem-solving, envision hypothetical situations, and understand complex relationships. This cognitive skill enables people to explore the realm of ideas, think critically, and conceptualize beyond the constraints of the present or the literal.

Abstract Thinking Vs Concrete Thinking

Concrete thinking is when you stick to the facts – you're all about what you can see, hear, or touch right now. It's like thinking in black and white.

But abstract thinking? That's where you add some color! Abstract thinking is when you let your mind go beyond the facts. You start thinking about things that might happen in the future, imagining new inventions, or figuring out different ways to solve problems. It's like using your brain as a playground for ideas.

Let us take an example to understand it better. Imagine you have a school garden with rows of neatly planted vegetables. You can see the carrots, tomatoes, and lettuce growing right in front of you. Concrete thinking in this scenario would be noticing and dealing with the actual plants – measuring their height, checking the color of the vegetables, and making sure they get enough water and sunlight. It's all about the real, tangible things you can observe in the garden at that moment.

Now, let's switch to abstract thinking. Picture yourself sitting in the same school garden, but instead of focusing on the plants right now, your mind starts wandering. You start thinking about how the garden could be even more awesome in the future. Maybe you imagine building a greenhouse to grow exotic fruits, or you think about organizing a community event in the garden. Abstract thinking here involves dreaming up possibilities that go beyond the current state of the garden. It's about envisioning what could happen down the road and coming up with creative ideas.

In summary, concrete thinking is like tending to the plants in the garden today, making sure everything is as it is. On the other hand, abstract thinking is like looking ahead, imagining exciting changes and improvements for the garden in the future. Both types of thinking have their time and place, and together, they make our minds wonderfully versatile.

Development of Abstract Thinking

The development of abstract thinking is a fascinating journey that unfolds throughout a person's life, with significant milestones and abstract thinking signs contributing to its growth. Let's explore how abstract thinking develops across different phases:

• Early Childhood (0-6 years): Introduction to basic cognitive skills through play and imaginative activities, setting the foundation for abstract thinking.
• Middle Childhood (7-11 years): Advancement in logical thought processes, understanding cause-and-effect relationships , and initial exposure to formal education.
• Adolescence (11-15 years): Significant leap in abstract thinking, ability to consider possibilities and grasp abstract concepts, contributing to the development of critical thinking skills.
• Adulthood: Ongoing refinement and diversification of abstract thinking, applied in personal, professional, and problem-solving contexts.
• Throughout Life: Lifelong learning, exposure to diverse experiences, and adaptation to changing circumstances contribute to continuous development.

Factors Influencing Abstract Thinking

• Quality education and exposure to diverse subjects that encourages critical thinking and exploration.
• Cultural experiences and societal expectations shape the ways individuals engage in abstract thinking, influencing perspectives and problem-solving approaches.
• Rich and varied environments, including exposure to art, literature, and diverse social interactions, provide stimuli that nurture abstract thinking.
• Beliefs, values, and societal norms shaping thought patterns and problem-solving approaches.
• Exposure to diverse sensory experiences, including art, literature, and nature.
• Encountering and overcoming challenges that require abstract problem-solving.
• High stress can hinder abstract thinking, while a positive emotional state can enhance creativity.
• The nature and extent of exposure to various forms of media, impacting information processing and abstract thought.

Characteristics of Abstract Thinking

Abstract thinking is like opening a door to a world where creativity, imagination, and conceptualization take center stage. Let's delve into abstract thinking causes and abstract thinking signs that define this extraordinary cognitive skill and explore how it plays out in everyday scenarios.

1. Creativity: Painting Outside the Lines

Abstract thinking is closely tied to creativity. It's about thinking beyond the ordinary and coming up with ideas that might seem a bit wild at first. Consider an artist creating a masterpiece. While concrete thinking might stick to realistic portrayals, abstract thinking lets the artist blend colors, distort shapes, and bring forth something entirely unique. It's like painting outside the lines and turning imagination into a vibrant canvas of possibilities.

2. Imagination: Turning Dreams into Reality

Imagination is the magic wand of abstract thinking. It's the ability to conjure up mental images, scenarios, and ideas that go beyond what's right in front of us. Think of a child playing with building blocks. While concrete thinking might involve stacking blocks neatly, abstract thinking kicks in when the child imagines building an entire city or creating a fantastical castle. Imagination turns the ordinary into the extraordinary.

3. Conceptualization: Connecting the Dots

Abstract thinking is all about connecting the dots in your mind. It's like being a detective, piecing together clues to see the bigger picture. Consider a student learning about historical events. While concrete thinking might focus on memorizing dates and facts, abstract thinking lets the student conceptualize the broader context – understanding the reasons behind events, recognizing patterns, and seeing how everything fits together like a puzzle.

4. Flexibility: Adapting to Change

Abstract thinking is marked by flexibility, the ability to adapt and adjust your thoughts when faced with new information or challenges. It's like being a gymnast of the mind, capable of shifting perspectives, considering different angles, and embracing change. In everyday life, this might manifest when problem-solving encounters unexpected twists, requiring a flexible mindset to navigate through uncertainties and find novel solutions.

5. Symbolic Representation: Beyond the Surface

It involves expressing ideas or concepts through symbols, metaphors, or analogies. Think of it as communicating through a language of symbols. For instance, a traffic light isn't just a signal to stop or go; it can symbolize the broader concept of order and control in various aspects of life. Abstract thinkers excel at using symbols to convey deeper meanings and representations.

6. Reflection and Metacognition: Thinking about Thinking

Abstract thinking goes beyond the immediate task at hand; it involves reflection and metacognition, which means thinking about thinking. It's like having an inner conversation with yourself to analyze your thoughts, evaluate your reasoning, and consider different perspectives. In practical terms, this might be seen when a student reflects on their learning process, identifying effective study strategies and adjusting their approach for better outcomes. Abstract thinking elevates awareness and introspection.

Everyday Scenarios: Bringing Abstract Thinking to Life

Abstract thinking, a cognitive superpower, paints everyday scenarios with creativity and innovation. From decorating living spaces and resolving conflicts to planning vacations and engaging in hobbies, it transforms routine activities into opportunities for imaginative expression and growth.

Planning a Career Path

It involves envisioning your future, contemplating different career options, and conceptualizing the steps needed to achieve your goals. Rather than focusing solely on the immediate job at hand, abstract thinking allows you to strategize for long-term success, anticipating challenges, and adapting to evolving professional landscapes.

Solving a Social Issue

Let's say you're passionate about environmental issues. Abstract thinking enables you to explore innovative solutions beyond the obvious, considering the interconnectedness of environmental, economic, and social factors. It involves imagining sustainable practices, advocating for change, and conceptualizing a better future for the community and the planet.

Navigating Interpersonal Relationships

In the realm of relationships, abstract thinking contributes to understanding emotions, motivations, and complexities. Rather than simply reacting to surface-level interactions, abstract thinking allows you to delve into the underlying dynamics. For example, resolving conflicts requires considering different perspectives, empathizing with others, and conceptualizing solutions that foster mutual understanding and growth.

Learning a New Skill

When tackling the challenge of learning a new skill, abstract thinking enhances the process. It goes beyond memorizing steps and involves understanding the underlying principles. For example, learning to play a musical instrument requires more than rote practice; abstract thinking allows you to grasp the fundamental concepts of music theory, fostering a deeper and more holistic understanding of the art.

Decorating a Living Space

Instead of merely arranging furniture, abstract thinkers consider the ambiance they want to create. They might envision color schemes, explore unique design elements, and conceptualize the space as a reflection of their personality. Abstract thinking in interior design goes beyond the concrete placement of objects, emphasizing the creation of an atmosphere that evokes specific emotions and moods.

Meal Planning and Cooking

Rather than following recipes rigidly, abstract thinkers might experiment with flavors, envision unique combinations, and conceptualize a meal as a creative expression. It involves understanding the principles of taste, experimenting with ingredients, and adapting recipes to suit individual preferences, turning the act of cooking into a culinary adventure.

Planning a Vacation Itinerary

Abstract thinking shines when planning a vacation. It goes beyond booking flights and accommodations; it involves conceptualizing the entire experience. Abstract thinkers might consider the cultural aspects of the destination, envision unique activities, and plan an itinerary that captures the essence of the place. It's about creating a travel experience that goes beyond the logistical details, embracing the broader adventure and exploration.

Hobbies and Creative Pursuits

Engaging in hobbies, such as painting, writing, or photography, highlights abstract thinking. Instead of following a strict set of rules, abstract thinkers express themselves creatively. For example, a painter might conceptualize a piece by blending colors intuitively, a writer might craft a narrative that explores abstract concepts, and a photographer might capture moments that convey emotions beyond the surface. Abstract thinking transforms hobbies into outlets for personal expression and innovation.

Limitations of Abstract Thinking 

• Abstract ideas may be open to subjective interpretation, leading to misunderstandings and miscommunications.
• Translating abstract concepts into practical actions can be challenging, as the gap between theory and real-world application may be significant.
• Abstract thinkers may face challenges when confronted with concrete, hands-on problem-solving tasks that require immediate and tangible solutions.
• A tendency to overanalyze or overthink situations, leading to indecision or difficulties in making practical decisions in a timely manner.
• Abstract thinking's effectiveness often depends on the context, and its application may not always be suitable or relevant across different situations.

Disorders & Conditions that May Impair Abstract Thinking

• Autism Spectrum Disorder (ASD) : Individuals with ASD may experience challenges in abstract thinking, including difficulties in understanding figurative language and abstract concepts.
• Traumatic Brain Injury (TBI): TBI can impact cognitive functions, potentially affecting abstract thinking abilities and problem-solving skills.
• Attention-Deficit/Hyperactivity Disorder (ADHD): ADHD may contribute to difficulties in sustained attention, which can hinder the development and application of abstract thinking skills.
• Schizophrenia : Schizophrenia can make it challenging for individuals to grasp complex concepts and engage in higher-level reasoning.
• Alzheimer's Disease : As Alzheimer's disease progresses, it can lead to cognitive decline, impacting abstract thinking and problem-solving abilities.
• Intellectual Disabilities : Individuals with intellectual disabilities may face limitations in various cognitive functions, including abstract thinking, depending on the severity of the condition.
• Specific Learning Disabilities : Conditions such as dyslexia or dyscalculia may affect the acquisition of abstract thinking skills, particularly in the context of reading and mathematical reasoning.
• Substance Use Disorders : Substance abuse can impair cognitive functions, including abstract thinking, as a result of the impact on brain structure and function.
• Obsessive-Compulsive Disorder (OCD) : OCD may lead to obsessive thoughts that could interfere with abstract thinking and the ability to focus on a broader conceptual level.
• Major Depressive Disorder : Depression can impact cognitive functioning, potentially affecting abstract thinking and the ability to generate creative or positive thoughts.

Ways to Improve Your Abstract Thinking Skills

Explore a diverse array of activities, from engaging in creative pursuits to participating in brainstorming sessions, to elevate your abstract thinking skills-a vital aspect of the abstract thinking treatment toolkit

Abstract thinking is a complex cognitive process that allows us to think about concepts that are not directly tied to our physical experiences. It is a critical skill for problem-solving, decision-making , and creativity. Abstract thinking is also essential for understanding and communicating complex ideas.

As we navigate the intricacies of this cognitive marvel, it becomes clear that abstract thinking holds limitless potential, transforming routine activities into opportunities for imaginative expression and growth. It is important to remember that abstract thinking is a skill that takes time and practice to develop. Don't get discouraged if you don't see results immediately. Just keep practicing and you will eventually see improvement. 

Frequently Asked Questions

Abstract thinking involves contemplating ideas, concepts, and scenarios beyond the literal and immediate, allowing for creativity, imagination, and complex problem-solving.

Abstract thinking is facilitated by neural networks and brain regions that support higher-level cognitive functions, allowing for the exploration of possibilities and the formation of creative connections.

Abstract thinking is crucial for creativity, innovation, and effective problem-solving. It enriches our understanding of the world and enables us to navigate complex situations with adaptability.

Yes, abstract thinking skills can be enhanced through activities such as creative endeavors, problem-solving exercises, diverse learning experiences, and engaging in reflective practices.

Absolutely! From planning a vacation itinerary to resolving complex societal issues, abstract thinking is evident in various scenarios where individuals envision possibilities, make connections, and think beyond the immediate and concrete.

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Piaget’s Formal Operational Stage: Definition & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

The formal operational stage begins at approximately age twelve and lasts into adulthood. As adolescents enter this stage, they can think abstractly by manipulating ideas in their head, without any dependence on concrete manipulation (Inhelder & Piaget, 1958).

In the formal operational stage, children tend to reason more abstractly, systematically, and reflectively. They are more likely to use logic to reason out the possible consequences of each action before carrying it out.

He/she can do mathematical calculations, think creatively, use abstract reasoning, and imagine the outcome of particular actions.

An example of the distinction between concrete and formal operational stages is the answer to the question, “If Kelly is taller than Ali and Ali is taller than Jo, who is tallest?”

This is an example of inferential reasoning, which is the ability to think about things which the child has not actually experienced and to draw conclusions from its thinking.

The child who needs to draw a picture or use objects is still in the concrete operational stage , whereas children who can reason the answer in their heads are using formal operational thinking.

Formal Operational Thought

Hypothetico-deductive reasoning.

Hypothetico-deductive reasoning is the ability to think scientifically through generating predictions, or hypotheses, about the world to answer questions.

The individual will approach problems in a systematic and organized manner rather than through trial-and-error.

A teenager can consider “what if” scenarios, like imagining the future consequences of climate change based on current trends.

Abstract Thought

Concrete operations are carried out on things, whereas formal operations are carried out on ideas. Individuals can think about hypothetical and abstract concepts they have yet to experience. Abstract thought is important for planning the future.

A student understands and manipulates concepts like justice, love, and freedom without needing concrete examples or experiences. For instance, they can comprehend and discuss a statement such as “Justice is not always fair.”

Scientific Reasoning

An example of formal operational thought could be the cognitive ability to plan and test different solutions to a problem systematically, a process often referred to as “scientific thinking.”

The ability to form hypotheses, conduct experiments, analyze results, and use deductive reasoning is an example of formal operational thought.

A student forms a hypothesis about a science experiment, predicts potential outcomes, systematically tests the hypothesis, and then analyzes the results.

For example, they could hypothesize that increasing sunlight exposure will increase a plant’s rate of growth, design an experiment to test this, and then understand and explain the results.

Metacognition

Adolescents can think about their own thought processes, reflecting on how they learn best or understanding why they might have made a mistake in judgment.

For example, they might realize that they rush decisions when they’re feeling stressed and plan to use stress-reducing techniques before making important decisions in the future.

Testing Formal Operations

Piaget (1970) devised several tests of formal operational thought. One of the simplest was the “third eye problem”.  Children were asked where they would put an extra eye, if they could have a third one, and why.

Schaffer (1988) reported that when asked this question, 9-year-olds all suggested that the third eye should be on the forehead.  However, 11-year-olds were more inventive, suggesting that a third eye placed on the hand would be useful for seeing round corners.

Formal operational thinking has also been tested experimentally using the pendulum task (Inhelder & Piaget, 1958). The method involved a length of string and a set of weights. Participants had to consider three factors (variables) the length of the string, the heaviness of the weight, and the strength of the push.

The task was to work out which factor was most important in determining the speed of swing of the pendulum.

Participants can vary the length of the pendulum string, and vary the weight. They can measure the pendulum speed by counting the number of swings per minute.

To find the correct answer, the participant has to grasp the idea of the experimental method -that is to vary one variable at a time (e.g., trying different lengths with the same weight). A participant who tries different lengths with different weights will likely end up with the wrong answer.

Children in the formal operational stage approached the task systematically, testing one variable (such as varying the string length) at a time to see its effect. However, younger children typically tried out these variations randomly or changed two things simultaneously.

Piaget concluded that the systematic approach indicated that children were thinking logically, in the abstract, and could see the relationships between things. These are the characteristics of the formal operational stage.

Critical Evaluation

Psychologists who have replicated this research, or used a similar problem, have generally found that children cannot complete the task successfully until they are older.

Robert Siegler (1979) gave children a balance beam task in which some discs were placed on either side of the center of balance. The researcher changed the number of discs or moved them along the beam, each time asking the child to predict which way the balance would go.

He studied the answers given by children from five years upwards, concluding that they apply rules which develop in the same sequence as, and thus reflect, Piaget’s findings.

Like Piaget, he found that eventually, the children were able to take into account the interaction between the weight of the discs and the distance from the center, and so successfully predict balance. However, this did not happen until participants were between 13 and 17 years of age.

He concluded that children’s cognitive development is based on acquiring and using rules in increasingly more complex situations, rather than in stages.

Learning Check

Which of the following is/are not an indication of an individual being in the formal operational stage?

Mark often struggles with planning for the future. He can’t envision different possible outcomes based on his actions. Which of the following is true about Mark? a. He is in the Formal Operational stage. b. He is in the Preoperational stage. c. He is in the Concrete Operational stage. d. He is in the Sensorimotor stage.

Which of the following actions does NOT indicate that Lucy is in the Formal Operational stage? a. Lucy can think about abstract concepts like justice and fairness. b. Lucy enjoys debates and discussions where she can express her thoughts. c. Lucy can only solve problems that are concrete and immediately present. d. Lucy enjoys conducting experiments to test her hypotheses.

Sam can play with his friends and imagine what they think about him. However, he can’t conceptualize different outcomes of a hypothetical situation. What stage is Sam likely in? a. He is in the Formal Operational stage. b. He is in the Preoperational stage. c. He is in the Concrete Operational stage. d. He is in the Sensorimotor stage.

• (b) He is in the Preoperational stage.
• (c) Lucy can only solve problems that are concrete and immediately present.
• (c) He is in the Concrete Operational stage.

According to Jean Piaget, in what stage do children begin to use abstract thinking processes?

According to Jean Piaget, children begin to use abstract thinking processes in the Formal Operational stage, which typically develops between 12 and adulthood.

In this stage, children develop the capacity for abstract thinking and hypothetical reasoning. They no longer rely solely on concrete experiences or objects in their immediate environment for understanding. Instead, they can imagine realities outside their own and consider various possibilities and perspectives.

They can formulate hypotheses, consider potential outcomes, and plan systematic approaches for problem-solving. Additionally, they can understand and manipulate abstract ideas such as moral reasoning, logic, and theoretical concepts in mathematics or science.

Based on Piaget’s theory, what should a teacher provide in the formal operational stage?

Based on Piaget’s theory, a teacher should provide the following for students in the Formal Operational stage:

Abstract Problems and Hypothetical Tasks : Encourage students to think abstractly and solve complex problems. Provide tasks that require logical reasoning, hypothesizing, and the consideration of multiple variables.

Opportunities for Debate and Discussion : Encourage students to express their thoughts and challenge the views of others. This can help them learn to view problems from multiple perspectives.

Experiments : Design lessons to allow students to develop hypotheses and conduct experiments. The scientific method is a valuable tool at this stage.

Real-world Applications : Connect classroom learning to real-world scenarios. This can help students understand the relevance and application of abstract ideas.

Higher-order Questions : Use questions involving analysis, synthesis, and evaluation to improve students’ critical thinking skills.

Guidance in Self-reflection : Encourage students to reflect on their thoughts, emotions, and behavior, which can help them understand their own cognitive processes better.

Moral and Ethical Discussions : As students in this stage begin to think more about abstract concepts such as justice, fairness, and rights, engage them in discussions around moral and ethical issues.

Piaget’s formal operational stage begins around age 11 or 12 and continues throughout adulthood. Does this suggest that once one reaches this level of cognitive development, they plateau? or are there different levels of formal operations?

According to Piaget’s theory, once individuals reach the Formal Operational stage, they have attained the highest level of cognitive development, as defined by his model. However, this does not suggest a cognitive plateau.

Cognitive development is individual and influenced by a range of factors beyond mere biological maturation.

The nature of human cognition is such that there’s always room for refinement, growth, and development throughout adulthood.

Furthermore, individual competence can vary greatly within the Formal Operational stage. For instance, a person might employ formal operational thinking in one area of life (such as their professional specialization) but not others.

Similarly, skills like problem-solving, logical reasoning, and handling abstract concepts can continue to improve with practice and experience.

Inhelder, B., & Piaget, J. (1958). Adolescent thinking.

Piaget, J. (1970). Science of education and the psychology of the child . Trans. D. Coltman.

Schaffer, H. R. (1988). Child Psychology: the future. In S. Chess & A. Thomas (eds), Annual Progress in Child Psychiatry and Child Development . NY: Brunner/Mazel.

Siegler, R. S. & Richards, D. (1979). Development of time, speed and distance concepts. Developmental Psychology, 15 , 288-298.

Abstractly Thinking: Unleashing Your Creative Potential

Peeling back the layers of our mind, we often stumble upon a concept that’s as intriguing as it is elusive – abstract thinking. It’s a term many have heard, yet few truly understand. I’m here to bridge that gap, to shed light on this profound form of cognition and illustrate how it shapes our understanding of the world around us.

At its core, abstract thinking is the ability to move beyond concrete and physical reality, allowing us to ponder complex concepts, imagine possibilities, and analyze information in a broader sense. We’ll delve into its significance in problem-solving scenarios, creative pursuits, and even social interactions.

