problem solving and creativity explanation

What is creative problem-solving?

Table of Contents

An introduction to creative problem-solving.

Creative problem-solving is an essential skill that goes beyond basic brainstorming . It entails a holistic approach to challenges, melding logical processes with imaginative techniques to conceive innovative solutions. As our world becomes increasingly complex and interconnected, the ability to think creatively and solve problems with fresh perspectives becomes invaluable for individuals, businesses, and communities alike.

Importance of divergent and convergent thinking

At the heart of creative problem-solving lies the balance between divergent and convergent thinking. Divergent thinking encourages free-flowing, unrestricted ideation, leading to a plethora of potential solutions. Convergent thinking, on the other hand, is about narrowing down those options to find the most viable solution. This dual approach ensures both breadth and depth in the problem-solving process.

Emphasis on collaboration and diverse perspectives

No single perspective has a monopoly on insight. Collaborating with individuals from different backgrounds, experiences, and areas of expertise offers a richer tapestry of ideas. Embracing diverse perspectives not only broadens the pool of solutions but also ensures more holistic and well-rounded outcomes.

Nurturing a risk-taking and experimental mindset

The fear of failure can be the most significant barrier to any undertaking. It's essential to foster an environment where risk-taking and experimentation are celebrated. This involves viewing failures not as setbacks but as invaluable learning experiences that pave the way for eventual success.

The role of intuition and lateral thinking

Sometimes, the path to a solution is not linear. Lateral thinking and intuition allow for making connections between seemingly unrelated elements. These 'eureka' moments often lead to breakthrough solutions that conventional methods might overlook.

Stages of the creative problem-solving process

The creative problem-solving process is typically broken down into several stages. Each stage plays a crucial role in understanding, addressing, and resolving challenges in innovative ways.

Clarifying: Understanding the real problem or challenge

Before diving into solutions, one must first understand the problem at its core. This involves asking probing questions, gathering data, and viewing the challenge from various angles. A clear comprehension of the problem ensures that effort and resources are channeled correctly.

Ideating: Generating diverse and multiple solutions

Once the problem is clarified, the focus shifts to generating as many solutions as possible. This stage champions quantity over quality, as the aim is to explore the breadth of possibilities without immediately passing judgment.

Developing: Refining and honing promising solutions

With a list of potential solutions in hand, it's time to refine and develop the most promising ones. This involves evaluating each idea's feasibility, potential impact, and any associated risks, then enhancing or combining solutions to maximize effectiveness.

Implementing: Acting on the best solutions

Once a solution has been honed, it's time to put it into action. This involves planning, allocating resources, and monitoring the results to ensure the solution is effectively addressing the problem.

Techniques for creative problem-solving

Solving complex problems in a fresh way can be a daunting task to start on. Here are a few techniques that can help kickstart the process:

Brainstorming

Brainstorming is a widely-used technique that involves generating as many ideas as possible within a set timeframe. Variants like brainwriting (where ideas are written down rather than spoken) and reverse brainstorming (thinking of ways to cause the problem) can offer fresh perspectives and ensure broader participation.

Mind mapping

Mind mapping is a visual tool that helps structure information, making connections between disparate pieces of data. It is particularly useful in organizing thoughts, visualizing relationships, and ensuring a comprehensive approach to a problem.

SCAMPER technique

SCAMPER stands for Substitute, Combine, Adapt, Modify, Put to another use, Eliminate, and Reverse. This technique prompts individuals to look at existing products, services, or processes in new ways, leading to innovative solutions.

Benefits of creative problem-solving

Creative problem-solving offers numerous benefits, both at the individual and organizational levels. Some of the most prominent advantages include:

Finding novel solutions to old problems

Traditional problems that have resisted conventional solutions often succumb to creative approaches. By looking at challenges from fresh angles and blending different techniques, we can unlock novel solutions previously deemed impossible.

Enhanced adaptability in changing environments

In our rapidly evolving world, the ability to adapt is critical. Creative problem-solving equips individuals and organizations with the agility to pivot and adapt to changing circumstances, ensuring resilience and longevity.