In essence, abstract thinking isn’t just about lofty ideas or philosophical musings; it’s an integral part of our everyday lives. Whether you’re solving a tricky math problem or brainstorming innovative solutions at work – chances are you’re employing this powerful cognitive process more often than you realize.

Understanding the Concept of Abstract Thinking

Ever wondered how your mind jumps from pondering over a cup of coffee to contemplating the cosmos? That’s abstract thinking in action. It’s our brain’s way of connecting the dots between unrelated concepts, enabling us to think beyond physical or present scenarios.

Diving deeper into this concept, abstract thinking is essentially the ability to understand concepts that are real, such as freedom or vulnerability, but which are not directly tied to concrete physical objects and experiences. It’s what allows us to analyze information and apply it to different contexts. For instance, if you’ve never visited a desert before, your brain can still use abstract thinking to imagine what being there might feel like.

Now let’s talk numbers. A study by Cambridge University found that children begin developing abstract reasoning skills around age 11-12. But this doesn’t mean they’re absent in younger kids! They just manifest differently – through imaginative play and curiosity.

Here are some key points about abstract thinking:

• It involves seeing beyond what’s obvious.
• Emotions like love and fear fall under its domain.
• Problem-solving often requires a strong grasp of abstraction.

Abstract thought is crucial for advanced learning and creative innovation. Without it, we’d be unable to anticipate future events or appreciate art forms like poetry and metaphors – which aren’t literally true but convey great truth all the same.

So next time you find yourself daydreaming about space travel while sipping on your morning latte, know that it’s your amazing capacity for abstract thought at work!

The Science Behind Abstract Thinking

I’ve always been fascinated by the way our brains work, particularly when it comes to abstract thinking. You see, abstract thinking is a critical part of human cognition. It’s what allows us to comprehend complex concepts, solve problems that don’t have clear-cut solutions, and adapt to new circumstances.

In fact, neuroscience has shown that different parts of our brain are involved in abstract thinking. For example:

• The prefrontal cortex (PFC) plays a key role in planning and decision making.
• The parietal lobe contributes to our understanding of numbers and spatial relationships.
• And the temporal lobe helps us recognize patterns.

Isn’t it incredible how all these different components come together to enable this higher order thinking? But let’s delve deeper into the role of each part.

The Prefrontal Cortex (PFC), often associated with executive functions like impulse control and long-term planning, is pivotal in abstract reasoning. When we’re faced with an unfamiliar situation or problem, it’s the PFC that steps up to help us strategize a solution.

Similarly important is the parietal lobe. This region handles numerical comprehension and spatial awareness – both crucial for abstraction. After all, if you can’t understand numbers or visualize space correctly, tackling mathematical equations or architectural designs could prove an uphill battle!

Lastly but not leastly – there’s the temporal lobe! It helps us identify patterns in information – which again is essential for abstract thought. Whether we’re trying to decipher code or spot trends in data sets – you bet it’s thanks mainly to this hardworking part of our brain!

So next time you find yourself pondering deeply over an intricate problem, take a moment to thank your brain for its abstract thinking prowess. The science behind it is truly mind-boggling!

How Abstractly Thinking Affects Creativity

Diving right into the heart of the matter, I can’t emphasize enough how significantly abstract thinking influences our creativity. It’s like unlocking a secret door in our minds that allows us to perceive things from a unique perspective.

When we think abstractly, we’re not just focusing on what meets the eye. We’re delving deeper and considering all possible dimensions, interpretations, and connections. This encourages us to break free from traditional boundaries and explore uncharted territories of thought. For example, an artist might be inspired by a simple leaf falling from a tree – but instead of merely replicating this scene on canvas, they could use it as a metaphor for change or transition.

Abstract thought also fosters problem-solving skills. Rather than viewing problems as concrete obstacles with only one solution, abstract thinkers see them as challenges with multiple potential outcomes. In fact, research has shown that people who frequently engage in abstract thinking are more likely to find innovative solutions to complex problems.

It’s worth noting too that abstract thinking isn’t just beneficial for artists or inventors; it’s valuable in virtually every field or profession:

• Marketing Professionals : They leverage their ability to think beyond product features and focus on symbolic meanings and emotional connections.
• Engineers : They often design solutions based on conceptual models before translating them into physical prototypes.
• Teachers : By employing abstract concepts during instruction, they can help students develop critical thinking skills.

So there you have it! Abstract thinking is more than just daydreaming or getting lost in your thoughts – it’s about seeing possibilities where others see dead ends; it’s about transforming ordinary ideas into extraordinary creations.

Role of Abstract Thought in Problem Solving

Diving into the world of abstract thought, it’s fascinating to see how it plays a significant role in problem-solving. Now you might ask, “What’s so special about thinking abstractly?” Well, let me break this down for you.

Abstract thinking is like taking a bird’s eye view of problems. It allows us to look beyond details and perceive situations from varied perspectives. When we’re faced with complex issues that can’t be solved using traditional or straightforward methods, that’s where abstract thinking comes into play.

For instance, consider trying to solve a jigsaw puzzle. If you focus solely on individual pieces (concrete thinking), it would be difficult to visualize the complete picture. But if you step back and think about how the pieces fit together as part of a larger image (abstract thinking), suddenly things start making sense!

Interestingly, research indicates that abstract thinkers are better at finding innovative solutions to problems. According to a study by Darya Zabelina and Michael Robinson at North Dakota State University:

These findings show that abstract thinkers could potentially lead the way in fields where problem-solving skills are crucial, such as engineering or management consulting.

The power of abstraction also shines through when brainstorming potential solutions for problems – known as ‘divergent thinking’. By generating numerous ideas without dwelling on their feasibility initially,

• We broaden our horizon
• Potential unconventional solutions come into light
• We challenge our conventional ways of doing things

So whether it’s piecing together puzzles or coming up with groundbreaking business strategies, applying an abstract approach can truly revolutionize the way we tackle problems!

Advantages and Disadvantages of Abstract Thinking

Dive into the world of abstract thinking, and you’ll find a realm full of possibilities. It’s like exploring an endless ocean, brimming with mystery and intrigue. But like every coin that has two sides, abstract thinking comes with its own set of advantages and disadvantages.

Let’s start on a positive note— the benefits it brings to the table. A knack for abstract thought can drastically improve problem-solving skills. Why? Because it allows you to look beyond just the surface level details. You can step back, assess different angles, connecting patterns that aren’t immediately apparent.

Another perk is enhanced creativity. Abstract thinkers are often the ones who come up with innovative ideas or out-of-the-box solutions because they’re not confined by traditional boundaries or norms.

Yet another benefit is empathy towards others’ perspectives. Since abstract thinking involves understanding concepts from various viewpoints, it enables better comprehension of diverse beliefs and feelings.

Here’s a quick recap:

• Enhanced problem-solving skills
• Increased creativity
• Improved empathy

But let’s not forget there are some downsides too! For one, abstract thinking might lead you down paths where concrete answers are hard to find—it can be more about exploration than resolution.

It may also result in overthinking—a common pitfall for many abstract thinkers—where analysis paralysis sets in as you get lost in your own thoughts.

Lastly, people who think abstractly might struggle with tasks requiring detailed focus since their mind tends to dwell on overarching concepts rather than minute particulars.

To summarize these points:

• Potential for overthinking
• Difficulty finding definitive answers
• Struggles with detail-oriented tasks

So there we have it—the upsides and downsides of abstract thinking laid bare! Like any cognitive ability, how well it serves largely depends on how effectively we harness this power within us.

Techniques to Improve Your Ability to Think Abstractly

Ever wondered how you could get better at abstract thinking? Don’t sweat it. I’ve got some tips and tricks that might just help. Firstly, let’s clear the air – abstract thinking isn’t an overnight skill. It takes practice, persistence, and a bit of creativity.

First up on my list is brainstorming sessions. Whether it’s solo or in a group, brainstorming can stimulate your brain and allow you to think outside the box. The trick is not to shoot down any ideas initially – no matter how crazy they appear. You’ll be surprised how often these “wild” ideas spark innovative solutions.

Next up is this little trick I like to call ‘the perspective switch’. Simply put, try looking at problems from a different angle or point of view. This technique forces you to step out of your comfort zone and expands your horizon of thoughts.

Let’s not forget about puzzles and games! Believe it or not, playing chess or solving Rubik’s cubes can do wonders for your abstract reasoning skills. These activities train your brain to see patterns and connections which are vital in building strong abstract thinking abilities.

Finally, there’s nothing like good old reading. Diving into philosophy books or complex novels helps expose you to intricate concepts – enhancing both comprehension skills and abstract thought processes.

Remember folks – Rome wasn’t built in a day! Developing your ability for abstract thinking will take time but with patience and consistent practice using these techniques, I’m confident that anyone can enhance their capacity for conceptual understanding over time.

Examples Demonstrating the Use of Abstract Thought

Diving straight into our first example, let’s consider planning a vacation. This seemingly simple task is brimming with abstract thought. I’m thinking about concepts like relaxation or adventure, and then deciding what those mean for me personally. Does relaxation mean lounging on a beach or exploring a new city? There’s no concrete answer because it all depends on my personal perspective.

Moving onto another instance, ponder over the last book you read. When we read, we’re constantly using abstract thought to interpret symbols (words) and construct an understanding in our minds. We’re not just decoding text; we’re creating worlds, imagining characters’ emotions, predicting outcomes – all without concrete references.

Moreover, the world of mathematics serves as an excellent playground for abstract thought too! Let’s take algebra for instance – it’s based entirely around manipulating symbols according to rules to solve problems. When I look at an equation like x + 2 = 5, there’s nothing tangible about ‘x’. Yet by applying rules of algebraic manipulation, I can solve that ‘x’ equals 3.

Let’s also remember how often we use metaphors and similes in daily conversation – they’re perfect examples of abstraction in language! When I say something like “Time is a thief”, there isn’t really some burglar named Time sneaking around stealing hours from us. Instead, it’s expressing the abstract idea that time passes quickly and is irreversible.

Finally yet importantly are moral decisions which are deeply rooted in abstract thinking. Deciding right from wrong isn’t often black-and-white since these judgments are largely based on societal constructs or personal beliefs which aren’t physically present or observable.

So next time when you’re reading your favorite novel or solving that tricky math problem – just remember – you’re beautifully demonstrating your capacity for abstract thought!

Conclusion: Embracing the Power of Abstractly Thinking

It’s been quite a journey, hasn’t it? We’ve delved deep into the realm of abstract thinking and unearthed its true potential. If there’s one thing I hope you’ll take away from this article, it’s that embracing abstract thinking isn’t just about being more creative or solving problems more effectively—it’s about transforming how we view and interact with the world.

This might sound like an exaggeration, but consider this: every great invention or innovation in history has been born from someone looking beyond the obvious. From Einstein’s theory of relativity to Steve Jobs’ iPhone, abstract thinking is at the heart of progress.

But let me be clear—I’m not saying everyone needs to be an Einstein or a Jobs. What I am saying is that anyone can harness the power of abstract thinking in their everyday lives. Whether you’re trying to solve a tricky problem at work, make sense of complex issues in your personal life, or even explore new hobbies and passions—abstract thinking can open up new pathways and possibilities.

Here are some key insights from our exploration:

• Abstract thoughts are universal : Regardless of age, culture, or background—we all have the capacity for abstract thought.
• It improves problem-solving : Abstract thinkers tend to find unique solutions by viewing problems from different perspectives.
• Encourages creativity : The ability to think outside-the-box often leads to innovative ideas and fresh perspectives.
• Promotes understanding : By focusing on underlying principles rather than surface details—abstract thinking aids in grasping complex concepts.

So don’t shy away from abstraction; embrace it! Try seeing things not just as they are—but what they could be. And who knows? You might surprise yourself with where your thoughts lead you next!

In closing, remember that like any skill—abstract thinking takes practice. So start small, keep an open mind—and most importantly—enjoy the journey. Because in the end, it’s not just about reaching a destination—it’s about experiencing new ways of thinking and seeing along the way.

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Thinking Outside The Box: The Difference Between Concrete Vs. Abstract Thinking

Abstract thought is a defining feature of human cognition . Scholars from diverse fields — including psychologists, linguists, anthropologists, neuroscientists, and even philosophers — have contributed to the scientific discussion of how abstract ideas are acquired and used by the brain. Concrete thought is somewhat better understood, as it represents a more grounded form of thinking than what is typically found in abstract thought. Concrete thinkers focus on physical objects and the physical world, making their thinking process more immediately obvious and tied to the literal form. Both modes of thinking are useful for human cognition.

Distinguishing between concrete and abstract thoughts

Understanding the differences between these two types of thinking may help illustrate their unique contributions to human thought.

Concrete thinking

Concrete thinking is grounded in facts and operates in a literal domain , focusing on objective facets such as physical attributes (e.g., color and shape) and verifiable occurrences (e.g., chronological sequences). Concrete thinkers often rely on concrete objects and specific examples to solve problems and classify objects. It avoids extrapolations, categorizing information superficially and within rigid boundaries. Concrete thinking is chiefly concerned with detail gathering, excluding analyses of trends and exploration of potentialities.

Rumination , a cognitive process characterized by excessive or repetitive thoughts, including intrusive memories, that interfere with daily life, might use concrete thinking to contemplate complex issues. These thoughts might include questions like "What happened in this situation?" and "What steps can I take to address the problem?" Although these questions address more than basic attributes, they are anchored in objectively definable detail.

Abstract thinking

It synthesizes and integrates information into broader contexts, forming the bedrock of creativity, critical analysis, and problem-solving. This thinking style is a vital skill for those who exercise creativity in fields like theoretical math or philosophical concepts. This allows individuals to transcend surface-level understanding. Abstract thinking is indispensable for grappling with intangible concepts, including emotions, and often involves contemplating hypothetical scenarios.

Rumination, explored above, also has an abstract component . Abstract ruminative thoughts may include questions like "Why do I always feel so unhappy?" or "Why didn’t I handle this better?" These queries pivot away from objective facts and explore concepts that may be interpreted in multiple ways.

When is each type of thinking most useful?

Several factors determine whether concrete or abstract thinking is most appropriate, but in practice, most deliberate thought processes benefit from the interplay between the two modes. Abstract thinking skills, including abstract reasoning skills, are crucial in understanding complex concepts and integrating existing knowledge. For instance, effective problem-solving necessitates the initial definition of its core features (concrete thinking) and subsequent high-level analysis (abstract thinking).

Psychologists and sociologists have scrutinized the relationship between abstract and concrete thought, often using  construal learning theory (CLT) as a framework. CLT identifies how psychological distance influences a person’s choice between abstract and concrete thinking. “Psychological distance” can be measured in various ways:

• Temporal distance: The amount of time between a person and their subject of contemplation.
• Spatial distance: The physical separation between a person and their subject of contemplation.
• Social distance: The emotional distance between individuals.
• Hypothetical distance: An individual’s assessment of the likelihood of their subject of contemplation occurring.

CLT suggests that individuals tend toward abstract thinking when they perceive substantial psychological distance and favor concrete thinking when that distance diminishes. This indicates that more abstract thinkers are likely to engage in abstract reasoning when dealing with subjects that are not immediately present or concrete. For example, a person planning to attend a family reunion next year (significant temporal distance) is more likely to think of big-picture, abstract elements of their plan — perhaps their excitement about attending the event. But as the event approaches, their thoughts shift toward concrete details, such as what they’ll wear to the party.

CLT can be used to assess a person's propensity for risk-taking behavior. Evidence suggests that individuals with a high construal level (greater psychological distance) employ more abstract thought processes and are more likely to engage in risky behaviors. Conversely, individuals with a low construal level (lesser psychological distance) display greater risk aversion as they are more aware of objective risk factors.

How do concrete and abstract thinking develop?

It’s worth noting that babies are not born with the ability to think abstractly. Jean Piaget’s stages of cognitive development illustrate how a child’s cognition develops over time. This cognitive development is crucial in the transition from a concrete thinker to an abstract thinker.

• Sensorimotor stage (birth to age two): Babies engage primarily with their sensory world, absorbing concrete information like a sponge without making abstract connections. This stage is fundamental in developing motor skills and concrete thinking skills.
• Preoperational stage (ages two to seven): Young children begin to develop abstract thinking, engaging in imaginary play, comprehending the rudiments of symbolism, and understanding someone else’s point. They start to understand figurative language and can interpret facial expressions, moving towards more abstract thinking abilities.
• Concrete operational stage (ages seven to 11): Children can understand that other people may experience the world differently than they do. They can recognize abstract concepts but remain tethered to empirical experiences. This stage involves processing theoretical concepts and developing concrete thinking skills to solve problems.
• Formal operational stage (age 11 to adulthood): Abstract thought matures as individuals use concrete information to derive abstract conclusions. Individuals expand their ability to empathize and discern patterns among abstract concepts. This stage is where strong abstract thinking skills are developed, allowing individuals to grapple with more complex concepts and engage in theoretical math and philosophical concepts, and solve abstract riddles such as brain teasers. This stage equips individuals with the capacity to analyze hypothetical scenarios and address "what-if" questions.

Key insights from Piaget's theory underscore the development of abstract thinking, where concrete thinking lays the foundation. This progression from being a concrete thinker to an abstract thinker is a vital aspect of cognitive development. That is, concrete thought is a prerequisite for abstract thought because objective facts must be defined before they can be analyzed. Proficiency in abstract thought unfolds gradually over many years.

Assessing the merits of abstract and concrete thinking

Abstract thinking allows humans to create art, reach conclusions through debate, and predict what the future may hold. It involves a thinking process that is less immediately obvious than concrete thinking, often requiring the individual to consider other meanings and exercise creativity. Because abstract thought empowers higher cognitive functions, it may seem that it is a preferable mode of cognition over concrete thought.

However, abstract thinking is not without its limitations. An unbalanced reliance on abstract rumination can lead to mental health concerns , such as depression. In individuals with mental health conditions like autism spectrum disorder or who have had a traumatic brain injury, the balance between abstract and concrete thinking can be particularly crucial, and reading body language and understanding figurative expressions may be difficult for some individuals. Conversely, a conscious preference for concrete thinking can potentially  mitigate negative mental health . Both concrete and abstract thinking are necessary for human cognition. For instance, abstract thinkers may engage in the active practice of new ideas, while concrete thinkers might focus on classifying objects and dealing with the literal form of information. While abstract thought may be associated with higher-order cognitive processes, those processes are built upon the foundation of concrete thinking.

Can therapy help manage cognitive and abstract thinking?

If you’re interested in recognizing and adapting your cognitive tendencies, a therapist can help. Therapists are trained in a variety of evidence-based techniques, including cognitive behavioral therapy , to analyze your mental processes and guide you toward meaningful conclusions about your thought patterns. This therapy can be particularly helpful for those struggling with difficulty relating to others due to their thinking style, whether they are more comfortable with abstract thinking vs concrete thinking.

You may wish to consider online therapy, which is available for individuals to avail the care of a skilled mental health professional. Working with a therapist online removes some common barriers to therapy, like having to commute to an office. Removing geographical constraints allows you to choose a therapist outside of your local area, which may be especially helpful to those who live in regions with limited mental health professionals. Online therapists have the same training and credentials as traditional therapists, and evidence indicates that therapy delivered remotely is just as effective as in-person therapy.

What is an example of concrete thinking?

Concrete thinking is literal. It focuses on physical attributes and things that can be verified with facts. Concrete thinking is more rigid and is chiefly concerned with gathering details or information. Someone who is a concrete thinker might take things very literally. For example, if you ask them to run to the store, they may think you want them to actually run to the store.

What is an example of abstract thinking?

An abstract thinking style involves processing theoretical concepts. It is more flexible and links causality, figurative language, themes, and intangible concepts and is the basis of things like problem-solving, creativity, and critical analysis. It often involves contemplating hypothetical scenarios, intangible concepts, and emotions. An excellent example of abstract thinking is making predictions. Any time someone assesses available information and processes it to determine what might happen next, they use abstract thinking.

Can you be both a concrete and abstract thinker?

Yes, people can be both concrete and abstract thinkers. According to construal level theory (CLT), psychological distance can affect whether a person uses concrete or abstract thinking . This theory measures psychological distance in four ways: temporal distance, or the amount of time between the person and the subject they’re thinking about; spatial distance, or the physical distance between the person and what they’re thinking about; spatial distance, or the physical separation between the person and what they’re thinking; and hypothetical distance, of the person’s assessment of the likelihood of what they’re thinking about occurring. 

CLT suggests that people tend to think more abstractly when they perceive a larger psychological distance and more concretely when they perceive less psychological distance. For example, someone who has a big vacation planned next year may think about how excited they are or a simple list of the things they hope to see, but as the trip approaches, they will likely focus on more concrete details, like making a list of what they need to pack, making sure they have their travel documents in order, and double-checking their itineraries.

Am I an abstract or concrete thinker?

Gaining abstract thinking is part of cognitive development; young children have concrete thinking first and develop abstract thinking as they mature. Some people may be prone to thinking more abstractly or concretely, but most are capable of both. People with good abstract reasoning skills may be better at imagining things that are not physically present, understanding complex concepts, and deciphering body language, and they may be more talented at creative endeavors or theoretical math or science concepts. On the other hand, concrete thinkers may be more likely to stick to rigid routines. They may think in more black-and-white terms and have difficulty considering gray areas or expanding their existing knowledge.

What are abstract thinkers good at?

People with strong abstract thinking skills can excel in many areas, including graphic design, landscape architecture, engineering, psychology, and psychology. They can also make excellent detectives, criminal investigators, and scientists.

An example of concrete thinking might be someone who sits down and lists items they need to accomplish in a day. In contrast, an abstract thinker might make the same kind of list, but they may rank it according to the order of importance or organize it according to the most efficient way to get all the tasks done.

What is a concrete thinking example for a student?

Specific examples of when students may use concrete thinking skills are when they organize their schedules or make a list of assignments they need to complete.

What is an example of a concrete task?

Many tasks might be considered concrete. For example, doing the dishes is a concrete task; they’re either clean or not. Other examples might be making the bed, folding laundry, washing the car, or vacuuming the carpet.

Is concrete thinking good or bad?

Concrete thinking isn’t necessarily good or bad; everyone needs to be able to think concretely at times. It can become a problem when people cannot switch out of concrete thinking in the physical world. Having abstract thinking abilities can help with problem-solving, creativity, and analysis, all of which can influence how someone interacts with the world. 

What is an example of concrete thinking in mental health?

Concrete thinking can be considered a feature of schizophrenia . People with this condition can be said to have an abstraction deficit or the inability to distinguish between symbolic, abstract ideas and the concrete. People with schizophrenia may not be able to deal with their experiences conceptually and cannot perceive objects as belonging to a class or category. Another example is autism spectrum disorder; people with this condition may have a very concrete way of thinking.

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Generate Insights with Abstract Thinking Exercises

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The best feeling in the world is finally cracking the solution to a problem you’ve been puzzling over

The worst feeling in the world: That moment when you’re ready to pound your head against your desk in frustration after being stuck on solving that problem for ages .

What if you could spend less time frustrated, and more time celebrating the solution? The key is tapping into the power of abstract thinking.

Abstract thinking is a great way to generate new ideas and gain new insights during any problem-solving process. Developers — who solve problems every day — will greatly benefit from exercising their abstract thinking muscles.

Before you encounter your next tricky problem, learn how to tap into your ability to think in an abstract way. It might be the key you need to find the solution.

What Is Abstract Thinking?

Abstract thinking has to do with seeing the context and bigger picture surrounding an event or idea. Abstract thinkers can reflect on events and ideas and think beyond just the “here and now”.

For example, a concrete thought would be thinking about your own dog. Abstract thoughts would be thinking about dogs in general, their relationship with your dog and with you, and how dogs fit into the bigger picture of your life and the world in general.

Another example may make more sense to engineers. Think about when you sit down to bang out some code. Before you even start, you have an idea of what you want the program to do and what features you want it to have.

These thoughts are abstract.

Then, after you write and deploy the code, you have a finished product — it has become concrete.

Put more simply, abstract thinking is thinking outside the box.

Don’t worry if that sounds vague. It’s hard to explain because abstract thinking is, in itself, an abstract idea.

You might be an abstract thinker if:

• You think about how everything relates to the bigger picture.
• You don’t just ask how — you ask why.
• You look for deeper meanings and underlying patterns in things.
• You seek to understand how everything relates to everything else.

You can tap into more abstract thinking by considering all the different parts of a problem, and thinking about them individually, as well as in relation to one another. We know that’s easier said than done, so here are some other strategies you can use to practice abstract thinking and tap into it when you need to solve a tough problem.

Everyday Ways to Tap Into Abstract Thinking

You might already be thinking in an abstract way without even knowing it. There are many ways to think abstractly that most of us do every day.

Thinking About Concepts

Any time you think about a non-concrete concept, that’s abstract thinking. Things like freedom and respect count — basically, anything that doesn’t have a concrete physical form is a concept that likely requires abstract thinking.

Coming Up With Theories

If you come up with a theory to explain an event, that’s abstract thinking. The theory may be based on concrete data, but it’s still conjecture, which makes it abstract.

Using Your Imagination

Even something as simple as using your imagination counts as abstract thinking. You’re thinking about things and possibilities that don’t exist in a physical form, which makes the thought abstract.

Using Metaphors and Analogies

Metaphors and analogies are another type of abstract thinking. They create relationships between two ideas that may be abstract or concrete. If they’re concrete, the act of thinking about them in relation to one another is a form of abstract thinking.

Problem Solving With Abstract Thinking: 5 Strategies

What abstract thinking can be really great for is solving tough problems, and that’s what makes it so useful for developers. Use these strategies to tap into your ability to think abstractly when you’re working on solving a problem.

Get Some Distance with Diffuse Thinking

One of the reasons we can get so stuck on a single problem is because we tend to get mired in the details.

So step back from the problem.

Don’t think about the detail you were stuck on. Think about the project as a whole — what is its purpose, what is your role in it, what are you and this project trying to accomplish?

If you’re having trouble getting away from the details and thinking about the project in terms of the big picture like this, try going for a walk. This triggers your brain into thinking about the problem in a diffuse way rather than with focused thought , which in itself can help inspiration to strike.

Reframe the Problem in a New Way

One of the simplest ways to use abstract thinking to solve a problem is to reframe the question you’re trying to answer.

For example, say you’re stuck working on a project because the question you’re asking yourself is simply, “How do I code this to complete the project?”

To get un-stuck, ask yourself questions that approach the problem from different directions, like “Why does this need to work this way?” “Can I make this simpler?” “Who is going to use this?” “What does the finished product need to be able to do?”

By asking a series of questions about the bigger picture of the project, you might stumble upon a solution that you wouldn’t have seen with a narrower view.

Keep Asking Why (Over and Over)

There are different levels of abstract thinking, and one way to move to higher and higher levels of abstraction is to keep asking “Why?”

• Why does your project have this feature?
• Why does it need to work this way?
• Why will the person using the finished product need that feature?

Keep asking why, and you’ll again be able to see the bigger picture surrounding the problem, rather than just the problem itself. 

Look for Patterns

If abstract thinking is about seeing the big picture, a great way to get there is by looking for patterns in your work. Have you seen a problem like this anywhere else in your work or life? Is this problem similar to or different from problems you’ve solved before? 

Sleep On It

When all else fails, take a break from the problem and sleep on it. Whether you just take a quick afternoon snooze or a full night’s rest, research shows that sleep can disrupt your thinking when working on a difficult problem, allowing you to reapproach the problem with fresh thoughts and reach a solution faster. Some of history’s most famous thinkers agree: Thomas Edison famously took naps in his workshop with a steel ball-bearing in each hand, so that when he fell asleep, the sound of the metal hitting the floor would wake him up, allowing him to get right back to work with fresh eyes and fresh thoughts.

Next time your reach that awful feeling of wanting to beat your head against the desk out of frustration, put these strategies to use. Abstract thinking isn’t always easy, and it doesn’t always come naturally (especially for detail-oriented people like developers tend to be). 

But it’s one of the best tools you can use to tackle the toughest engineering problems, and when you’re celebrating the victory of cracking the solution, you’ll be thankful for abstract thinking.

Rethinking Timekeeping for Developers:

Turning a timesuck into time well spent.

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Cognitive Development in the Teen Years

What is cognitive development.

Cognitive development means the growth of a child’s ability to think and reason. This growth happens differently from ages 6 to 12, and from ages 12 to 18.

Children ages 6 to 12 years old develop the ability to think in concrete ways. These are called concrete operations. These things are called concrete because they’re done around objects and events. This includes knowing how to:

Combine (add)

Separate (subtract or divide)

Order (alphabetize and sort)

Transform objects and actions (change things, such as 5 pennies = 1 nickel)

Ages 12 to 18 is called adolescence. Kids and teens in this age group do more complex thinking. This type of thinking is also known as formal logical operations. This includes the ability to:

Do abstract thinking. This means thinking about possibilities.

Reason from known principles. This means forming own new ideas or questions.

Consider many points of view. This means to compare or debate ideas or opinions.

Think about the process of thinking. This means being aware of the act of thought processes.

How cognitive growth happens during the teen years

From ages 12 to 18, children grow in the way they think. They move from concrete thinking to formal logical operations. It’s important to note that:

Each child moves ahead at their own rate in their ability to think in more complex ways.

Each child develops their own view of the world.

Some children may be able to use logical operations in schoolwork long before they can use them for personal problems.

When emotional issues come up, they can cause problems with a child’s ability to think in complex ways.

The ability to consider possibilities and facts may affect decision-making. This can happen in either positive or negative ways.

Types of cognitive growth through the years

A child in early adolescence:

Uses more complex thinking focused on personal decision-making in school and at home

Begins to show use of formal logical operations in schoolwork

Begins to question authority and society's standards

Begins to form and speak his or her own thoughts and views on many topics. You may hear your child talk about which sports or groups he or she prefers, what kinds of personal appearance is attractive, and what parental rules should be changed.

A child in middle adolescence:

Has some experience in using more complex thinking processes

Expands thinking to include more philosophical and futuristic concerns

Often questions more extensively

Often analyzes more extensively

Thinks about and begins to form his or her own code of ethics (for example, What do I think is right?)

Thinks about different possibilities and begins to develop own identity (for example, Who am I? )

Thinks about and begins to systematically consider possible future goals (for example, What do I want? )

Thinks about and begins to make his or her own plans

Begins to think long-term

Uses systematic thinking and begins to influence relationships with others

A child in late adolescence:

Uses complex thinking to focus on less self-centered concepts and personal decision-making

Has increased thoughts about more global concepts, such as justice, history, politics, and patriotism

Often develops idealistic views on specific topics or concerns

May debate and develop intolerance of opposing views

Begins to focus thinking on making career decisions

Begins to focus thinking on their emerging role in adult society

How you can encourage healthy cognitive growth

To help encourage positive and healthy cognitive growth in your teen, you can:

Include him or her in discussions about a variety of topics, issues, and current events.

Encourage your child to share ideas and thoughts with you.

Encourage your teen to think independently and develop his or her own ideas.

Help your child in setting goals.

Challenge him or her to think about possibilities for the future.

Compliment and praise your teen for well-thought-out decisions.

Help him or her in re-evaluating poorly made decisions.

If you have concerns about your child's cognitive development, talk with your child's healthcare provider. 

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Abstract Thinking: Meaning And Examples

Abstract thinking skills are essential to succeed in the workplace. Yes, we all have abstract thinking skills, but they’re of…

Abstract thinking skills are essential to succeed in the workplace. Yes, we all have abstract thinking skills, but they’re of varying degrees. Certain jobs require a higher level of abstract thinking skills.

Abstract thinking helps us solve problems, make evaluations and select the right team. To give an example of abstract thinking , how does an HR Head reviewing two candidates with similar resumes make a selection? They probably observe the two candidates during their interviews and deduce their personality types, which involves using abstract thinking skills.

Meaning Of Abstract Thinking

Concrete vs. abstract thinking, examples of abstract thinking, development of abstract thinking, how to improve abstract thinking, training with harappa.

So, let’s understand the meaning of abstract thinking.

  Abstract thinking is a way of reasoning—a systematic approach to problem-solving that involves conceptualizing, making generalizations and arriving at conclusions. In abstract thinking, we process information received through our senses and try to connect it to the world.

Here’s another example of abstract thinking: two supervisors have been asked to inspect 100 boxes of mangoes to see if they’ve ripened. Supervisor A checks 10 mangoes per box. If he finds them ripe, he assumes the rest are too and finishes his task in 10 minutes. Supervisor B checks every mango in every box.

  From the above abstract thinking example, it’s clear Supervisor A is able to identify a pattern, whereas Supervisor B painstakingly adopts the longer route.

  The opposite of abstract thinking is concrete thinking, which is also sometimes called literal thinking. To better understand the meaning of abstract thinking , let’s look at the difference between the two.

  Concrete thinking is reasoning based on what you can see, hear, feel and experience in the present moment. It’s sometimes called literal thinking because it focuses on the exact meaning of things. A concrete thinker will think of specific steps in a task and ‘how’ they’ll perform it, unconcerned about anything beyond the assigned task. An abstract thinker will want to know the ‘why’ behind the task.

  Abstract thinking means possessing the ability to comprehend concepts that aren’t directly tethered to concrete, physical objects or experiences but are ‘invisible’, such as wisdom or strength. They can conceptualize without the need to see or touch. Abstract thinking is considered part of higher-order reasoning. People who think abstractly can analyze situations, understand concepts, innovate and formulate theories. They’re usually good at:

• Solving complex problems
• Creating art of all types
• Coming up with innovative solutions

However, a combination of both abstract and concrete thinking skills is required in a work environment for creativity and productivity. Organizations can select the right people for a task, depending on the type of thinking they veer toward.

  Abstract skills are valued not only in the workplace but also in educational institutions. The study of languages is an example of abstract thinking because it entails the expression of abstract concepts. So do science and math, which involve testing hypotheses and theories.

  The meaning of abstract thinking can be best expressed through examples.

A wonderful example of abstract thinking is humor. A person sharing a joke is usually able to find connections between seemingly unrelated things.

  Let’s have a look at some more examples to get a better idea of the meaning of abstract thinking . A storyteller who can visualize the whole narrative before they start writing it has strong abstract thinking skills. The ability to envision the whole picture without relying solely on existing knowledge is very useful in an organization. It enables one to think critically and find creative solutions to problems.

  But, are people born with this ability or is it developed? Jean Piaget, a renowned Swiss psychologist, explained that the development of abstract thinking begins in childhood. According to Piaget, abstract thinking skills develop as children get older, interact with their environment and learn from new experiences.

  Let’s now look at Piaget’s Theory of Cognitive Development to understand the development of abstract thinking.

  According to Piaget, abstract thinking develops throughout the course of childhood—from birth through adolescence to early childhood. Piaget’s Theory of Cognitive Development identifies four distinct stages of intellectual development during childhood. They are:

• Birth—around two years: Babies think only concretely. They think about what they can observe. They lack object permanence, which means that an object ceases to exist for them if they can’t see or hear it. So, if they can’t hear or see the rattle, they will not remember it.
•   Two—seven years: Children start to understand symbols, which is when, according to Piaget, abstract thinking starts to develop in them. For example, they begin to understand that A is for Apple and realize that things that aren’t physically in front of them can exist.
•   Seven—eleven years: Children are capable of logical reasoning, though their thinking still remains ‘concrete’ and connected to what they directly experience through their five senses.
•   Twelve—adulthood : According to Piaget, abstract thinking skills come into their own in this period. This is the stage where the full development of abstract thinking takes place. For example, individuals learn how to empathize and put themselves in another’s shoes. Being able to think about hypothetical situations, they start making plans for the future.

The core idea of Piaget’s t heory is that intellectual development in children is not a quantitative process achieved by adding knowledge. As they grow older, there is a qualitative change in their thinking. According to Piaget, abstract thinking naturally develops as children begin to interact with the people and objects around them. The question then arises: Does the development of abstract thinking stop in adulthood?

  Yes, it’s possible to improve abstract thinking skills , which in turn enhance your ability to solve problems, understand and share complex concepts and get more involved in creative activities. Once you know how to improve abstract thinking skills, you can make a conscious effort to practice them.

  Activities that involve recognizing patterns, analyzing ideas, synthesizing information, solving problems and creating things help improve abstract thinking skills. Extempore theatre, playing with puzzles, optical illusions, creating models, writing poetry and all forms of art train the mind to think in multiple ways beyond the obvious. Abstract skills are also domain-specific. Research has shown those in the field of science can improve their abstract thinking abilities by pursuing art-related activities. Metaphors and analogies also stimulate abstract thinking as they connect the concrete to the abstract. So, abstract thinking is not really abstract but a matter of creating connections, a matter of training.

Harappa’s Thinking Critically course helps professionals, managers and team leaders think through situations before making decisions, engage with opposing views to evaluate all possible outcomes and articulate the reasons behind their decisions. Strengthen your problem-solving skills and grow as a leader with Harappa. Sign up today!

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Intelligence and Creativity in Problem Solving: The Importance of Test Features in Cognition Research

Associated data.

This paper discusses the importance of three features of psychometric tests for cognition research: construct definition, problem space, and knowledge domain. Definition of constructs, e.g., intelligence or creativity, forms the theoretical basis for test construction. Problem space, being well or ill-defined, is determined by the cognitive abilities considered to belong to the constructs, e.g., convergent thinking to intelligence, divergent thinking to creativity. Knowledge domain and the possibilities it offers cognition are reflected in test results. We argue that (a) comparing results of tests with different problem spaces is more informative when cognition operates in both tests on an identical knowledge domain, and (b) intertwining of abilities related to both constructs can only be expected in tests developed to instigate such a process. Test features should guarantee that abilities can contribute to self-generated and goal-directed processes bringing forth solutions that are both new and applicable. We propose and discuss a test example that was developed to address these issues.

The definition of the construct a test is to measure is most important in test construction and application, because cognitive processes reflect the possibilities a task offers. For instance, a test constructed to assess intelligence will operationalize the definition of this construct, being, in short, finding the correct answer. Also, the definition of a construct becomes important when selecting tests for the confirmation of a specific hypothesis. One can only find confirmation for a hypothesis if the chosen task instigates the necessary cognitive operations. For instance, in trying to confirm the assumed intertwining of certain cognitive abilities (e.g., convergent thinking and divergent thinking), tasks should be applied that have shown to yield the necessary cognitive process.

The second test feature, problem space , determines the degrees of freedom cognition has to its disposal in solving a problem. For instance, cognition will go through a wider search path when problem constraints are less well defined and, consequently, data will differ accordingly.

The third test feature, knowledge domain , is important when comparing results from two different tests. When tests differ in problem space, it is not advisable they should differ in knowledge domain. For instance, when studying the differences in cognitive abilities between tests constructed to asses convergent thinking (mostly defined problem space) and divergent thinking (mostly ill-defined problem space), in general test practice, both tests also differ in knowledge domain. Hence, data will reflect cognition operating not only in different problem spaces, but also operating on different knowledge domains, which makes the interpretation of results ambiguous.

The proposed approach for test development and test application holds the promise of, firstly, studying cognitive abilities in different problem spaces while operating on an identical knowledge domain. Although cognitions’ operations have been studied extensively and superbly in both contexts separately, they have rarely been studied in test situations where one or the other test feature is controlled for. The proposed approach also presents a unique method for studying thinking processes in which cognitive abilities intertwine. On the basis of defined abilities, tasks can be developed that have a higher probability of yielding the hypothesized results.

The construct of intelligence is defined as the ability to produce the single best (or correct) answer to a clearly defined question, such as a proof to a theorem ( Simon, 1973 ). It may also be seen as a domain-general ability ( g -factor; Spearman, 1904 ; Cattell, 1967 ) that has much in common with meta cognitive functions, such as metacognitive knowledge, metacognitive monitoring, and metacognitive control ( Saraç et al., 2014 ).

The construct of creativity, in contrast, is defined as the ability to innovate and move beyond what is already known ( Wertheimer , 1945/1968 ; Ghiselin , 1952/1985 ; Vernon, 1970 ). In other words, it emphasizes the aspect of innovation. This involves the ability to consider things from an uncommon perspective, transcend the old order ( Ghiselin , 1952/1985 ; Chi, 1997 ; Ward, 2007 ), and explore loosely associated ideas ( Guilford, 1950 ; Mednick, 1962 ; Koestler, 1964 ; Gentner, 1983 ; Boden, 1990 ; Christensen, 2007 ). Creativity could also be defined as the ability to generate a solution to problems with ill-defined problem spaces ( Wertheimer , 1945/1968 ; Getzels and Csikszentmihalyi, 1976 ). In this sense it involves the ability to identify problematic aspects of a given situation ( Ghiselin , 1952/1985 ) and, in a wider sense, the ability to define completely new problems ( Getzels, 1975 , 1987 ).

Guilford (1956) introduced the constructs of convergent thinking and divergent thinking abilities. Both thinking abilities are important because they allow us insights in human problem solving. On the basis of their definitions convergent and divergent thinking help us to structurally study human cognitive operations in different situations and over different developmental stages. Convergent thinking is defined as the ability to apply conventional and logical search, recognition, and decision-making strategies to stored information in order to produce an already known answer ( Cropley, 2006 ). Divergent thinking, by contrast, is defined as the ability to produce new approaches and original ideas by forming unexpected combinations from available information and by applying such abilities as semantic flexibility, and fluency of association, ideation, and transformation ( Guilford, 1959 , as cited in Cropley, 2006 , p. 1). Divergent thinking brings forth answers that may never have existed before and are often novel, unusual, or surprising ( Cropley, 2006 ).

Guilford (1967) introduced convergent and divergent thinking as part of a set of five operations that apply in his Structure of Intellect model (SOI model) on six products and four kinds of content, to produce 120 different factors of cognitive abilities. With the SOI model Guilford wanted to give the construct of intelligence a comprehensive model. He wanted the model to include all aspects of intelligence, many of which had been seriously neglected in traditional intelligence testing because of a persistent adherence to the belief in Spearman’s g ( Guilford, 1967 , p. vii). Hence, Guilford envisaged cognition to embrace, among other abilities, both convergent and divergent thinking abilities. After these new constructs were introduced and defined, tests for convergent and divergent thinking emerged. Despite the fact that Guilford reported significant loadings of tests for divergent production on tests constructed to measure convergent production ( Guilford, 1967 , p. 155), over the years, both modes of thinking were considered as separate identities where convergent thinking tests associated with intelligence and divergent thinking tests with creativity ( Cropley, 2006 ; Shye and Yuhas, 2004 ). Even intelligence tests that assess aspects of intelligence that supposedly reflect creative abilities do not actually measure creativity ( Kaufman, 2015 ).