Building collaborative and innovative teams

Teams that embrace creative problem-solving tend to be more collaborative and innovative. They value diversity of thought, are open to experimentation, and are more likely to challenge the status quo, leading to groundbreaking results.

Fostering a culture of continuous learning and improvement

Creative problem-solving is not just about finding solutions; it's also about continuous learning and improvement. By encouraging an environment of curiosity and exploration, organizations can ensure that they are always at the cutting edge, ready to tackle future challenges head-on.

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Article • 8 min read

A Powerful Methodology for Creative Problem Solving

By the Mind Tools Content Team

Projects don't always run smoothly. Even with all the analysis and data you need at your fingertips, sometimes you just can't see a way forward. At times like these, you need to develop creative solutions to the problems you face.

Chances are you already know about brainstorming , which can help with this sort of situation. But brainstorming depends on intuition and the existing knowledge of team members, and its results are often unpredictable and unrepeatable.

TRIZ, however, is a problem-solving philosophy based on logic, data and research, rather than on intuition.

It draws on the past knowledge and ingenuity of thousands of engineers to speed up creative problem solving for project teams. Its approach brings repeatability, predictability and reliability to the problem-solving process and delivers a set of dependable tools.

This article walks you through the essentials of TRIZ.

What is TRIZ?

TRIZ is the Russian acronym for the "Theory of Inventive Problem Solving," an international system of creativity developed in the U.S.S.R. between 1946 and 1985, by engineer and scientist Genrich S. Altshuller and his colleagues.

According to TRIZ, universal principles of creativity form the basis of innovation. TRIZ identifies and codifies these principles, and uses them to make the creative process more predictable.

In other words, whatever problem you're facing, somebody, somewhere, has already solved it (or one very like it). Creative problem solving involves finding that solution and adapting it to your problem.

TRIZ is most useful in roles such as product development, design engineering, and process management. For example, Six Sigma quality improvement processes often make use of TRIZ.

The Key TRIZ Tools

Let's look at two of the central concepts behind TRIZ: generalizing problems and solutions, and eliminating contradictions.

1. Generalizing Problems and Solutions

The primary findings of TRIZ research are as follows:

• Problems and solutions are repeated across industries and sciences. By representing a problem as a "contradiction" (we explore this later in this article), you can predict creative solutions to that problem.
• Patterns of technical evolution tend to repeat themselves across industries and sciences.
• Creative innovations often use scientific effects outside the field where they were developed.

Using TRIZ consists of learning these repeating patterns of problem and solution, understanding the contradictions present in a situation, and developing new methods of using scientific effects.

You then apply the general TRIZ patterns to the specific situation that confronts you, and discover a generalized version of the problem.

Figure 1, below, illustrates this process.

Figure 1 – The TRIZ Problem-Solving Method

Here, you take the specific problem that you face and generalize it to one of the TRIZ general problems. From the TRIZ general problems, you identify the general TRIZ solution you need, and then consider how you can apply it to your specific problem.

The TRIZ databases are actually a collection of "open source" resources compiled by users and aficionados of the system (such as the 40 Principles and 76 Standard Solutions, which we look at, below).

2. Eliminating Contradictions

Another fundamental TRIZ concept is that there are fundamental contradictions at the root of most problems. In many cases, a reliable way to solve a problem is to eliminate these contradictions.

TRIZ recognizes two categories of contradictions:

• The product gets stronger (good), but the weight increases (bad).
• Service is customized to each customer (good), but the service delivery system gets complicated (bad).
• Training is comprehensive (good), but it keeps employees away from their assignments (bad).

The key technical contradictions are summarized in the TRIZ Contradiction Matrix . As with all TRIZ resources, it takes time and study to become familiar with the Contradiction Matrix.

• Software should be complex (to have many features), but simple (to be easy to learn).
• Coffee should be hot (to be enjoyed), but cool (to avoid burning the drinker).
• An umbrella should be large (to keep the rain off), but small (to be maneuverable in a crowd).

You can solve physical contradictions with the TRIZ Separation Principles . These separate your requirements according to basic categories of Space, Time and Scale.