The idea that both convergent and divergent thinking are important for solving problems, and that intelligence helps in the creative process, is not really new. In literature we find models of the creative process that define certain stages to convergent and divergent thinking; the stages of purposeful preparation at the start and those of critical verification at the end of the process, respectively ( Wallas, 1926 ; Webb Young , 1939/2003 ). In this view, divergent thinking enables the generation of new ideas whereas the exploratory activities of convergent thinking enable the conversion of ideas into something new and appropriate ( Cropley and Cropley, 2008 ).

We argue that studying the abilities of divergent and convergent thinking in isolation does not suffice to give us complete insight of all possible aspects of human problem solving, its constituent abilities and the structure of its processes. Processes that in a sequence of thoughts and actions lead to novel and adaptive productions ( Lubart, 2001 ) are more demanding of cognition for understanding the situation at hand and planning a path to a possible solution, than abilities involved in less complex situations ( Jaušovec, 1999 ). Processes that yield self-generated and goal-directed thought are the most complex cognitive processes that can be studied ( Beaty et al., 2016 ). Creative cognition literature is moving toward the view that especially in those processes that yield original and appropriate solutions within a specific context, convergent and divergent abilities intertwine ( Cropley, 2006 ; Ward, 2007 ; Gabora, 2010 ).

The approach of intertwining cognitive abilities is also developed within cognitive neuroscience by focusing on the intertwining of brain networks ( Beaty et al., 2016 ). In this approach divergent thinking relates to the default brain network. This network operates in defocused or associative mode of thought yielding spontaneous and self-generated cognition ( Beaty et al., 2015 ). Convergent thinking relates to the executive control network operating in focused or analytic modes of thought, yielding updating, shifting, and inhibition ( Benedek et al., 2014 ). Defocused attention theory ( Mendelssohn, 1976 ) states that less creative individuals operate with a more focused attention than do creative individuals. This theory argues that e.g., attending to two things at the same time, might result in one analogy, while attending to four things might yield six analogies ( Martindale, 1999 ).

In the process of shifting back and forth along the spectrum between associative and analytic modes of thinking, the fruits of associative thought become ingredients for analytic thought processes, and vice versa ( Gabora, 2010 ). In this process, mental imagery is involved as one sensory aspect of the human ability to gather and process information ( Jung and Haier, 2013 ). Mental imagery is fed by scenes in the environment that provide crucial visual clues for creative problem solving and actuates the need for sketching ( Verstijnen et al., 2001 ).

Creative problem solving processes often involve an interactive relationship between imagining, sketching, and evaluating the result of the sketch ( van Leeuwen et al., 1999 ). This interactive process evolves within a type of imagery called “visual reasoning” where forms and shapes are manipulated in order to specify the configurations and properties of the design entities ( Goldschmidt, 2013 ). The originality of inventions is predicted by the application of visualization, whereas their practicality is predicted by the vividness of imagery ( Palmiero et al., 2015 ). Imaginative thought processes emerge from our conceptual knowledge of the world that is represented in our semantic memory system. In constrained divergent thinking, the neural correlates of this semantic memory system partially overlap with those of the creative cognition system ( Abraham and Bubic, 2015 ).

Studies of convergent and divergent thinking abilities have yielded innumerable valuable insights on the cognitive and neurological aspects involved, e.g., reaction times, strategies, brain areas involved, mental representations, and short and long time memory components. Studies on the relationship between both constructs suggest that it is unlikely that individuals employ similar cognitive strategies when solving more convergent than more divergent thinking tasks ( Jaušovec, 2000 ). However, to arrive at a quality formulation the creative process cannot do without the application of both, convergent and divergent thinking abilities (e.g., Kaufmann, 2003 ; Runco, 2003 ; Sternberg, 2005 ; Dietrich, 2007 ; Cropley and Cropley, 2008 ; Silvia et al., 2013 ; Jung, 2014 ).

When it is our aim to study the networks addressed by the intertwining of convergent and divergent thinking processes that are considered to operate when new, original, and yet appropriate solutions are generated, then traditional thinking tests like intelligence tests and creativity tests are not appropriate; they yield processes related to the definition of one or the other type of construct.

Creative Reasoning Task

According to the new insights gained in cognition research, we need tasks that are developed with the aim to instigate precisely the kind of thinking processes we are looking for. Tasks should also provide a method of scoring independently the contribution of convergent and divergent thinking. As one possible solution for such tasks we present the Creative Reasoning Task (CRT; Jaarsveld, 2007 ; Jaarsveld et al., 2010 , 2012 , 2013 ).

The CRT presents participants with an empty 3 × 3 matrix and asks them to fill it out, as original and complex as possible, by creating components and the relationships that connect them. The created matrix can, in principle, be solved by another person. The creation of components is entirely free, as is the generation of the relationships that connects them into a completed pattern. Created matrices are scored with two sub scores; Relations , which scores the logical complexity of a matrix and is, therefore, considered a measure for convergent thinking, and Components and Specifications , which scores the originality, fluency, and flexibility and, therefore, is considered an indication for divergent thinking (for a more detailed description of the score method, see Appendix 1 in Supplementary Material).

Psychometric studies with the CRT showed, firstly, that convergent and divergent thinking abilities apply within this task and can be assessed independently. The CRT sub score Relations correlated with the Standard Progressive Matrices test (SPM) and the CRT sub score Components and Specifications correlated with a standard creativity test (TCT–DP, Test of Creative Thinking–Drawing Production; Urban and Jellen, 1995 ; Jaarsveld et al., 2010 , 2012 , 2013 ). Studies further showed that, although a correlation was observed for the intelligence and creativity test scores, no correlation was observed between the CRT sub scores relating to intelligent and creative performances ( Jaarsveld et al., 2012 , 2013 ; for further details about the CRT’s objectivity, validity, and reliability, see Appendix 2 in Supplementary Material).

Reasoning in creative thinking can be defined as the involvement of executive/convergent abilities in the inhibition of ideas and the updating of information ( Benedek et al., 2014 ). Jung (2014) describes a dichotomy for cognitive abilities with at one end the dedicated system that relies on explicit and conscious knowledge and at the other end the improvisational system that relies more upon implicit or unconscious knowledge systems. The link between explicit and implicit systems can actually be traced back to Kris’ psychoanalytic approach to creativity dating from the 1950s. The implicit system refers to Kris’ primary process of adaptive regression, where unmodulated thoughts intrude into consciousness; the explicit system refers to the secondary process, where the reworking and transformation of primary process material takes place through reality-oriented and ego-controlled thinking ( Sternberg and Lubart, 1999 ). The interaction between explicit and implicit systems can be seen to form the basis of creative reasoning, i.e., the cognitive ability to solve problems in an effective and adaptive way. This interaction evolved as a cognitive mechanism when human survival depended on finding effective solutions to both common and novel problem situations ( Gabora and Kaufman, 2010 ). Creative reasoning solves that minority of problems that are unforeseen and yet of high adaptability ( Jung, 2014 ).

Hence, common tests are insufficient when it comes to solving problems that are unforeseen and yet of high adaptability, because they present problems that are either unforeseen and measure certain abilities contained in the construct of creativity or they address adaptability and measure certain abilities contained in the construct of intelligence. The CRT presents participants with a problem that they could not have foreseen; the form is blank and offers no stimuli. All tests, even creativity tests, present participants with some kind of stimuli. The CRT addresses adaptability; to invent from scratch a coherent structure that can be solved by another person, like creating a crossword puzzle. Problems, that are unforeseen and of high adaptability, are solved by the application of abilities from both constructs.

Neuroscience of Creative Cognition

Studies in neuroscience showed that cognition operating in ill-defined problem space not only applies divergent thinking but also benefits from additional convergent operations ( Gabora, 2010 ; Jung, 2014 ). Understanding creative cognition may be advanced when we study the flow of information among brain areas ( Jung et al., 2010 ).

In a cognitive neuroscience study with the CRT we focused on the cognitive process evolving within this task. Participants performed the CRT while EEG alpha activity was registered. EEG alpha synchronization in frontal areas is understood as an indication of top-down control ( Cooper et al., 2003 ). When observed in frontal areas, for divergent and convergent thinking tasks, it may not reflect a brain state that is specific for creative cognition but could be attributed to the high processing demands typically involved in creative thinking ( Benedek et al., 2011 ). Top-down control, relates to volitionally focusing attention to task demands ( Buschman and Miller, 2007 ). That this control plays a role in tasks with an ill-defined problem space showed when electroencephalography (EEG) alpha synchronization was stronger for individuals engaged in creative ideation tasks compared to an intelligence related tasks ( Fink et al., 2007 , 2009 ; Fink and Benedek, 2014 ). This activation was also found for the CRT; task related alpha synchronization showed that convergent thinking was integrated in the divergent thinking processes. Analyzes of the stages in the CRT process showed that this alpha synchronization was especially visible at the start of the creative process at prefrontal and frontal sites when information processing was most demanding, i.e., due to multiplicity of ideas, and it was visible at the end of the process, due to narrowing down of alternatives ( Jaarsveld et al., 2015 ).

A functional magnetic resonance imaging (fMRI) study ( Beaty et al., 2015 ) with a creativity task in which cognition had to meet specific constraints, showed the networks involved. The default mode network which drives toward abstraction and metaphorical thinking and the executive control network driving toward certainty ( Jung, 2014 ). Control involves not only maintenance of patterns of activity that represent goals and the means to achieve those ( Miller and Cohen, 2001 ), but also their voluntary suppression when no longer needed, as well as the flexible shift between different goals and mental sets ( Abraham and Windmann, 2007 ). Attention can be focused volitionally by top-down signals derived from task demands and automatically by bottom-up signals from salient stimuli ( Buschman and Miller, 2007 ). Intertwining between top-down and bottom-up attention processes in creative cognition ensures a broadening of attention in free associative thinking ( Abraham and Windmann, 2007 ).

These studies support and enhance the findings of creative cognition research in showing that the generation of original and applicable ideas involves an intertwining between different abilities, networks, and attention processes.

Problem Space

A problem space is an abstract representation, in the mind of the problem solver, of the encountered problem and of the asked for solution ( Simon and Newell, 1971 ; Simon, 1973 ; Hayes and Flowers, 1986 ; Kulkarni and Simon, 1988 ; Runco, 2007 ). The space that comes with a certain problem can, according to the constraints that are formulated for the solution, be labeled well-defined or ill-defined ( Simon and Newell, 1971 ). Consequently, the original problems are labeled closed and open problems, respectively ( Jaušovec, 2000 ).

A problem space contains all possible states that are accessible to the problem solver from the initial state , through iterative application of transformation rules , to the goal state ( Newell and Simon, 1972 ; Anderson, 1983 ). The initial state presents the problem solver with a task description that defines which requirements a solution has to answer. The goal state represents the solution. The proposed solution is a product of the application of transformation rules (algorithms and heuristics) on a series of successive intermediate solutions. The proposed solution is also a product of the iterative evaluations of preceding solutions and decisions based upon these evaluations ( Boden, 1990 ; Gabora, 2002 ; Jaarsveld and van Leeuwen, 2005 ; Goldschmidt, 2014 ). Whether all possible states need to be passed through depends on the problem space being well or ill-defined and this, in turn, depends on the character of the task descriptions.

When task descriptions clearly state which requirements a solution has to answer then the inferences made will show little idiosyncratic aspects and will adhere to the task constraints. As a result, fewer options for alternative paths are open to the problem solver and search for a solution evolves in a well-defined space. Vice versa, when task or problem descriptions are fuzzy and under specified, the problem solver’s inferences are more idiosyncratic; the resulting process will evolve within an ill-defined space and will contain more generative-evaluative cycles in which new goals are set, and the cycle is repeated ( Dennett, 1978 , as cited in Gabora, 2002 , p. 126).

Tasks that evolve in defined problem space are, e.g., traditional intelligence tests (e.g., Wechsler Adult Intelligence Scale, WAIS; and SPM, Raven , 1938/1998 ). The above tests consist of different types of questions, each testing a different component of intelligence. They are used in test practice to assess reasoning abilities in diverse domains, such as, abstract, logical, spatial, verbal, numerical, and mathematical domains. These tests have clearly stated task descriptions and each item has one and only one correct solution that has to be generated from memory or chosen from a set of alternatives, like in multiple choice formats. Tests can be constructed to assess crystallized or fluid intelligence. Crystallized intelligence represents abilities acquired through learning, practice, and exposure to education, while fluid intelligence represents a more basic capacity that is valuable to reasoning and problem solving in contexts not necessarily related to school education ( Carroll, 1982 ).

Tasks that evolve in ill-defined problem space are, e.g., standard creativity tests. These types of test ask for a multitude of ideas to be generated in association with a given item or situation (e.g., “think of as many titles for this story”). Therefore, they are also labeled as divergent thinking test. Although they assess originality, fluency, flexibility of responses, and elaboration, they are not constructed, however, to score appropriateness or applicability. Divergent thinking tests assess one limited aspect of what makes an individual creative. Creativity depends also on variables like affect and intuition; therefore, divergent thinking can only be considered an indication of an individual’s creative potential ( Runco, 2008 ). More precisely, divergent thinking explains just under half of the variance in adult creative potential, which is more than three times that of the contribution of intelligence ( Plucker, 1999 , p. 103). Creative achievement , by contrast, is commonly assessed by means of self-reports such as biographical questionnaires in which participants indicate their achievement across various domains (e.g., literature, music, or theater).

Studies with the CRT showed that problem space differently affects processing of and comprehension of relationships between components. Problem space did not affect the ability to process complex information. This ability showed equal performance in well and ill-defined problem spaces ( Jaarsveld et al., 2012 , 2013 ). However, problem space did affect the comprehension of relationships, which showed in the different frequencies of relationships solved and created ( Jaarsveld et al., 2010 , 2012 ). Problem space also affected the neurological activity as displayed when individuals solve open or closed problems ( Jaušovec, 2000 ).

Problem space further affected trends over grade levels of primary school children for relationships solved in well-defined and applied in ill-defined problem space. Only one of the 12 relationships defined in the CRT, namely Combination, showed an increase with grade for both types of problem spaces ( Jaarsveld et al., 2013 ). In the same study, cognitive development in the CRT showed in the shifts of preference for a certain relationship. These shifts seem to correspond to Piaget’s developmental stages ( Piaget et al., 1977 ; Siegler, 1998 ) which are in evidence in the CRT, but not in the SPM ( Jaarsveld et al., 2013 ).

Design Problems

A sub category of problems with an ill-defined problem space are represented by design problems. In contrast to divergent thinking tasks that ask for the generation of a multitude of ideas, in design tasks interim ideas are nurtured and incrementally developed until they are appropriate for the task. Ideas are rarely discarded and replaced with new ideas ( Goel and Pirolli, 1992 ). The CRT could be considered a design problem because it yields (a) one possible solution and (b) an iterative thinking process that involves the realization of a vague initial idea. In the CRT a created matrix, which is a closed problem, is created within an ill-defined problem space. Design problems can be found, e.g., in engineering, industrial design, advertising, software design, and architecture ( Sakar and Chakrabarti, 2013 ), however, they can also be found in the arts, e.g., poetry, sculpting, and dance geography.

These complex problems are partly determined by unalterable needs, requirements and intentions but the major part of the design problem is undetermined ( Dorst, 2004 ). This author points out that besides containing an original and a functional value, these types of problems contain an aesthetic value. He further states that the interpretation of the design problem and the creation and selection of possible suitable solutions can only be decided during the design process on the basis of proposals made by the designer.

In design problems the generation stage may be considered a divergent thinking process. However, not in the sense that it moves in multiple directions or generates multiple possibilities as in a divergent thinking tests, but in the sense that it unrolls by considering an initially vague idea from different perspectives until it comes into focus and requires further processing to become viable. These processes can be characterized by a set of invariant features ( Goel and Pirolli, 1992 ), e.g., structuring. iteration , and coherence .

Structuring of the initial situation is required in design processes before solving can commence. The problem contains little structured and clear information about its initial state and about the requirements of its solution. Therefore, design problems allow or even require re-interpretation of transformation rules; for instance, rearranging the location of furniture in a room according to a set of desirable outcomes. Here one uncovers implicit requirements that introduce a set of new transformations and/or eliminate existing ones ( Barsalou, 1992 ; Goel and Pirolli, 1992 ) or, when conflicting requirements arise, one creates alternatives and/or introduces new trade-offs between the conflicting constraints ( Yamamoto et al., 2000 ; Dorst, 2011 ).

A second aspect of design processes is their iterative character. After structuring and planning a vague idea emerges, which is the result of the merging of memory items. A vague idea is a cognitive structure that, halfway the creative process is still ill defined and, therefore, can be said to exist in a state of potentiality ( Gabora and Saab, 2011 ). Design processes unroll in an iterative way by the inspection and adjustment of the generated ideas ( Goldschmidt, 2014 ). New meanings are created and realized while the creative mind imposes its own order and meaning on the sensory data and through creative production furthers its own understanding of the world ( Arnheim , 1962/1974 , as cited in Grube and Davis, 1988 , pp. 263–264).

A third aspect of design processes is coherence. Coherence theories characterize coherence in, for instance, philosophical problems and psychological processes, in terms of maximal satisfaction of multiple constraints and compute coherence by using, a.o., connectionist algorithms ( Thagard and Verbeurgt, 1998 ). Another measure of coherence is characterized as continuity in design processes. This measure was developed for a design task ( Jaarsveld and van Leeuwen, 2005 ) and calculated by the occurrence of a given pair of objects in a sketch, expressed as a percentage of all the sketches of a series. In a series of sketches participants designed a logo for a new soft drink. Design series strong in coherence also received a high score for their final design, as assessed by professionals in various domains. Indicating that participants with a high score for the creative quality of their final sketch seemed better in assessing their design activity in relation to the continuity in the process and, thereby, seemed better in navigating the ill-defined space of a design problem ( Jaarsveld and van Leeuwen, 2005 ). In design problems the quality of cognitive production depends, in part, on the abilities to reflect on one’s own creative behavior ( Boden, 1996 ) and to monitor how far along in the process one is in solving it ( Gabora, 2002 ). Hence, design problems are especially suited to study more complex problem solving processes.

Knowledge Domain

Knowledge domain represents disciplines or fields of study organized by general principles, e.g., domains of various arts and sciences. It contains accumulated knowledge that can be divided in diverse content domains, and the relevant algorithms and heuristics. We also speak of knowledge domains when referring to, e.g., visuo-spatial and verbal domains. This latter differentiation may refer to the method by which performance in a certain knowledge domain is assessed, e.g., a visuo-spatial physics task that assesses the content domain of the workings of mass and weights of objects.

In comparing tests results, we should keep in mind that apart from reflecting cognitive processes evolving in different problem spaces, the results also arise from cognition operating on different knowledge domains. We argue that, the still contradictory and inconclusive discussion about the relationship between intelligence and creativity ( Silvia, 2008 ), should involve the issue of knowledge domain.

Intelligence tests contain items that pertain to, e.g., verbal, abstract, mechanical and spatial reasoning abilities, while their content mostly operates on knowledge domains that are related to contents contained in school curricula. Items of creativity tests, by contrast, pertain to more idiosyncratic knowledge domains, their contents relating to associations between stored personal experiences ( Karmiloff-Smith, 1992 ). The influence of knowledge domain on the relationships between different test scores was already mentioned by Guilford (1956 , p. 169). This author expected a higher correlation between scores from a typical intelligence test and a divergent thinking test than between scores from two divergent thinking tests because the former pair operated on identical information and the latter pair on different information.

Studies with the CRT showed that when knowledge domain is controlled for, the development of intelligence operating in ill-defined problem space does not compare to that of traditional intelligence but develops more similarly to the development of creativity ( Welter et al., in press ).

Relationship Intelligence and Creativity

The Threshold theory ( Guilford, 1967 ) predicts a relationship between intelligence and creativity up to approximately an intelligence quotient (IQ) level of 120 but not beyond ( Lubart, 2003 ; Runco, 2007 ). Threshold theory was corroborated when creative potential was found to be related to intelligence up to certain IQ levels; however, the theory was refuted, when focusing on achievement in creative domains; it showed that creative achievement benefited from higher intelligence even at fairly high levels of intellectual ability ( Jauk et al., 2013 ).

Distinguishing between subtypes of general intelligence known as fluent and crystallized intelligence ( Cattell, 1967 ), Sligh et al. (2005) observed an inverse threshold effect with fluid IQ: a correlation with creativity test scores in the high IQ group but not in the average IQ group. Also creative achievement showed to be affected by fluid intelligence ( Beaty et al., 2014 ). Intelligence, defined as fluid IQ, verbal fluency, and strategic abilities, showed a higher correlation with creativity scores ( Silvia, 2008 ) than when defined as crystallized intelligence. Creativity tests, which involved convergent thinking (e.g., Remote Association Test; Mednick, 1962 ) showed higher correlations with intelligence than ones that involved only divergent thinking (e.g., the Alternate Uses Test; Guilford et al., 1978 ).

That the Remote Association test also involves convergent thinking follows from the instructions; one is asked, when presented with a stimulus word (e.g., table) to produce the first word one thinks of (e.g., chair). The word pair table–chair is a common association, more remote is the pair table–plate, and quite remote is table–shark. According to Mednick’s theory (a) all cognitive work is done essentially by combining or associating ideas and (b) individuals with more commonplace associations have an advantage in well-defined problem spaces, because the class of relevant associations is already implicit in the statement of the problem ( Eysenck, 2003 ).

To circumvent the problem of tests differing in knowledge domain, one can develop out of one task a more divergent and a more convergent thinking task by asking, on the one hand, for the generation of original responses, and by asking, on the other hand, for more common responses ( Jauk et al., 2012 ). By changing the instruction of a task, from convergent to divergent, one changes the constraints the solution has to answer and, thereby, one changes for cognition its freedom of operation ( Razumnikova et al., 2009 ; Limb, 2010 ; Jauk et al., 2012 ). However, asking for more common responses is still a divergent thinking task because it instigates a generative and ideational process.

Indeed, studying the relationship between intelligence and creativity with knowledge domain controlled for yielded different results as defined in the Threshold theory. A study in which knowledge domain was controlled for showed, firstly, that intelligence is no predictor for the development of creativity ( Welter et al., 2016 ). Secondly, that the relationship between scores of intelligence and creativity tests as defined under the Threshold theory was only observed in a small subset of primary school children, namely, female children in Grade 4 ( Welter et al., 2016 ). We state that relating results of operations yielded by cognitive abilities performing in defined and in ill-defined problem spaces can only be informative when it is ensured that cognitive processes also operate on an identical knowledge domain.

Intertwining of Cognitive Abilities

Eysenck (2003) observed that there is little justification for considering the constructs of divergent and convergent thinking in categorical terms in which one construct excludes the other. In processes that yield original and appropriate solutions convergent and divergent thinking both operate on the same large knowledge base and the underlying cognitive processes are not entirely dissimilar ( Eysenck, 2003 , p. 110–111).

Divergent thinking is especially effective when it is coupled with convergent thinking ( Runco, 2003 ; Gabora and Ranjan, 2013 ). A design problem study ( Jaarsveld and van Leeuwen, 2005 ) showed that divergent production was active throughout the design, as new meanings are continuously added to the evolving structure ( Akin, 1986 ), and that convergent production was increasingly important toward the end of the process, as earlier productions are wrapped up and integrated in the final design. These findings are in line with the assumptions of Wertheimer (1945/1968) who stated that thinking within ill-defined problem space is characterized by two points of focus; one is to work on the parts, the other to make the central idea clearer.

Parallel to the discussion about the intertwining of convergent and divergent thinking abilities in processes that evolve in ill-defined problem space we find the discussion about how intelligence may facilitate creative thought. This showed when top-down cognitive control advanced divergent processing in the generation of original ideas and a certain measure of cognitive inhibition advanced the fluency of idea generation ( Nusbaum and Silvia, 2011 ). Fluid intelligence and broad retrieval considered as intelligence factors in a structural equation study contributed both to the production of creative ideas in a metaphor generation task ( Beaty and Silvia, 2013 ). The notion that creative thought involves top-down, executive processes showed in a latent variable analysis where inhibition primarily promoted the fluency of ideas, and intelligence promoted their originality ( Benedek et al., 2012 ).

Definitions of the Constructs Intelligence and Creativity

The various definitions of the constructs of intelligence and creativity show a problematic overlap. This overlap stems from the enormous endeavor to unanimously agree on valid descriptions for each construct. Spearman (1927) , after having attended many symposia that aimed at defining intelligence, stated that “in truth, ‘intelligence’ has become a mere vocal sound, a word with so many meanings that finally it has none” (p. 14).

Intelligence is expressed in terms of adaptive, goal-directed behavior; and the subset of such behavior that is labeled “intelligent” seems to be determined in large part by cultural or societal norms ( Sternberg and Salter, 1982 ). The development of the IQ measure is discussed by Carroll (1982) : “Binet (around 1905) realized that intelligent behavior or mental ability can be ranged along a scale. Not much later, Stern (around 1912) noticed that, as chronological age increased, variation in mental age changes proportionally. He developed the IQ ratio, whose standard deviation would be approximately constant over chronological age if mental age was divided by chronological age. With the development of multiple-factor-analyses (Thurstone, around 1935) it could be shown that intelligence is not a simple unitary trait because at least seven somewhat independent factors of mental ability were identified.”

Creativity is defined as a combined manifestation of novelty and usefulness ( Jung et al., 2010 ). Although it is identified with divergent thinking, and performance on divergent thinking tasks predicts, e.g., quantity of creative achievements ( Torrance, 1988 , as cited in Beaty et al., 2014 ) and quality of creative performance ( Beaty et al., 2013 ), it cannot be identified uniquely with divergent thinking.

Divergent thinking often leads to highly original ideas that are honed to appropriate ideas by evaluative processes of critical thinking, and valuative and appreciative considerations ( Runco, 2008 ). Divergent thinking tests should be more considered as estimates of creative problem solving potential rather than of actual creativity ( Runco, 1991 ). Divergent thinking is not specific enough to help us understand what, exactly, are the mental processes—or the cognitive abilities—that yield creative thoughts ( Dietrich, 2007 ).

Although current definitions of intelligence and creativity try to determine for each separate construct a unique set of cognitive abilities, analyses show that definitions vary in the degree to which each includes abilities that are generally considered to belong to the other construct ( Runco, 2003 ; Jaarsveld et al., 2012 ). Abilities considered belonging to the construct of intelligence such as hypothesis testing, inhibition of alternative responses, and creating mental images of new actions or plans are also considered to be involved in creative thinking ( Fuster, 1997 , as cited in Colom et al., 2009 , p. 215). The ability, for instance, to evaluate , which is considered to belong to the construct of intelligence and assesses the match between a proposed solution and task constraints, has long been considered to play a role in creative processes that goes beyond the mere generation of a series of ideas as in creativity tasks ( Wallas, 1926 , as cited in Gabora, 2002 , p. 1; Boden, 1990 ).

The Geneplore model ( Finke et al., 1992 ) explicitly models this idea; after stages in which objects are merely generated, follow phases in which an object’s utility is explored and estimated. The generation phase brings forth pre inventive objects, imaginary objects that are generated without any constraints in mind. In exploration, these objects are evaluated for their possible functionalities. In anticipating the functional characteristics of generated ideas, convergent thinking is needed to apprehend the situation, make evaluations ( Kozbelt, 2008 ), and consider the consequences of a chosen solution ( Goel and Pirolli, 1992 ). Convergent reasoning in creativity tasks invokes criteria of functionality and appropriateness ( Halpern, 2003 ; Kaufmann, 2003 ), goal directedness and adaptive behavior ( Sternberg, 1982 ), as well as the abilities of planning and attention. Convergent thinking stages may even require divergent thinking sub processes to identify restrictions on proposed new ideas and suggest requisite revision strategies ( Mumford et al., 2007 ). Hence, evaluation, which is considered to belong to the construct of intelligence, is also functional in creative processes.

In contrast, the ability of flexibility , which is considered to belong to the construct of creativity and denotes an openness of mind that ensures the generation of ideas from different domains, showed, as a factor component for latent divergent thinking, a relationship with intelligence ( Silvia, 2008 ). Flexibility was also found to play an important role in intelligent behavior where it enables us to do novel things smartly in new situations ( Colunga and Smith, 2008 ). These authors studied children’s generalizations of novel nouns and concluded that if we are to understand human intelligence, we must understand the processes that make inventiveness. They propose to include the construct of flexibility within that of intelligence. Therefore, definitions of the constructs we are to measure affect test construction and the resulting data. However, an overlap between definitions, as discussed, yields a test diversity that makes it impossible to interpret the different findings across studies with any confidence ( Arden et al., 2010 ). Also Kim (2005) concluded that because of differences in tests and administration methods, the observed correlation between intelligence and creativity was negligible. As the various definitions of the constructs of intelligence and creativity show problematic overlap, we propose to circumvent the discussion about which cognitive abilities are assessed by which construct, and to consider both constructs as being involved in one design process. This approach allows us to study the contribution to this process of the various defined abilities, without one construct excluding the other.

Reasoning Abilities

The CRT is a psychometrical tool constructed on the basis of an alternative construct of human cognitive functioning that considers creative reasoning as a thinking process understood as the cooperation between cognitive abilities related to intelligent and creative thinking.

In generating relationships for a matrix, reasoning and more specifically the ability of rule invention is applied. The ability of rule invention could be considered as an extension of the sequence of abilities of rule learning, rule inference, and rule application, implying that creativity is an extension of intelligence ( Shye and Goldzweig, 1999 ). According to this model, we could expect different results between a task assessing abilities of rule learning and rule inference, and a task assessing abilities of rule application. In two studies rule learning and rule inference was assessed with the RPM and rule application was assessed with the CRT. Results showed that from Grades 1 to 4, the frequencies of relationships applied did not correlate with those solved ( Jaarsveld et al., 2010 , 2012 ). Results showed that performance in the CRT allows an insight of cognitive abilities operating on relationships among components that differs from the insight based on performance within the same knowledge domain in a matrix solving task. Hence, reasoning abilities lead to different performances when applied in solving closed as to open problems.

We assume that reasoning abilities are more clearly reflected when one formulates a matrix from scratch; in the process of thinking and drawing one has, so to speak, to solve one’s own matrix. In doing so one explains to oneself the relationship(s) realized so far and what one would like to attain. Drawing is thinking aloud a problem and aids the designer’s thinking processes in providing some “talk-back” ( Cross and Clayburn Cross, 1996 ). Explanatory activity enhances learning through increased depth of processing ( Siegler, 2005 ). Analyzing explanations of examples given with physics problems showed that they clarify and specify the conditions and consequences of actions, and that they explicate tacit knowledge; thereby enhancing and completing an individual’s understanding of principles relevant to the task ( Chi and VanLehn, 1991 ). Constraint of the CRT is that the matrix, in principle, can be solved by another person. Therefore, in a kind of inner explanatory discussion, the designer makes observations of progress, and uses evaluations and decisions to answer this constraint. Because of this, open problems where certain constraints have to be met, constitute a powerful mechanism for promoting understanding and conceptual advancement ( Chi and VanLehn, 1991 ; Mestre, 2002 ; Siegler, 2005 ).

Convergent and divergent thinking processes have been studied with a variety of intelligence and creativity tests, respectively. Relationships between performances on these tests have been demonstrated and a large number of research questions have been addressed. However, the fact that intelligence and creativity tests vary in the definition of their construct, in their problem space, and in their knowledge domain, poses methodological problems regarding the validity of comparisons of test results. When we want to focus on one cognitive process, e.g., intelligent thinking, and on its different performances in well or ill-defined problem situations, we need pairs of tasks that are constructed along identical definitions of the construct to be assessed, that differ, however, in the description of their constraints but are identical regarding their knowledge domain.

One such possible pair, the Progressive Matrices Test and the CRT was suggested here. The CRT was developed on the basis of creative reasoning , a construct that assumes the intertwining of intelligent and creativity related abilities when looking for original and applicable solutions. Matched with the Matrices test, results indicated that, besides similarities, intelligent thinking also yielded considerable differences for both problem spaces. Hence, with knowledge domain controlled, and only differences in problem space remaining, comparison of data yielded new results on intelligence’s operations. Data gathered from intelligence and creativity tests, whether they are performance scores or physiological measurements on the basis of, e.g., EEG, and fMRI methods, are reflections of cognitive processes performing on a certain test that was constructed on the basis of a certain definition of the construct it was meant to measure. Data are also reflections of the processes evolving within a certain problem space and of cognitive abilities operating on a certain knowledge domain.

Data can unhide brain networks that are involved in the performance of certain tasks, e.g., traditional intelligence and creativity tests, but data will always be related to the characteristics of the task. The characteristics of the task, such as problem space and knowledge domain originated at the construction of the task, and the construction, on its turn, is affected by the definition of the construct the task is meant to measure.

Here we present the CRT as one possible solution for the described problems in cognition research. However, for research on relationships among test scores other pairs of tests are imaginable, e.g., pairs of tasks operating on the same domain where one task has a defined problem space and the other one an ill-defined space. It is conceivable that pairs of test could operate, besides on the domain of mathematics, on content of e.g., visuo-spatial, verbal, and musical domains. Pairs of test have been constructed by changing the instruction of a task; instructions instigated a more convergent or a more a divergent mode of response ( Razumnikova et al., 2009 ; Limb, 2010 ; Jauk et al., 2012 ; Beaty et al., 2013 ).

The CRT involves the creation of components and their relationships for a 3 × 3 matrix. Hence, matrices created in the CRT are original in the sense that they all bear individual markers and they are applicable in the sense, that they can, in principle, be solved by another person. We showed that the CRT instigates a real design process; creators’ cognitive abilities are wrapped up in a process that should produce a closed problem within an ill-defined problem space.

For research on the relationship among convergent and divergent thinking, we need pairs of test that differ in the problem spaces related to each test but are identical in the knowledge domain on which cognition operates. The test pair of RPM and CRT provides such a pair. For research on the intertwining of convergent and divergent thinking, we need tasks that measure more than tests assessing each construct alone. We need tasks that are developed on the definition of intertwining cognitive abilities; the CRT is one such test.

Hence, we hope to have sufficiently discussed and demonstrated the importance of the three test features, construct definition, problem space, and knowledge domain, for research questions in creative cognition research.

Author Contributions

All authors listed, have made substantial, direct and intellectual contribution to the work, and approved it for publication.

Conflict of Interest Statement

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

Supplementary Material

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fpsyg.2017.00134/full#supplementary-material

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What is abstract thinking benefits and how to improve it.

Abstract thinking is the mental process of conceptualizing ideas that transcend the real world. It involves the ability to grasp concepts, patterns, and relationships that aren't directly observable. This type of thinking enables individuals to analyze, synthesize, and manipulate information on a higher level, leading to enhanced problem-solving skills, creativity, and critical reasoning. 

In daily life, abstract thinking allows us to understand metaphors and symbolism, as well as make connections between seemingly unrelated concepts. Abstract thinking also plays a crucial role in cognitive development, promoting growth by encouraging little ones to think beyond the surface, question assumptions, and explore new perspectives.

Abstract Thinking vs. Concrete Thinking

Abstract thinking and concrete thinking are two distinct processes that influence how people understand and interact with the world around them. 

The concrete thinking process is grounded in literal interpretations and tangible experiences, the “here and now.” It involves understanding things based on their physical attributes and immediate sensory perceptions. For example, a concrete thinker might see a tree and only focus on its size, shape, and color without delving into broader concepts like the environment's impact on the tree or the tree's symbolic significance.

On the other hand, abstract thinking involves conceptualizing ideas beyond the immediate sensory experience and seeing the bigger picture . It entails grasping concepts, relationships, and meanings that may not have a direct physical manifestation. Abstract thinkers can comprehend metaphors, symbols, and complex theories, drawing connections between seemingly unrelated concepts and thinking critically about intangible things like love or friendship.

While both types of thinking have their place, abstract thinking is crucial for higher-order cognitive abilities such as problem-solving, creativity, and philosophical questioning. Concrete thinking is foundational, providing a practical understanding of the world. Abstract thinking expands our intellectual horizons, allowing us to explore life’s complexities and contribute to the advancement of knowledge and ideas.

Abstract Thinking in Neurodivergent Children

Neurodivergent children, including those with conditions such as autism spectrum disorder (ASD), learning disabilities, and various mental health conditions, often navigate a distinct path in developing abstract thinking skills. Abstract thinking involves comprehending concepts beyond immediate sensory input, a cognitive process that can be influenced by neurological differences. 

For children on the autism spectrum, abstract thinking might pose challenges due to a tendency toward concrete thinking and difficulty with interpreting non-literal language . However, this doesn't mean they lack abstract thinking altogether. Many exhibit strengths in focused areas and may develop unique strategies to navigate abstract concepts.

Learning disabilities can also affect the development of abstract thinking. Difficulties in reading, writing, or mathematical reasoning can impact a child's exposure to abstract ideas. Tailored approaches that incorporate visual aids, hands-on activities, and individualized learning plans can help bridge the gap.

Psychologist Jean Piaget's theory of cognitive development, particularly the " formal operational stage ," sheds light on abstract thinking. This stage, typically reached during adolescence, involves the ability to think abstractly, reason hypothetically, and consider multiple perspectives. While neurodivergent children might not follow Piaget's stages linearly, they can still progress in uniquely meaningful ways.

Recognizing and nurturing the abstract thinking potential in neurodivergent children is crucial. By embracing their strengths, providing targeted support, and celebrating their individual growth trajectories, we can help them unlock their full cognitive potential and contribute their distinct perspectives to the diverse tapestry of human thought.

The Role of Physical Objects: Blocks and Cubes

Building blocks and cubes, while seemingly simple objects, play a pivotal role in fostering abstract thinking abilities in young children. While these toys are tangible and concrete, they hold the potential to spark and nurture abstract cognitive processes in remarkable ways.

Interacting with blocks and cubes encourages children to engage in spatial reasoning, problem-solving, and imaginative play . As they manipulate these objects, they begin to understand concepts like balance, stability, and symmetry. These foundational experiences lay the basis for more advanced abstract thinking.

When children stack blocks to create a tower, they're not just arranging objects — they're experimenting with concepts of height, weight distribution, and stability. As they combine blocks of different shapes to construct imaginative structures , they explore how different materials can work together. Such activities lay the groundwork for abstract thought by encouraging children to visualize possibilities, plan ahead, and analyze outcomes.

As children engage in collaborative block play, they learn the art of negotiation and compromise, navigating social interactions while contemplating shared goals. They develop the ability to see a single object as part of a larger structure, honing skills in recognizing patterns and connections, which are crucial aspects of abstract thinking.

The seemingly basic act of playing with blocks and cubes serves as a precursor to higher-order cognitive processes. By encouraging children to manipulate and experiment with these objects, we pave the way for the development of abstract thinking abilities that will shape their problem-solving skills, creativity, and critical reasoning in the years to come.

How Can Big Heart Toys Blocks Help With Abstract Thinking?

Our new 3D building blocks provide a unique building experience that can help your child develop their abstract thinking skills in their day-to-day life . Each three-dimensional cube has an abstract image that can be arranged into different designs and patterns. While the tactile play provides an engaging sensory experience, the solitary abstract shapes open their minds to different possibilities.

Abstract blocks provide opportunities for problem-solving , enhance creativity skills, and teach the concept of patterns and recreating images. These building blocks allow for both independent play and the opportunity for you to play with your child .

When building together, it can help to narrate what you’re creating with the abstract images. By showing your child what you can create and how to view things from different perspectives, you are modeling the ability to think outside the box.

Once your child is ready to play and build independently, you will be shocked at the magic their little minds are able to produce. When watching your little one create pictures and abstract designs, you may notice that they are learning to emotionally regulate themselves.

Creating abstract structures induces a sense of calmness through the unrestricted channeling of imagination and creativity, offering an escape from the constraints of routine. The absence of strict rules or predefined outcomes in abstract creation provides a judgment-free space, eliminating the pressure associated with conventional tasks.

Benefits of Abstract Thinking

First and foremost, abstract thinking is a powerhouse for problem-solving skills and decision-making enhancements. It equips individuals with the ability to understand complex scenarios, identify patterns, and draw connections between seemingly unrelated factors. This skill set empowers efficient and effective solutions to challenges, from daily problems to intricate puzzles.

Moreover, abstract thinking is the cornerstone of divergent thinking, critical thinking, and creative thinking. It encourages individuals to explore various angles, imagining multiple solutions to a single issue. This capacity for divergent thinking opens pathways to innovation and novel approaches. 

Beyond individual growth, abstract thinking plays a crucial role in understanding different perspectives and seeing the big picture. It enables empathy by encouraging individuals to step into others' shoes, appreciate varied viewpoints, and foster open-mindedness. This ability to navigate complexities is particularly essential in our interconnected world, promoting effective communication and collaboration across diverse cultures and contexts.

In essence, abstract thinking unlocks a cascade of benefits. It empowers us to solve problems creatively, make sound decisions, and embrace a comprehensive view of the world. 

Challenges in Abstract Thought Processes

Abstract thought processes, while powerful, can also give rise to a range of challenges that impact individuals' mental well-being and cognitive functioning.

One common challenge is rumination or overthinking, where individuals become entangled in repetitive, often negative thoughts. Abstract thinking's ability to delve deeply into concepts can lead to dwelling on things, which, if unchecked, may increase stress and anxiety.

Mental health implications are intertwined with abstract thinking. For instance, individuals prone to rumination may experience heightened levels of anxiety and depression. Additionally, overemphasis on abstract thoughts can contribute to feelings of isolation as intricate ideas might be hard to convey to others.

A significant connection exists between abstract thought and conditions like traumatic brain injury (TBI) — specifically, TBI can lead to difficulties in abstract thinking. Individuals may struggle to comprehend complex concepts or plan for the future, contributing to frustration or feelings of inadequacy.

Navigating these challenges requires a balanced approach. Cognitive strategies like mindfulness can help manage these potential downfalls. For mental health, it's crucial to recognize when abstract thinking takes a toll and to seek appropriate support. For TBI, tailored cognitive rehabilitation can aid in rebuilding abstract thinking skills, enhancing both cognitive and emotional recovery.

Tools and Techniques To Enhance Abstract Reasoning

Analogies : Analogical reasoning involves identifying relationships between different concepts. Engaging in analogy exercises, where individuals relate similar patterns across diverse scenarios, sharpens abstract thinking by encouraging the recognition of underlying connections.