How to Use TRIZ Principles – an Example

Begin to explore TRIZ by applying it to a simple, practical problem.

For example, consider the specific problem of a furniture store in a small building. The store wants to attract customers, so it needs to have its goods on display. But it also needs to have enough storage space to keep a range of products ready for sale.

Using TRIZ, you can establish that the store has a physical contradiction. The furniture needs to be large (to be useful and attractive), but also small (to be stored in as little space as possible). Using TRIZ, the store owners generalize this contradiction into a general problem and apply one of the 40 Principles of Problem Solving – a key TRIZ technique – to it.

They find a viable general solution in Principle 1 – Segmentation. This advocates dividing an object or system into different parts, or making it easy to take apart. This could lead the owners to devise flat-pack versions of their furniture, so that display models can take up the room that they need while inventory occupies much less space per unit. This is the specific solution.

You, too, can use the 40 Principles of Problem Solving, or the 40 Inventive Principles, and the Contradiction Matrix to help you with your problem-solving.

Five Top TRIZ Concepts and Techniques

TRIZ comes with a range of ideas and techniques beyond the basic principles outlined above. Some are conceptual and analytical, such as:

• The Law of Ideality. This states that any system tends to become more reliable throughout its life, through regular improvement.
• Functional Modeling, Analysis and Trimming. TRIZ uses these methods to define problems.
• Locating the Zones of Conflict. (This is known to Six Sigma problem-solvers as " Root Cause Analysis .")

Some are more prescriptive. For example:

• The Laws of Technical Evolution and Technology Forecasting . These categorize technical evolution by demand, function and system.
• The 76 Standard Solutions . These are specific solutions devised to a range of common problems in design and innovation.

You can use one such tool or many to solve a problem, depending on its nature.

TRIZ is a system of creative problem solving, commonly used in engineering and process management. It follows four basic steps:

• Define your specific problem.
• Find the TRIZ generalized problem that matches it.
• Find the generalized solution that solves the generalized problem.
• Adapt the generalized solution to solve your specific problem.

Most problems stem from technical or physical contradictions. Apply one of hundreds of TRIZ principles and laws to eliminate these contradictions, and you can solve the problem.

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How to Be a More Creative Problem-Solver at Work: 8 Tips

• 01 Mar 2022

The importance of creativity in the workplace—particularly when problem-solving—is undeniable. Business leaders can’t approach new problems with old solutions and expect the same result.

This is where innovation-based processes need to guide problem-solving. Here’s an overview of what creative problem-solving is, along with tips on how to use it in conjunction with design thinking.

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What Is Creative Problem-Solving?

Encountering problems with no clear cause can be frustrating. This occurs when there’s disagreement around a defined problem or research yields unclear results. In such situations, creative problem-solving helps develop solutions, despite a lack of clarity.

While creative problem-solving is less structured than other forms of innovation, it encourages exploring open-ended ideas and shifting perspectives—thereby fostering innovation and easier adaptation in the workplace. It also works best when paired with other innovation-based processes, such as design thinking .

Creative Problem-Solving and Design Thinking

Design thinking is a solutions-based mentality that encourages innovation and problem-solving. It’s guided by an iterative process that Harvard Business School Dean Srikant Datar outlines in four stages in the online course Design Thinking and Innovation :

• Clarify: This stage involves researching a problem through empathic observation and insights.
• Ideate: This stage focuses on generating ideas and asking open-ended questions based on observations made during the clarification stage.
• Develop: The development stage involves exploring possible solutions based on the ideas you generate. Experimentation and prototyping are both encouraged.
• Implement: The final stage is a culmination of the previous three. It involves finalizing a solution’s development and communicating its value to stakeholders.

Although user research is an essential first step in the design thinking process, there are times when it can’t identify a problem’s root cause. Creative problem-solving addresses this challenge by promoting the development of new perspectives.

Leveraging tools like design thinking and creativity at work can further your problem-solving abilities. Here are eight tips for doing so.

8 Creative Problem-Solving Tips

1. empathize with your audience.

A fundamental practice of design thinking’s clarify stage is empathy. Understanding your target audience can help you find creative and relevant solutions for their pain points through observing them and asking questions.