Crossword Puzzles : Crosswords necessitate lateral thinking, where individuals deduce words from limited clues. Solving these puzzles strengthens cognitive flexibility and abstract reasoning, requiring the ability to manipulate letters and words in unconventional ways.

Mind Mapping : Creating visual mind maps to represent complex ideas fosters abstract thinking. This technique encourages individuals to break down concepts into interconnected nodes, enhancing comprehension and analytical skills.

Visual Arts and Music : Engaging in artistic pursuits, like painting or playing a musical instrument, nurtures abstract thinking. These activities encourage the interpretation of abstract concepts, such as emotions or ideas, through non-verbal means.

Chess and Strategy Games : Games that demand strategic planning, like chess or strategic board games, boost abstract reasoning. Players must anticipate future moves, analyze patterns, and adapt to evolving situations.

Incorporating these tools, techniques, and intelligence tests into learning and daily routines can cultivate robust abstract reasoning skills. As individuals train their minds to navigate intricate concepts, they enrich their problem-solving skills, creativity, and critical thinking capacities.

Abstract Thinking in Daily Life

Children, too, possess the capacity for abstract thinking, and their imaginative minds often shine in surprising ways. When a group of students collaborates on a school project, and they seamlessly combine unrelated elements like art, science, and storytelling to present a comprehensive narrative, they are using the skill of abstract thinking to turn ideas into a cohesive whole.

In mathematics, a child might recognize patterns across numbers, leading them to understand the concept of multiplication as a condensed form of addition. This insight showcases how abstract thought aids in comprehending complex mathematical relationships.

As children encounter abstract art, they embrace creativity without boundaries. They interpret emotions and concepts through color, shape, and form, demonstrating how abstract thinking lets them explore feelings beyond words.

Fostering abstract thinking in children equips them with tools for a lifelong journey of learning.

Concrete Actions To Foster Abstract Thought in Children

You can integrate day-to-day activities that spark abstract thinking. Encourage children to explore diverse perspectives, whether through discussing varying viewpoints on current events or immersing themselves in books with complex themes. Promote open-ended questions during conversations, inviting them to ponder "what if" scenarios and envision creative solutions. 

By weaving these practices into their routines, children develop the cognitive flexibility and analytical skills needed to thrive in a complex world.

Working To Improve Abstract Thought Processes

Nurturing abstract thinking skills leaves a lasting imprint. Armed with the ability to see beyond the surface, they approach life's complexities with a holistic perspective. It empowers them to dissect complex problems, recognize hidden patterns, and envision innovative solutions. 

For interactive stories, toys, and props that can help foster abstract thinking, check out the Big Heart Toys collection .

Figurative Language Comprehension in Individuals with Autism Spectrum Disorder | A Meta-Analytic Review | PMC

Piaget's Formal Operational Stage | Definition & Examples | Simply Psychology

Psychiatry.org | Rumination | A Cycle of Negative Thinking | Psychiatry

Traumatic Brain Injury (TBI) | National Institute of Neurological Disorders and Stroke

Mindfulness Exercises | Mayo Clinic

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What Is Cognitive Psychology?

The Science of How We Think

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

Steven Gans, MD is board-certified in psychiatry and is an active supervisor, teacher, and mentor at Massachusetts General Hospital.

Topics in Cognitive Psychology

• Current Research
• Cognitive Approach in Practice

Careers in Cognitive Psychology

How cognitive psychology differs from other branches of psychology, frequently asked questions.

Cognitive psychology involves the study of internal mental processes—all of the workings inside your brain, including perception, thinking, memory, attention, language, problem-solving, and learning.

Cognitive psychology--the study of how people think and process information--helps researchers understand the human brain. It also allows psychologists to help people deal with psychological difficulties.

This article discusses what cognitive psychology is, the history of this field, and current directions for research. It also covers some of the practical applications for cognitive psychology research and related career options you might consider.

Findings from cognitive psychology help us understand how people think, including how they acquire and store memories. By knowing more about how these processes work, psychologists can develop new ways of helping people with cognitive problems.

Cognitive psychologists explore a wide variety of topics related to thinking processes. Some of these include: 

• Attention --our ability to process information in the environment while tuning out irrelevant details
• Choice-based behavior --actions driven by a choice among other possibilities
• Decision-making
• Information processing
• Language acquisition --how we learn to read, write, and express ourselves
• Problem-solving
• Speech perception -how we process what others are saying
• Visual perception --how we see the physical world around us

History of Cognitive Psychology

Although it is a relatively young branch of psychology , it has quickly grown to become one of the most popular subfields. Cognitive psychology grew into prominence between the 1950s and 1970s.

Prior to this time, behaviorism was the dominant perspective in psychology. This theory holds that we learn all our behaviors from interacting with our environment. It focuses strictly on observable behavior, not thought and emotion. Then, researchers became more interested in the internal processes that affect behavior instead of just the behavior itself. 

This shift is often referred to as the cognitive revolution in psychology. During this time, a great deal of research on topics including memory, attention, and language acquisition began to emerge. 

In 1967, the psychologist Ulric Neisser introduced the term cognitive psychology, which he defined as the study of the processes behind the perception, transformation, storage, and recovery of information.

Cognitive psychology became more prominent after the 1950s as a result of the cognitive revolution.

Current Research in Cognitive Psychology

The field of cognitive psychology is both broad and diverse. It touches on many aspects of daily life. There are numerous practical applications for this research, such as providing help coping with memory disorders, making better decisions , recovering from brain injury, treating learning disorders, and structuring educational curricula to enhance learning.

Current research on cognitive psychology helps play a role in how professionals approach the treatment of mental illness, traumatic brain injury, and degenerative brain diseases.

Thanks to the work of cognitive psychologists, we can better pinpoint ways to measure human intellectual abilities, develop new strategies to combat memory problems, and decode the workings of the human brain—all of which ultimately have a powerful impact on how we treat cognitive disorders.

The field of cognitive psychology is a rapidly growing area that continues to add to our understanding of the many influences that mental processes have on our health and daily lives.

From understanding how cognitive processes change as a child develops to looking at how the brain transforms sensory inputs into perceptions, cognitive psychology has helped us gain a deeper and richer understanding of the many mental events that contribute to our daily existence and overall well-being.

The Cognitive Approach in Practice

In addition to adding to our understanding of how the human mind works, the field of cognitive psychology has also had an impact on approaches to mental health. Before the 1970s, many mental health treatments were focused more on psychoanalytic , behavioral , and humanistic approaches.

The so-called "cognitive revolution" put a greater emphasis on understanding the way people process information and how thinking patterns might contribute to psychological distress. Thanks to research in this area, new approaches to treatment were developed to help treat depression, anxiety, phobias, and other psychological disorders .

Cognitive behavioral therapy and rational emotive behavior therapy are two methods in which clients and therapists focus on the underlying cognitions, or thoughts, that contribute to psychological distress.

What Is Cognitive Behavioral Therapy?

Cognitive behavioral therapy (CBT) is an approach that helps clients identify irrational beliefs and other cognitive distortions that are in conflict with reality and then aid them in replacing such thoughts with more realistic, healthy beliefs.

If you are experiencing symptoms of a psychological disorder that would benefit from the use of cognitive approaches, you might see a psychologist who has specific training in these cognitive treatment methods.

These professionals frequently go by titles other than cognitive psychologists, such as psychiatrists, clinical psychologists , or counseling psychologists , but many of the strategies they use are rooted in the cognitive tradition.

Many cognitive psychologists specialize in research with universities or government agencies. Others take a clinical focus and work directly with people who are experiencing challenges related to mental processes. They work in hospitals, mental health clinics, and private practices.

Research psychologists in this area often concentrate on a particular topic, such as memory. Others work directly on health concerns related to cognition, such as degenerative brain disorders and brain injuries.

Treatments rooted in cognitive research focus on helping people replace negative thought patterns with more positive, realistic ones. With the help of cognitive psychologists, people are often able to find ways to cope and even overcome such difficulties.

Reasons to Consult a Cognitive Psychologist

• Alzheimer's disease, dementia, or memory loss
• Brain trauma treatment
• Cognitive therapy for a mental health condition
• Interventions for learning disabilities
• Perceptual or sensory issues
• Therapy for a speech or language disorder

Whereas behavioral and some other realms of psychology focus on actions--which are external and observable--cognitive psychology is instead concerned with the thought processes behind the behavior. Cognitive psychologists see the mind as if it were a computer, taking in and processing information, and seek to understand the various factors involved.

A Word From Verywell

Cognitive psychology plays an important role in understanding the processes of memory, attention, and learning. It can also provide insights into cognitive conditions that may affect how people function.

Being diagnosed with a brain or cognitive health problem can be daunting, but it is important to remember that you are not alone. Together with a healthcare provider, you can come up with an effective treatment plan to help address brain health and cognitive problems.

Your treatment may involve consulting with a cognitive psychologist who has a background in the specific area of concern that you are facing, or you may be referred to another mental health professional that has training and experience with your particular condition.

Ulric Neisser is considered the founder of cognitive psychology. He was the first to introduce the term and to define the field of cognitive psychology. His primary interests were in the areas of perception and memory, but he suggested that all aspects of human thought and behavior were relevant to the study of cognition.

A cognitive map refers to a mental representation of an environment. Such maps can be formed through observation as well as through trial and error. These cognitive maps allow people to orient themselves in their environment.

While they share some similarities, there are some important differences between cognitive neuroscience and cognitive psychology. While cognitive psychology focuses on thinking processes, cognitive neuroscience is focused on finding connections between thinking and specific brain activity. Cognitive neuroscience also looks at the underlying biology that influences how information is processed.

Cognitive psychology is a form of experimental psychology. Cognitive psychologists use experimental methods to study the internal mental processes that play a role in behavior.

Sternberg RJ, Sternberg K. Cognitive Psychology . Wadsworth/Cengage Learning. 

Krapfl JE. Behaviorism and society . Behav Anal. 2016;39(1):123-9. doi:10.1007/s40614-016-0063-8

Cutting JE. Ulric Neisser (1928-2012) . Am Psychol . 2012;67(6):492. doi:10.1037/a0029351

Ruggiero GM, Spada MM, Caselli G, Sassaroli S. A historical and theoretical review of cognitive behavioral therapies: from structural self-knowledge to functional processes .  J Ration Emot Cogn Behav Ther . 2018;36(4):378-403. doi:10.1007/s10942-018-0292-8

Parvin P. Ulric Neisser, cognitive psychology pioneer, dies . Emory News Center.

APA Dictionary of Psychology. Cognitive map . American Psychological Association.

Forstmann BU, Wagenmakers EJ, Eichele T, Brown S, Serences JT. Reciprocal relations between cognitive neuroscience and formal cognitive models: opposites attract? . Trends Cogn Sci . 2011;15(6):272-279. doi:10.1016/j.tics.2011.04.002

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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21 Problem Solving

Miriam Bassok, Department of Psychology, University of Washington, Seattle, WA

Laura R. Novick, Department of Psychology and Human Development, Vanderbilt University, Nashville, TN

• Published: 21 November 2012
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This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: ( 1 ) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and ( 2 ) research on search in a problem space (the legacy of Newell and Simon) that examined how people generate the problem's solution. It then describes some developments in the field that fueled the integration of these two lines of research: work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. Next, it presents examples of recent work on problem solving in science and mathematics that highlight the impact of visual perception and background knowledge on how people represent problems and search for problem solutions. The final section considers possible directions for future research.

People are confronted with problems on a daily basis, be it trying to extract a broken light bulb from a socket, finding a detour when the regular route is blocked, fixing dinner for unexpected guests, dealing with a medical emergency, or deciding what house to buy. Obviously, the problems people encounter differ in many ways, and their solutions require different types of knowledge and skills. Yet we have a sense that all the situations we classify as problems share a common core. Karl Duncker defined this core as follows: “A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action [i.e., by the performance of obvious operations], then there has to be recourse to thinking” (Duncker, 1945 , p. 1). Consider the broken light bulb. The obvious operation—holding the glass part of the bulb with one's fingers while unscrewing the base from the socket—is prevented by the fact that the glass is broken. Thus, there must be “recourse to thinking” about possible ways to solve the problem. For example, one might try mounting half a potato on the broken bulb (we do not know the source of this creative solution, which is described on many “how to” Web sites).

The above definition and examples make it clear that what constitutes a problem for one person may not be a problem for another person, or for that same person at another point in time. For example, the second time one has to remove a broken light bulb from a socket, the solution likely can be retrieved from memory; there is no problem. Similarly, tying shoes may be considered a problem for 5-year-olds but not for readers of this chapter. And, of course, people may change their goal and either no longer have a problem (e.g., take the guests to a restaurant instead of fixing dinner) or attempt to solve a different problem (e.g., decide what restaurant to go to). Given the highly subjective nature of what constitutes a problem, researchers who study problem solving have often presented people with novel problems that they should be capable of solving and attempted to find regularities in the resulting problem-solving behavior. Despite the variety of possible problem situations, researchers have identified important regularities in the thinking processes by which people (a) represent , or understand, problem situations and (b) search for possible ways to get to their goal.

A problem representation is a model constructed by the solver that summarizes his or her understanding of the problem components—the initial state (e.g., a broken light bulb in a socket), the goal state (the light bulb extracted), and the set of possible operators one may apply to get from the initial state to the goal state (e.g., use pliers). According to Reitman ( 1965 ), problem components differ in the extent to which they are well defined . Some components leave little room for interpretation (e.g., the initial state in the broken light bulb example is relatively well defined), whereas other components may be ill defined and have to be defined by the solver (e.g., the possible actions one may take to extract the broken bulb). The solver's representation of the problem guides the search for a possible solution (e.g., possible attempts at extracting the light bulb). This search may, in turn, change the representation of the problem (e.g., finding that the goal cannot be achieved using pliers) and lead to a new search. Such a recursive process of representation and search continues until the problem is solved or until the solver decides to abort the goal.

Duncker ( 1945 , pp. 28–37) documented the interplay between representation and search based on his careful analysis of one person's solution to the “Radiation Problem” (later to be used extensively in research analogy, see Holyoak, Chapter 13 ). This problem requires using some rays to destroy a patient's stomach tumor without harming the patient. At sufficiently high intensity, the rays will destroy the tumor. However, at that intensity, they will also destroy the healthy tissue surrounding the tumor. At lower intensity, the rays will not harm the healthy tissue, but they also will not destroy the tumor. Duncker's analysis revealed that the solver's solution attempts were guided by three distinct problem representations. He depicted these solution attempts as an inverted search tree in which the three main branches correspond to the three general problem representations (Duncker, 1945 , p. 32). We reproduce this diagram in Figure 21.1 . The desired solution appears on the rightmost branch of the tree, within the general problem representation in which the solver aims to “lower the intensity of the rays on their way through healthy tissue.” The actual solution is to project multiple low-intensity rays at the tumor from several points around the patient “by use of lens.” The low-intensity rays will converge on the tumor, where their individual intensities will sum to a level sufficient to destroy the tumor.

A search-tree representation of one subject's solution to the radiation problem, reproduced from Duncker ( 1945 , p. 32).

Although there are inherent interactions between representation and search, some researchers focus their efforts on understanding the factors that affect how solvers represent problems, whereas others look for regularities in how they search for a solution within a particular representation. Based on their main focus of interest, researchers devise or select problems with solutions that mainly require either constructing a particular representation or finding the appropriate sequence of steps leading from the initial state to the goal state. In most cases, researchers who are interested in problem representation select problems in which one or more of the components are ill defined, whereas those who are interested in search select problems in which the components are well defined. The following examples illustrate, respectively, these two problem types.

The Bird-and-Trains problem (Posner, 1973 , pp. 150–151) is a mathematical word problem that tends to elicit two distinct problem representations (see Fig. 21.2a and b ):

Two train stations are 50 miles apart. At 2 p.m. one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies ahead to the front of the second train. When the bird reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If both trains travel at the rate of 25 miles per hour and the bird flies at 100 miles per hour, how many miles will the bird have flown before the trains meet? Fig. 21.2 Open in new tab Download slide Alternative representations of Posner's ( 1973 ) trains-and-bird problem. Adapted from Novick and Hmelo ( 1994 ).

Some solvers focus on the back-and-forth path of the bird (Fig. 21.2a ). This representation yields a problem that would be difficult for most people to solve (e.g., a series of differential equations). Other solvers focus on the paths of the trains (Fig. 21.2b ), a representation that yields a relatively easy distance-rate-time problem.

The Tower of Hanoi problem falls on the other end of the representation-search continuum. It leaves little room for differences in problem representations, and the primary work is to discover a solution path (or the best solution path) from the initial state to the goal state .

There are three pegs mounted on a base. On the leftmost peg, there are three disks of differing sizes. The disks are arranged in order of size with the largest disk on the bottom and the smallest disk on the top. The disks may be moved one at a time, but only the top disk on a peg may be moved, and at no time may a larger disk be placed on a smaller disk. The goal is to move the three-disk tower from the leftmost peg to the rightmost peg.

Figure 21.3 shows all the possible legal arrangements of disks on pegs. The arrows indicate transitions between states that result from moving a single disk, with the thicker gray arrows indicating the shortest path that connects the initial state to the goal state.

The division of labor between research on representation versus search has distinct historical antecedents and research traditions. In the next two sections, we review the main findings from these two historical traditions. Then, we describe some developments in the field that fueled the integration of these lines of research—work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. In the fifth section, we present some examples of recent work on problem solving in science and mathematics. This work highlights the role of visual perception and background knowledge in the way people represent problems and search for problem solutions. In the final section, we consider possible directions for future research.

Our review is by no means an exhaustive one. It follows the historical development of the field and highlights findings that pertain to a wide variety of problems. Research pertaining to specific types of problems (e.g., medical problems), specific processes that are involved in problem solving (e.g., analogical inferences), and developmental changes in problem solving due to learning and maturation may be found elsewhere in this volume (e.g., Holyoak, Chapter 13 ; Smith & Ward, Chapter 23 ; van Steenburgh et al., Chapter 24 ; Simonton, Chapter 25 ; Opfer & Siegler, Chapter 30 ; Hegarty & Stull, Chapter 31 ; Dunbar & Klahr, Chapter 35 ; Patel et al., Chapter 37 ; Lowenstein, Chapter 38 ; Koedinger & Roll, Chapter 40 ).

All possible problem states for the three-disk Tower of Hanoi problem. The thicker gray arrows show the optimum solution path connecting the initial state (State #1) to the goal state (State #27).

Problem Representation: The Gestalt Legacy

Research on problem representation has its origins in Gestalt psychology, an influential approach in European psychology during the first half of the 20th century. (Behaviorism was the dominant perspective in American psychology at this time.) Karl Duncker published a book on the topic in his native German in 1935, which was translated into English and published 10 years later as the monograph On Problem-Solving (Duncker, 1945 ). Max Wertheimer also published a book on the topic in 1945, titled Productive Thinking . An enlarged edition published posthumously includes previously unpublished material (Wertheimer, 1959 ). Interestingly, 1945 seems to have been a watershed year for problem solving, as mathematician George Polya's book, How to Solve It , also appeared then (a second edition was published 12 years later; Polya, 1957 ).

The Gestalt psychologists extended the organizational principles of visual perception to the domain of problem solving. They showed that various visual aspects of the problem, as well the solver's prior knowledge, affect how people understand problems and, therefore, generate problem solutions. The principles of visual perception (e.g., proximity, closure, grouping, good continuation) are directly relevant to problem solving when the physical layout of the problem, or a diagram that accompanies the problem description, elicits inferences that solvers include in their problem representations. Such effects are nicely illustrated by Maier's ( 1930 ) nine-dot problem: Nine dots are arrayed in a 3x3 grid, and the task is to connect all the dots by drawing four straight lines without lifting one's pencil from the paper. People have difficulty solving this problem because their initial representations generally include a constraint, inferred from the configuration of the dots, that the lines should not go outside the boundary of the imaginary square formed by the outer dots. With this constraint, the problem cannot be solved (but see Adams, 1979 ). Without this constraint, the problem may be solved as shown in Figure 21.4 (though the problem is still difficult for many people; see Weisberg & Alba, 1981 ).

The nine-dot problem is a classic insight problem (see van Steenburgh et al., Chapter 24 ). According to the Gestalt view (e.g., Duncker, 1945 ; Kohler, 1925 ; Maier, 1931 ; see Ohlsson, 1984 , for a review), the solution to an insight problem appears suddenly, accompanied by an “aha!” sensation, immediately following the sudden “restructuring” of one's understanding of the problem (i.e., a change in the problem representation): “The decisive points in thought-processes, the moments of sudden comprehension, of the ‘Aha!,’ of the new, are always at the same time moments in which such a sudden restructuring of the thought-material takes place” (Duncker, 1945 , p. 29). For the nine-dot problem, one view of the required restructuring is that the solver relaxes the constraint implied by the perceptual form of the problem and realizes that the lines may, in fact, extend past the boundary of the imaginary square. Later in the chapter, we present more recent accounts of insight.

The entities that appear in a problem also tend to evoke various inferences that people incorporate into their problem representations. A classic demonstration of this is the phenomenon of functional fixedness , introduced by Duncker ( 1945 ): If an object is habitually used for a certain purpose (e.g., a box serves as a container), it is difficult to see

A solution to the nine-dot problem.

that object as having properties that would enable it to be used for a dissimilar purpose. Duncker's basic experimental paradigm involved two conditions that varied in terms of whether the object that was crucial for solution was initially used for a function other than that required for solution.

Consider the candles problem—the best known of the five “practical problems” Duncker ( 1945 ) investigated. Three candles are to be mounted at eye height on a door. On the table, for use in completing this task, are some tacks and three boxes. The solution is to tack the three boxes to the door to serve as platforms for the candles. In the control condition, the three boxes were presented to subjects empty. In the functional-fixedness condition, they were filled with candles, tacks, and matches. Thus, in the latter condition, the boxes initially served the function of container, whereas the solution requires that they serve the function of platform. The results showed that 100% of the subjects who received empty boxes solved the candles problem, compared with only 43% of subjects who received filled boxes. Every one of the five problems in this study showed a difference favoring the control condition over the functional-fixedness condition, with average solution rates across the five problems of 97% and 58%, respectively.

The function of the objects in a problem can be also “fixed” by their most recent use. For example, Birch and Rabinowitz ( 1951 ) had subjects perform two consecutive tasks. In the first task, people had to use either a switch or a relay to form an electric circuit. After completing this task, both groups of subjects were asked to solve Maier's ( 1931 ) two-ropes problem. The solution to this problem requires tying an object to one of the ropes and making the rope swing as a pendulum. Subjects could create the pendulum using either the object from the electric-circuit task or the other object. Birch and Rabinowitz found that subjects avoided using the same object for two unrelated functions. That is, those who used the switch in the first task made the pendulum using the relay, and vice versa. The explanations subjects subsequently gave for their object choices revealed that they were unaware of the functional-fixedness constraint they imposed on themselves.

In addition to investigating people's solutions to such practical problems as irradiating a tumor, mounting candles on the wall, or tying ropes, the Gestalt psychologists examined how people understand and solve mathematical problems that require domain-specific knowledge. For example, Wertheimer ( 1959 ) observed individual differences in students' learning and subsequent application of the formula for finding the area of a parallelogram (see Fig. 21.5a ). Some students understood the logic underlying the learned formula (i.e., the fact that a parallelogram can be transformed into a rectangle by cutting off a triangle from one side and pasting it onto the other side) and exhibited “productive thinking”—using the same logic to find the area of the quadrilateral in Figure 21.5b and the irregularly shaped geometric figure in Figure 21.5c . Other students memorized the formula and exhibited “reproductive thinking”—reproducing the learned solution only to novel parallelograms that were highly similar to the original one.

The psychological study of human problem solving faded into the background after the demise of the Gestalt tradition (during World War II), and problem solving was investigated only sporadically until Allen Newell and Herbert Simon's ( 1972 ) landmark book Human Problem Solving sparked a flurry of research on this topic. Newell and Simon adopted and refined Duncker's ( 1945 ) methodology of collecting and analyzing the think-aloud protocols that accompany problem solutions and extended Duncker's conceptualization of a problem solution as a search tree. However, their initial work did not aim to extend the Gestalt findings

Finding the area of ( a ) a parallelogram, ( b ) a quadrilateral, and ( c ) an irregularly shaped geometric figure. The solid lines indicate the geometric figures whose areas are desired. The dashed lines show how to convert the given figures into rectangles (i.e., they show solutions with understanding).

pertaining to problem representation. Instead, as we explain in the next section, their objective was to identify the general-purpose strategies people use in searching for a problem solution.

Search in a Problem Space: The Legacy of Newell and Simon

Newell and Simon ( 1972 ) wrote a magnum opus detailing their theory of problem solving and the supporting research they conducted with various collaborators. This theory was grounded in the information-processing approach to cognitive psychology and guided by an analogy between human and artificial intelligence (i.e., both people and computers being “Physical Symbol Systems,” Newell & Simon, 1976 ; see Doumas & Hummel, Chapter 5 ). They conceptualized problem solving as a process of search through a problem space for a path that connects the initial state to the goal state—a metaphor that alludes to the visual or spatial nature of problem solving (Simon, 1990 ). The term problem space refers to the solver's representation of the task as presented (Simon, 1978 ). It consists of ( 1 ) a set of knowledge states (the initial state, the goal state, and all possible intermediate states), ( 2 ) a set of operators that allow movement from one knowledge state to another, ( 3 ) a set of constraints, and ( 4 ) local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

We illustrate the components of a problem space for the three-disk Tower of Hanoi problem, as depicted in Figure 21.3 . The initial state appears at the top (State #1) and the goal state at the bottom right (State #27). The remaining knowledge states in the figure are possible intermediate states. The current knowledge state is the one at which the solver is located at any given point in the solution process. For example, the current state for a solver who has made three moves along the optimum solution path would be State #9. The solver presumably would know that he or she arrived at this state from State #5. This knowledge allows the solver to recognize a move that involves backtracking. The three operators in this problem are moving each of the three disks from one peg to another. These operators are subject to the constraint that a larger disk may not be placed on a smaller disk.

Newell and Simon ( 1972 ), as well as other contemporaneous researchers (e.g., Atwood & Polson, 1976 ; Greeno, 1974 ; Thomas, 1974 ), examined how people traverse the spaces of various well-defined problems (e.g., the Tower of Hanoi, Hobbits and Orcs). They discovered that solvers' search is guided by a number of shortcut strategies, or heuristics , which are likely to get the solver to the goal state without an extensive amount of search. Heuristics are often contrasted with algorithms —methods that are guaranteed to yield the correct solution. For example, one could try every possible move in the three-disk Tower of Hanoi problem and, eventually, find the correct solution. Although such an exhaustive search is a valid algorithm for this problem, for many problems its application is very time consuming and impractical (e.g., consider the game of chess).

In their attempts to identify people's search heuristics, Newell and Simon ( 1972 ) relied on two primary methodologies: think-aloud protocols and computer simulations. Their use of think-aloud protocols brought a high degree of scientific rigor to the methodology used by Duncker ( 1945 ; see Ericsson & Simon, 1980 ). Solvers were required to say out loud everything they were thinking as they solved the problem, that is, everything that went through their verbal working memory. Subjects' verbalizations—their think-aloud protocols—were tape-recorded and then transcribed verbatim for analysis. This method is extremely time consuming (e.g., a transcript of one person's solution to the cryptarithmetic problem DONALD + GERALD = ROBERT, with D = 5, generated a 17-page transcript), but it provides a detailed record of the solver's ongoing solution process.

An important caveat to keep in mind while interpreting a subject's verbalizations is that “a protocol is relatively reliable only for what it positively contains, but not for that which it omits” (Duncker, 1945 , p. 11). Ericsson and Simon ( 1980 ) provided an in-depth discussion of the conditions under which this method is valid (but see Russo, Johnson, & Stephens, 1989 , for an alternative perspective). To test their interpretation of a subject's problem solution, inferred from the subject's verbal protocol, Newell and Simon ( 1972 ) created a computer simulation program and examined whether it solved the problem the same way the subject did. To the extent that the computer simulation provided a close approximation of the solver's step-by-step solution process, it lent credence to the researcher's interpretation of the verbal protocol.

Newell and Simon's ( 1972 ) most famous simulation was the General Problem Solver or GPS (Ernst & Newell, 1969 ). GPS successfully modeled human solutions to problems as different as the Tower of Hanoi and the construction of logic proofs using a single general-purpose heuristic: means-ends analysis . This heuristic captures people's tendency to devise a solution plan by setting subgoals that could help them achieve their final goal. It consists of the following steps: ( 1 ) Identify a difference between the current state and the goal (or subgoal ) state; ( 2 ) Find an operator that will remove (or reduce) the difference; (3a) If the operator can be directly applied, do so, or (3b) If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator; ( 4 ) Repeat steps 1–3 until the problem is solved. Next, we illustrate the implementation of this heuristic for the Tower of Hanoi problem, using the problem space in Figure 21.3 .

As can be seen in Figure 21.3 , a key difference between the initial state and the goal state is that the large disk is on the wrong peg (step 1). To remove this difference (step 2), one needs to apply the operator “move-large-disk.” However, this operator cannot be applied because of the presence of the medium and small disks on top of the large disk. Therefore, the solver may set a subgoal to move that two-disk tower to the middle peg (step 3b), leaving the rightmost peg free for the large disk. A key difference between the initial state and this new subgoal state is that the medium disk is on the wrong peg. Because application of the move-medium-disk operator is blocked, the solver sets another subgoal to move the small disk to the right peg. This subgoal can be satisfied immediately by applying the move-small-disk operator (step 3a), generating State #3. The solver then returns to the previous subgoal—moving the tower consisting of the small and medium disks to the middle peg. The differences between the current state (#3) and the subgoal state (#9) can be removed by first applying the move-medium-disk operator (yielding State #5) and then the move-small-disk operator (yielding State #9). Finally, the move-large-disk operator is no longer blocked. Hence, the solver moves the large disk to the right peg, yielding State #11.

Notice that the subgoals are stacked up in the order in which they are generated, so that they pop up in the order of last in first out. Given the first subgoal in our example, repeated application of the means-ends analysis heuristic will yield the shortest-path solution, indicated by the large gray arrows. In general, subgoals provide direction to the search and allow solvers to plan several moves ahead. By assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise. To take a concrete example, consider the transition from State #1 to State #3 in Figure 21.3 . Comparing the initial state to the goal state, this move seems unwise because it places the small disk on the bottom of the right peg, whereas it ultimately needs to be at the top of the tower on that peg. But comparing the initial state to the solver-generated subgoal state of having the medium disk on the middle peg, this is exactly where the small disk needs to go.

Means-ends analysis and various other heuristics (e.g., the hill-climbing heuristic that exploits the similarity, or distance, between the state generated by the next operator and the goal state; working backward from the goal state to the initial state) are flexible strategies that people often use to successfully solve a large variety of problems. However, the generality of these heuristics comes at a cost: They are relatively weak and fallible (e.g., in the means-ends solution to the problem of fixing a hole in a bucket, “Dear Liza” leads “Dear Henry” in a loop that ends back at the initial state; the lyrics of this famous song can be readily found on the Web). Hence, although people use general-purpose heuristics when they encounter novel problems, they replace them as soon as they acquire experience with and sufficient knowledge about the particular problem space (e.g., Anzai & Simon, 1979 ).

Despite the fruitfulness of this research agenda, it soon became evident that a fundamental weakness was that it minimized the importance of people's background knowledge. Of course, Newell and Simon ( 1972 ) were aware that problem solutions require relevant knowledge (e.g., the rules of logical proofs, or rules for stacking disks). Hence, in programming GPS, they supplemented every problem they modeled with the necessary background knowledge. This practice highlighted the generality and flexibility of means-ends analysis but failed to capture how people's background knowledge affects their solutions. As we discussed in the previous section, domain knowledge is likely to affect how people represent problems and, therefore, how they generate problem solutions. Moreover, as people gain experience solving problems in a particular knowledge domain (e.g., math, physics), they change their representations of these problems (e.g., Chi, Feltovich, & Glaser, 1981 ; Haverty, Koedinger, Klahr, & Alibali, 2000 ; Schoenfeld & Herrmann, 1982 ) and learn domain-specific heuristics (e.g., Polya, 1957 ; Schoenfeld, 1979 ) that trump the general-purpose strategies.

It is perhaps inevitable that the two traditions in problem-solving research—one emphasizing representation and the other emphasizing search strategies—would eventually come together. In the next section we review developments that led to this integration.

The Two Legacies Converge

Because Newell and Simon ( 1972 ) aimed to discover the strategies people use in searching for a solution, they investigated problems that minimized the impact of factors that tend to evoke differences in problem representations, of the sort documented by the Gestalt psychologists. In subsequent work, however, Simon and his collaborators showed that such factors are highly relevant to people's solutions of well-defined problems, and Simon ( 1986 ) incorporated these findings into the theoretical framework that views problem solving as search in a problem space.

In this section, we first describe illustrative examples of this work. We then describe research on insight solutions that incorporates ideas from the two legacies described in the previous sections.

Relevance of the Gestalt Ideas to the Solution of Search Problems

In this subsection we describe two lines of research by Simon and his colleagues, and by other researchers, that document the importance of perception and of background knowledge to the way people search for a problem solution. The first line of research used variants of relatively well-defined riddle problems that had the same structure (i.e., “problem isomorphs”) and, therefore, supposedly the same problem space. It documented that people's search depended on various perceptual and conceptual inferences they tended to draw from a specific instantiation of the problem's structure. The second line of research documented that people's search strategies crucially depend on their domain knowledge and on their prior experience with related problems.

Problem Isomorphs

Hayes and Simon ( 1977 ) used two variants of the Tower of Hanoi problem that, instead of disks and pegs, involved monsters and globes that differed in size (small, medium, and large). In both variants, the initial state had the small monster holding the large globe, the medium-sized monster holding the small globe, and the large monster holding the medium-sized globe. Moreover, in both variants the goal was for each monster to hold a globe proportionate to its own size. The only difference between the problems concerned the description of the operators. In one variant (“transfer”), subjects were told that the monsters could transfer the globes from one to another as long as they followed a set of rules, adapted from the rules in the original Tower of Hanoi problem (e.g., only one globe may be transferred at a time). In the other variant (“change”), subjects were told that the monsters could shrink and expand themselves according to a set of rules, which corresponded to the rules in the transfer version of the problem (e.g., only one monster may change its size at a time). Despite the isomorphism of the two variants, subjects conducted their search in two qualitatively different problem spaces, which led to solution times for the change variant being almost twice as long as those for the transfer variant. This difference arose because subjects could more readily envision and track an object that was changing its location with every move than one that was changing its size.

Recent work by Patsenko and Altmann ( 2010 ) found that, even in the standard Tower of Hanoi problem, people's solutions involve object-bound routines that depend on perception and selective attention. The subjects in their study solved various Tower of Hanoi problems on a computer. During the solution of a particular “critical” problem, the computer screen changed at various points without subjects' awareness (e.g., a disk was added, such that a subject who started with a five-disc tower ended with a six-disc tower). Patsenko and Altmann found that subjects' moves were guided by the configurations of the objects on the screen rather than by solution plans they had stored in memory (e.g., the next subgoal).

The Gestalt psychologists highlighted the role of perceptual factors in the formation of problem representations (e.g., Maier's, 1930 , nine-dot problem) but were generally silent about the corresponding implications for how the problem was solved (although they did note effects on solution accuracy). An important contribution of the work on people's solutions of the Tower of Hanoi problem and its variants was to show the relevance of perceptual factors to the application of various operators during search for a problem solution—that is, to the how of problem solving. In the next section, we describe recent work that documents the involvement of perceptual factors in how people understand and use equations and diagrams in the context of solving math and science problems.

Kotovsky, Hayes, and Simon ( 1985 ) further investigated factors that affect people's representation and search in isomorphs of the Tower of Hanoi problem. In one of their isomorphs, three disks were stacked on top of each other to form an inverted pyramid, with the smallest disc on the bottom and the largest on top. Subjects' solutions of the inverted pyramid version were similar to their solutions of the standard version that has the largest disc on the bottom and the smallest on top. However, the two versions were solved very differently when subjects were told that the discs represent acrobats. Subjects readily solved the version in which they had to place a small acrobat on the shoulders of a large one, but they refrained from letting a large acrobat stand on the shoulders of a small one. In other words, object-based inferences that draw on people's semantic knowledge affected the solution of search problems, much as they affect the solution of the ill-defined problems investigated by the Gestalt psychologists (e.g., Duncker's, 1945 , candles problem). In the next section, we describe more recent work that shows similar effects in people's solutions to mathematical word problems.

The work on differences in the representation and solution of problem isomorphs is highly relevant to research on analogical problem solving (or analogical transfer), which examines when and how people realize that two problems that differ in their cover stories have a similar structure (or a similar problem space) and, therefore, can be solved in a similar way. This research shows that minor differences between example problems, such as the use of X-rays versus ultrasound waves to fuse a broken filament of a light bulb, can elicit different problem representations that significantly affect the likelihood of subsequent transfer to novel problem analogs (Holyoak & Koh, 1987 ). Analogical transfer has played a central role in research on human problem solving, in part because it can shed light on people's understanding of a given problem and its solution and in part because it is believed to provide a window onto understanding and investigating creativity (see Smith & Ward, Chapter 23 ). We briefly mention some findings from the analogy literature in the next subsection on expertise, but we do not discuss analogical transfer in detail because this topic is covered elsewhere in this volume (Holyoak, Chapter 13 ).

Expertise and Its Development

In another line of research, Simon and his colleagues examined how people solve ecologically valid problems from various rule-governed and knowledge-rich domains. They found that people's level of expertise in such domains, be it in chess (Chase & Simon, 1973 ; Gobet & Simon, 1996 ), mathematics (Hinsley, Hayes, & Simon, 1977 ; Paige & Simon, 1966 ), or physics (Larkin, McDermott, Simon, & Simon, 1980 ; Simon & Simon, 1978 ), plays a crucial role in how they represent problems and search for solutions. This work, and the work of numerous other researchers, led to the discovery (and rediscovery, see Duncker, 1945 ) of important differences between experts and novices, and between “good” and “poor” students.

One difference between experts and novices pertains to pattern recognition. Experts' attention is quickly captured by familiar configurations within a problem situation (e.g., a familiar configuration of pieces in a chess game). In contrast, novices' attention is focused on isolated components of the problem (e.g., individual chess pieces). This difference, which has been found in numerous domains, indicates that experts have stored in memory many meaningful groups (chunks) of information: for example, chess (Chase & Simon, 1973 ), circuit diagrams (Egan & Schwartz, 1979 ), computer programs (McKeithen, Reitman, Rueter, & Hirtle, 1981 ), medicine (Coughlin & Patel, 1987 ; Myles-Worsley, Johnston, & Simons, 1988 ), basketball and field hockey (Allard & Starkes, 1991 ), and figure skating (Deakin & Allard, 1991 ).

The perceptual configurations that domain experts readily recognize are associated with stored solution plans and/or compiled procedures (Anderson, 1982 ). As a result, experts' solutions are much faster than, and often qualitatively different from, the piecemeal solutions that novice solvers tend to construct (e.g., Larkin et al., 1980 ). In effect, experts often see the solutions that novices have yet to compute (e.g., Chase & Simon, 1973 ; Novick & Sherman, 2003 , 2008 ). These findings have led to the design of various successful instructional interventions (e.g., Catrambone, 1998 ; Kellman et al., 2008 ). For example, Catrambone ( 1998 ) perceptually isolated the subgoals of a statistics problem. This perceptual chunking of meaningful components of the problem prompted novice students to self-explain the meaning of the chunks, leading to a conceptual understanding of the learned solution. In the next section, we describe some recent work that shows the beneficial effects of perceptual pattern recognition on the solution of familiar mathematics problems, as well as the potentially detrimental effects of familiar perceptual chunks to understanding and reasoning with diagrams depicting evolutionary relationships among taxa.

Another difference between experts and novices pertains to their understanding of the solution-relevant problem structure. Experts' knowledge is highly organized around domain principles, and their problem representations tend to reflect this principled understanding. In particular, they can extract the solution-relevant structure of the problems they encounter (e.g., meaningful causal relations among the objects in the problem; see Cheng & Buehner, Chapter 12 ). In contrast, novices' representations tend to be bound to surface features of the problems that may be irrelevant to solution (e.g., the particular objects in a problem). For example, Chi, Feltovich, and Glaser ( 1981 ) examined how students with different levels of physics expertise group mechanics word problems. They found that advanced graduate students grouped the problems based on the physics principles relevant to the problems' solutions (e.g., conservation of energy, Newton's second law). In contrast, undergraduates who had successfully completed an introductory course in mechanics grouped the problems based on the specific objects involved (e.g., pulley problems, inclined plane problems). Other researchers have found similar results in the domains of biology, chemistry, computer programming, and math (Adelson, 1981 ; Kindfield, 1993 / 1994 ; Kozma & Russell, 1997 ; McKeithen et al., 1981 ; Silver, 1979 , 1981 ; Weiser & Shertz, 1983 ).

The level of domain expertise and the corresponding representational differences are, of course, a matter of degree. With increasing expertise, there is a gradual change in people's focus of attention from aspects that are not relevant to solution to those that are (e.g., Deakin & Allard, 1991 ; Hardiman, Dufresne, & Mestre, 1989 ; McKeithen et al., 1981 ; Myles-Worsley et al., 1988 ; Schoenfeld & Herrmann, 1982 ; Silver, 1981 ). Interestingly, Chi, Bassok, Lewis, Reimann, and Glaser ( 1989 ) found similar differences in focus on structural versus surface features among a group of novices who studied worked-out examples of mechanics problems. These differences, which echo Wertheimer's ( 1959 ) observations of individual differences in students' learning about the area of parallelograms, suggest that individual differences in people's interests and natural abilities may affect whether, or how quickly, they acquire domain expertise.

An important benefit of experts' ability to focus their attention on solution-relevant aspects of problems is that they are more likely than novices to recognize analogous problems that involve different objects and cover stories (e.g., Chi et al., 1989 ; Novick, 1988 ; Novick & Holyoak, 1991 ; Wertheimer, 1959 ) or that come from other knowledge domains (e.g., Bassok & Holyoak, 1989 ; Dunbar, 2001 ; Goldstone & Sakamoto, 2003 ). For example, Bassok and Holyoak ( 1989 ) found that, after learning to solve arithmetic-progression problems in algebra, subjects spontaneously applied these algebraic solutions to analogous physics problems that dealt with constantly accelerated motion. Note, however, that experts and good students do not simply ignore the surface features of problems. Rather, as was the case in the problem isomorphs we described earlier (Kotovsky et al., 1985 ), they tend to use such features to infer what the problem's structure could be (e.g., Alibali, Bassok, Solomon, Syc, & Goldin-Meadow, 1999 ; Blessing & Ross, 1996 ). For example, Hinsley et al. ( 1977 ) found that, after reading no more than the first few words of an algebra word problem, expert solvers classified the problem into a likely problem category (e.g., a work problem, a distance problem) and could predict what questions they might be asked and the equations they likely would need to use.

Surface-based problem categorization has a heuristic value (Medin & Ross, 1989 ): It does not ensure a correct categorization (Blessing & Ross, 1996 ), but it does allow solvers to retrieve potentially appropriate solutions from memory and to use them, possibly with some adaptation, to solve a variety of novel problems. Indeed, although experts exploit surface-structure correlations to save cognitive effort, they have the capability to realize that a particular surface cue is misleading (Hegarty, Mayer, & Green, 1992 ; Lewis & Mayer, 1987 ; Martin & Bassok, 2005 ; Novick 1988 , 1995 ; Novick & Holyoak, 1991 ). It is not surprising, therefore, that experts may revert to novice-like heuristic methods when solving problems under pressure (e.g., Beilock, 2008 ) or in subdomains in which they have general but not specific expertise (e.g., Patel, Groen, & Arocha, 1990 ).

Relevance of Search to Insight Solutions

We introduced the notion of insight in our discussion of the nine-dot problem in the section on the Gestalt tradition. The Gestalt view (e.g., Duncker, 1945 ; Maier, 1931 ; see Ohlsson, 1984 , for a review) was that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one's problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving problems by insight was believed to be all about representation, with essentially no role for a step-by-step solution process (i.e., search). Subsequent and contemporary researchers have generally concurred with the Gestalt view that getting the right representation is crucial. However, research has shown that insight solutions do not necessarily arise suddenly or full blown after restructuring (e.g., Weisberg & Alba, 1981 ); and even when they do, the underlying solution process (in this case outside of awareness) may reflect incremental progress toward the goal (Bowden & Jung-Beeman, 2003 ; Durso, Rea, & Dayton, 1994 ; Novick & Sherman, 2003 ).

“Demystifying insight,” to borrow a phrase from Bowden, Jung-Beeman, Fleck, and Kounios ( 2005 ), requires explaining ( 1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, ( 2 ) how the restructuring occurred, and ( 3 ) how it led to the solution. A detailed discussion of these topics appears elsewhere in this volume (van Steenburgh et al., Chapter 24 ). Here, we describe briefly three recent theories that have attempted to account for various aspects of these phenomena: Knoblich, Ohlsson, Haider, and Rhenius's ( 1999 ) representational change theory, MacGregor, Ormerod, and Chronicle's ( 2001 ) progress monitoring theory, and Bowden et al.'s ( 2005 ) neurological model. We then propose the need for an integrated approach to demystifying insight that considers both representation and search.

According to Knoblich et al.'s ( 1999 ) representational change theory, problems that are solved with insight are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts, leading to an impasse. An impasse can be resolved by revising one's representation of the problem. Knoblich and his colleagues tested this theory using Roman numeral matchstick arithmetic problems in which solvers must move one stick to a new location to change a false numerical statement (e.g., I = II + II ) into a statement that is true. According to representational change theory, re-representation may occur through either constraint relaxation or chunk decomposition. (The solution to the example problem is to change II + to III – , which requires both methods of re-representation, yielding I = III – II ). Good support for this theory has been found based on measures of solution rate, solution time, and eye fixation (Knoblich et al., 1999 ; Knoblich, Ohlsson, & Raney, 2001 ; Öllinger, Jones, & Knoblich, 2008 ).

Progress monitoring theory (MacGregor et al., 2001 ) was proposed to account for subjects' difficulty in solving the nine-dot problem, which has traditionally been classified as an insight problem. According to this theory, solvers use the hill-climbing search heuristic to solve this problem, just as they do for traditional search problems (e.g., Hobbits and Orcs). In particular, solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem's current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints. MacGregor et al. found support for this theory using several variants of the nine-dot problem (also see Ormerod, MacGregor, & Chronicle, 2002 ). Jones ( 2003 ) suggested that progress monitoring theory provides an account of the solution process up to the point an impasse is reached and representational change is sought, at which point representational change theory picks up and explains how insight may be achieved. Hence, it appears that a complete account of insight may require an integration of concepts from the Gestalt (representation) and Newell and Simon's (search) legacies.

Bowden et al.'s ( 2005 ) neurological model emphasizes the overlap between problem solving and language comprehension, and it hinges on differential processing in the right and left hemispheres. They proposed that an impasse is reached because initial processing of the problem produces strong activation of information irrelevant to solution in the left hemisphere. At the same time, weak semantic activation of alternative semantic interpretations, critical for solution, occurs in the right hemisphere. Insight arises when the weakly activated concepts reinforce each other, eventually rising above the threshold required for conscious awareness. Several studies of problem solving using compound remote associates problems, involving both behavioral and neuroimaging data, have found support for this model (Bowden & Jung-Beeman, 1998 , 2003 ; Jung-Beeman & Bowden, 2000 ; Jung-Beeman et al., 2004 ; also see Moss, Kotovsky, & Cagan, 2011 ).

Note that these three views of insight have received support using three quite distinct types of problems (Roman numeral matchstick arithmetic problems, the nine-dot problem, and compound remote associates problems, respectively). It remains to be established, therefore, whether these accounts can be generalized across problems. Kershaw and Ohlsson ( 2004 ) argued that insight problems are difficult because the key behavior required for solution may be hindered by perceptual factors (the Gestalt view), background knowledge (so expertise may be important; e.g., see Novick & Sherman, 2003 , 2008 ), and/or process factors (e.g., those affecting search). From this perspective, solving visual problems (e.g., the nine-dot problem) with insight may call upon more general visual processes, whereas solving verbal problems (e.g., anagrams, compound remote associates) with insight may call upon general verbal/semantic processes.

The work we reviewed in this section shows the relevance of problem representation (the Gestalt legacy) to the way people search the problem space (the legacy of Newell and Simon), and the relevance of search to the solution of insight problems that require a representational change. In addition to this inevitable integration of the two legacies, the work we described here underscores the fact that problem solving crucially depends on perceptual factors and on the solvers' background knowledge. In the next section, we describe some recent work that shows the involvement of these factors in the solution of problems in math and science.

Effects of Perception and Knowledge in Problem Solving in Academic Disciplines

Although the use of puzzle problems continues in research on problem solving, especially in investigations of insight, many contemporary researchers tackle problem solving in knowledge-rich domains, often in academic disciplines (e.g., mathematics, biology, physics, chemistry, meteorology). In this section, we provide a sampling of this research that highlights the importance of visual perception and background knowledge for successful problem solving.

The Role of Visual Perception

We stated at the outset that a problem representation (e.g., the problem space) is a model of the problem constructed by solvers to summarize their understanding of the problem's essential nature. This informal definition refers to the internal representations people construct and hold in working memory. Of course, people may also construct various external representations (Markman, 1999 ) and even manipulate those representations to aid in solution (see Hegarty & Stull, Chapter 31 ). For example, solvers often use paper and pencil to write notes or draw diagrams, especially when solving problems from formal domains (e.g., Cox, 1999 ; Kindfield, 1993 / 1994 ; S. Schwartz, 1971 ). In problems that provide solvers with external representation, such as the Tower of Hanoi problem, people's planning and memory of the current state is guided by the actual configurations of disks on pegs (Garber & Goldin-Meadow, 2002 ) or by the displays they see on a computer screen (Chen & Holyoak, 2010 ; Patsenko & Altmann, 2010 ).

In STEM (science, technology, engineering, and mathematics) disciplines, it is common for problems to be accompanied by diagrams or other external representations (e.g., equations) to be used in determining the solution. Larkin and Simon ( 1987 ) examined whether isomorphic sentential and diagrammatic representations are interchangeable in terms of facilitating solution. They argued that although the two formats may be equivalent in the sense that all of the information in each format can be inferred from the other format (informational equivalence), the ease or speed of making inferences from the two formats might differ (lack of computational equivalence). Based on their analysis of several problems in physics and math, Larkin and Simon further argued for the general superiority of diagrammatic representations (but see Mayer & Gallini, 1990 , for constraints on this general conclusion).

Novick and Hurley ( 2001 , p. 221) succinctly summarized the reasons for the general superiority of diagrams (especially abstract or schematic diagrams) over verbal representations: They “(a) simplify complex situations by discarding unnecessary details (e.g., Lynch, 1990 ; Winn, 1989 ), (b) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989 ), and (c) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991 ; Larkin & Simon, 1987 ).” Despite these benefits of diagrammatic representations, there is an important caveat, noted by Larkin and Simon ( 1987 , p. 99) at the very end of their paper: “Although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process.” We will see evidence of this in several of the studies reviewed in this section.

Next we describe recent work on perceptual factors that are involved in people's use of two types of external representations that are provided as part of the problem in two STEM disciplines: equations in algebra and diagrams in evolutionary biology. Although we focus here on effects of perceptual factors per se, it is important to note that such factors only influence performance when subjects have background knowledge that supports differential interpretation of the alternative diagrammatic depictions presented (Hegarty, Canham, & Fabricant, 2010 ).

In the previous section, we described the work of Patsenko and Altmann ( 2010 ) that shows direct involvement of visual attention and perception in the sequential application of move operators during the solution of the Tower of Hanoi problem. A related body of work documents similar effects in tasks that require the interpretation and use of mathematical equations (Goldstone, Landy, & Son, 2010 ; Landy & Goldstone, 2007a , b). For example, Landy and Goldstone ( 2007b ) varied the spatial proximity of arguments to the addition (+) and multiplication (*) operators in algebraic equations, such that the spatial layout of the equation was either consistent or inconsistent with the order-of-operations rule that multiplication precedes addition. In consistent equations , the space was narrower around multiplication than around addition (e.g., g*m + r*w = m*g + w*r ), whereas in inconsistent equations this relative spacing was reversed (e.g., s * n+e * c = n * s+c * e ). Subjects' judgments of the validity of such equations (i.e., whether the expressions on the two sides of the equal sign are equivalent) were significantly faster and more accurate for consistent than inconsistent equations.

In discussing these findings and related work with other external representations, Goldstone et al. ( 2010 ) proposed that experience with solving domain-specific problems leads people to “rig up” their perceptual system such that it allows them to look at the problem in a way that is consistent with the correct rules. Similar logic guides the Perceptual Learning Modules developed by Kellman and his collaborators to help students interpret and use algebraic equations and graphs (Kellman et al., 2008 ; Kellman, Massey, & Son, 2009 ). These authors argued and showed that, consistent with the previously reviewed work on expertise, perceptual training with particular external representations supports the development of perceptual fluency. This fluency, in turn, supports students' subsequent use of these external representations for problem solving.

This research suggests that extensive experience with particular equations or graphs may lead to perceptual fluency that could replace the more mindful application of domain-specific rules. Fisher, Borchert, and Bassok ( 2011 ) reported results from algebraic-modeling tasks that are consistent with this hypothesis. For example, college students were asked to represent verbal statements with algebraic equations, a task that typically elicits systematic errors (e.g., Clement, Lochhead, & Monk, 1981 ). Fisher et al. found that such errors were very common when subjects were asked to construct “standard form” equations ( y = ax ), which support fluent left-to-right translation of words to equations, but were relatively rare when subjects were asked to construct nonstandard division-format equations (x = y/a) that do not afford such translation fluency.

In part because of the left-to-right order in which people process equations, which mirrors the linear order in which they process text, equations have traditionally been viewed as sentential representations. However, Landy and Goldstone ( 2007a ) have proposed that equations also share some properties with diagrammatic displays and that, in fact, in some ways they are processed like diagrams. That is, spatial information is used to represent and to support inferences about syntactic structure. This hypothesis received support from Landy and Goldstone's ( 2007b ) results, described earlier, in which subjects' judgments of the validity of equations were affected by the Gestalt principle of grouping: Subjects did better when the grouping was consistent rather than inconsistent with the underlying structure of the problem (order of operations). Moreover, Landy and Goldstone ( 2007a ) found that when subjects wrote their own equations they grouped numbers and operators (+, *, =) in a way that reflected the hierarchical structure imposed by the order-of-operations rule.

In a recent line of research, Novick and Catley ( 2007 ; Novick, Catley, & Funk, 2010 ; Novick, Shade, & Catley, 2011 ) have examined effects of the spatial layout of diagrams depicting the evolutionary history of a set of taxa on people's ability to reason about patterns of relationship among those taxa. We consider here their work that investigates the role of another Gestalt perceptual principle—good continuation—in guiding students' reasoning. According to this principle, a continuous line is perceived as a single entity (Kellman, 2000 ). Consider the diagrams shown in Figure 21.6 . Each is a cladogram, a diagram that depicts nested sets of taxa that are related in terms of levels of most recent common ancestry. For example, chimpanzees and starfish are more closely related to each other than either is to spiders. The supporting evidence for their close relationship is their most recent common ancestor, which evolved the novel character of having radial cleavage. Spiders do not share this ancestor and thus do not have this character.

Cladograms are typically drawn in two isomorphic formats, which Novick and Catley ( 2007 ) referred to as trees and ladders. Although these formats are informationally equivalent (Larkin & Simon, 1987 ), Novick and Catley's ( 2007 ) research shows that they are not computationally equivalent (Larkin & Simon, 1987 ). Imagine that you are given evolutionary relationships in the ladder format, such as in Figure 21.6a (but without the four characters—hydrostatic skeleton, bilateral symmetry, radial cleavage, and trocophore larvae—and associated short lines indicating their locations on the cladogram), and your task is to translate that diagram to the tree format. A correct translation is shown in Figure 21.6b . Novick and Catley ( 2007 ) found that college students were much more likely to get such problems correct when the presented cladogram was in the nested circles (e.g., Figure 21.6d ) rather than the ladder format. Because the Gestalt principle of good continuation makes the long slanted line at the base of the ladder appear to represent a single hierarchical level, a common translation error for the ladder to tree problems was to draw a diagram such as that shown in Figure 21.6c .

The difficulty that good continuation presents for interpreting relationships depicted in the ladder format extends to answering reasoning questions as well. Novick and Catley (unpublished data) asked comparable questions about relationships depicted in the ladder and tree formats. For example, using the cladograms depicted in Figures 21.6a and 21.6b , consider the following questions: (a) Which taxon—jellyfish or earthworm—is the closest evolutionary relation to starfish, and what evidence supports your answer? (b) Do the bracketed taxa comprise a clade (a set of taxa consisting of the most recent common ancestor and all of its descendants), and what evidence supports your answer? For both such questions, students had higher accuracy and evidence quality composite scores when the relationships were depicted in the tree than the ladder format.

Four cladograms depicting evolutionary relationships among six animal taxa. Cladogram ( a ) is in the ladder format, cladograms ( b ) and ( c ) are in the tree format, and cladogram ( d ) is in the nested circles format. Cladograms ( a ), ( b ), and ( d ) are isomorphic.

If the difficulty in extracting the hierarchical structure of the ladder format is due to good continuation (which leads problem solvers to interpret continuous lines that depict multiple hierarchical levels as depicting only a single level), then a manipulation that breaks good continuation at the points where a new hierarchical level occurs should improve understanding. Novick et al. ( 2010 ) tested this hypothesis using a translation task by manipulating whether characters that are the markers for the most recent common ancestor of each nested set of taxa were included on the ladders. Figure 21.6a shows a ladder with such characters. As predicted, translation accuracy increased dramatically simply by adding these characters to the ladders, despite the additional information subjects had to account for in their translations.

The Role of Background Knowledge

As we mentioned earlier, the specific entities in the problems people encounter evoke inferences that affect how people represent these problems (e.g., the candle problem; Duncker, 1945 ) and how they apply the operators in searching for the solution (e.g., the disks vs. acrobats versions of the Tower of Hanoi problem; Kotovsky et al., 1985 ). Such object-based inferences draw on people's knowledge about the properties of the objects (e.g., a box is a container, an acrobat is a person who can be hurt). Here, we describe the work of Bassok and her colleagues, who found that similar inferences affect how people select mathematical procedures to solve problems in various formal domains. This work shows that the objects in the texts of mathematical word problems affect how people represent the problem situation (i.e., the situation model they construct; Kintsch & Greeno, 1985 ) and, in turn, lead them to select mathematical models that have a corresponding structure. To illustrate, a word problem that describes constant change in the rate at which ice is melting off a glacier evokes a model of continuous change, whereas a word problem that describes constant change in the rate at which ice is delivered to a restaurant evokes a model of discrete change. These distinct situation models lead subjects to select corresponding visual representations (e.g., Bassok & Olseth, 1995 ) and solutions methods, such as calculating the average change over time versus adding the consecutive changes (e.g., Alibali et al., 1999 ).

In a similar manner, people draw on their general knowledge to infer how the objects in a given problem are related to each other and construct mathematical solutions that correspond to these inferred object relations. For example, a word problem that involves doctors from two hospitals elicits a situation model in which the two sets of doctors play symmetric roles (e.g., work with each other), whereas a mathematically isomorphic problem that involves mechanics and cars elicits a situation model in which the sets play asymmetric roles (e.g., mechanics fix cars). The mathematical solutions people construct to such problems reflect this difference in symmetry (Bassok, Wu, & Olseth, 1995 ). In general, people tend to add objects that belong to the same taxonomic category (e.g., doctors + doctors) but divide functionally related objects (e.g., cars ÷ mechanics). People establish this correspondence by a process of analogical alignment between semantic and arithmetic relations, which Bassok and her colleagues refer to as “semantic alignment” (Bassok, Chase, & Martin, 1998 ; Doumas, Bassok, Guthormsen, & Hummel, 2006 ; Fisher, Bassok, & Osterhout, 2010 ).

Semantic alignment occurs very early in the solution process and can prime arithmetic facts that are potentially relevant to the problem solution (Bassok, Pedigo, & Oskarsson, 2008 ). Although such alignments can lead to erroneous solutions, they have a high heuristic value because, in most textbook problems, object relations indeed correspond to analogous mathematical relations (Bassok et al., 1998 ). Interestingly, unlike in the case of reliance on specific surface-structure correlations (e.g., the keyword “more” typically appears in word problems that require addition; Lewis & Mayer, 1987 ), people are more likely to exploit semantic alignment when they have more, rather than less modeling experience. For example, Martin and Bassok ( 2005 ) found very strong semantic-alignment effects when subjects solved simple division word problems, but not when they constructed algebraic equations to represent the relational statements that appeared in the problems. Of course, these subjects had significantly more experience with solving numerical word problems than with constructing algebraic models of relational statements. In a subsequent study, Fisher and Bassok ( 2009 ) found semantic-alignment effects for subjects who constructed correct algebraic models, but not for those who committed modeling errors.

Conclusions and Future Directions

In this chapter, we examined two broad components of the problem-solving process: representation (the Gestalt legacy) and search (the legacy of Newell and Simon). Although many researchers choose to focus their investigation on one or the other of these components, both Duncker ( 1945 ) and Simon ( 1986 ) underscored the necessity to investigate their interaction, as the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution, and searching the problem space may lead to a change in problem representation. Indeed, Duncker's ( 1945 ) initial account of one subject's solution to the radiation problem was followed up by extensive and experimentally sophisticated work by Simon and his colleagues and by other researchers, documenting the involvement of visual perception and background knowledge in how people represent problems and search for problem solutions.

The relevance of perception and background knowledge to problem solving illustrates the fact that, when people attempt to find or devise ways to reach their goals, they draw on a variety of cognitive resources and engage in a host of cognitive activities. According to Duncker ( 1945 ), such goal-directed activities may include (a) placing objects into categories and making inferences based on category membership, (b) making inductive inferences from multiple instances, (c) reasoning by analogy, (d) identifying the causes of events, (e) deducing logical implications of given information, (f) making legal judgments, and (g) diagnosing medical conditions from historical and laboratory data. As this list suggests, many of the chapters in the present volume describe research that is highly relevant to the understanding of problem-solving behavior. We believe that important advancements in problem-solving research would emerge by integrating it with research in other areas of thinking and reasoning, and that research in these other areas could be similarly advanced by incorporating the insights gained from research on what has more traditionally been identified as problem solving.

As we have described in this chapter, many of the important findings in the field have been established by a careful investigation of various riddle problems. Although there are good methodological reasons for using such problems, many researchers choose to investigate problem solving using ecologically valid educational materials. This choice, which is increasingly common in contemporary research, provides researchers with the opportunity to apply their basic understanding of problem solving to benefit the design of instruction and, at the same time, allows them to gain a better understanding of the processes by which domain knowledge and educational conventions affect the solution process. We believe that the trend of conducting educationally relevant research is likely to continue, and we expect a significant expansion of research on people's understanding and use of dynamic and technologically rich external representations (e.g., Kellman et al., 2008 ; Mayer, Griffith, Jurkowitz, & Rothman, 2008 ; Richland & McDonough, 2010 ; Son & Goldstone, 2009 ). Such investigations are likely to yield both practical and theoretical payoffs.

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