Practice empathy by paying attention to others’ needs and avoiding personal comparisons. The more you understand your audience, the more effective your solutions will be.

2. Reframe Problems as Questions

If a problem is difficult to define, reframe it as a question rather than a statement. For example, instead of saying, "The problem is," try framing around a question like, "How might we?" Think creatively by shifting your focus from the problem to potential solutions.

Consider this hypothetical case study: You’re the owner of a local coffee shop trying to fill your tip jar. Approaching the situation with a problem-focused mindset frames this as: "We need to find a way to get customers to tip more." If you reframe this as a question, however, you can explore: "How might we make it easier for customers to tip?" When you shift your focus from the shop to the customer, you empathize with your audience. You can take this train of thought one step further and consider questions such as: "How might we provide a tipping method for customers who don't carry cash?"

Whether you work at a coffee shop, a startup, or a Fortune 500 company, reframing can help surface creative solutions to problems that are difficult to define.

3. Defer Judgment of Ideas

If you encounter an idea that seems outlandish or unreasonable, a natural response would be to reject it. This instant judgment impedes creativity. Even if ideas seem implausible, they can play a huge part in ideation. It's important to permit the exploration of original ideas.

While judgment can be perceived as negative, it’s crucial to avoid accepting ideas too quickly. If you love an idea, don’t immediately pursue it. Give equal consideration to each proposal and build on different concepts instead of acting on them immediately.

4. Overcome Cognitive Fixedness

Cognitive fixedness is a state of mind that prevents you from recognizing a situation’s alternative solutions or interpretations instead of considering every situation through the lens of past experiences.

Although it's efficient in the short-term, cognitive fixedness interferes with creative thinking because it prevents you from approaching situations unbiased. It's important to be aware of this tendency so you can avoid it.

5. Balance Divergent and Convergent Thinking

One of the key principles of creative problem-solving is the balance of divergent and convergent thinking. Divergent thinking is the process of brainstorming multiple ideas without limitation; open-ended creativity is encouraged. It’s an effective tool for generating ideas, but not every idea can be explored. Divergent thinking eventually needs to be grounded in reality.

Convergent thinking, on the other hand, is the process of narrowing ideas down into a few options. While converging ideas too quickly stifles creativity, it’s an important step that bridges the gap between ideation and development. It's important to strike a healthy balance between both to allow for the ideation and exploration of creative ideas.

6. Use Creative Tools

Using creative tools is another way to foster innovation. Without a clear cause for a problem, such tools can help you avoid cognitive fixedness and abrupt decision-making. Here are several examples:

Problem Stories

Creating a problem story requires identifying undesired phenomena (UDP) and taking note of events that precede and result from them. The goal is to reframe the situations to visualize their cause and effect.

To start, identify a UDP. Then, discover what events led to it. Observe and ask questions of your consumer base to determine the UDP’s cause.

Next, identify why the UDP is a problem. What effect does the UDP have that necessitates changing the status quo? It's helpful to visualize each event in boxes adjacent to one another when answering such questions.

The problem story can be extended in either direction, as long as there are additional cause-and-effect relationships. Once complete, focus on breaking the chains connecting two subsequent events by disrupting the cause-and-effect relationship between them.

Alternate Worlds

The alternate worlds tool encourages you to consider how people from different backgrounds would approach similar situations. For instance, how would someone in hospitality versus manufacturing approach the same problem? This tool isn't intended to instantly solve problems but, rather, to encourage idea generation and creativity.

7. Use Positive Language

It's vital to maintain a positive mindset when problem-solving and avoid negative words that interfere with creativity. Positive language prevents quick judgments and overcomes cognitive fixedness. Instead of "no, but," use words like "yes, and."

Positive language makes others feel heard and valued rather than shut down. This practice doesn’t necessitate agreeing with every idea but instead approaching each from a positive perspective.

Using “yes, and” as a tool for further idea exploration is also effective. If someone presents an idea, build upon it using “yes, and.” What additional features could improve it? How could it benefit consumers beyond its intended purpose?

While it may not seem essential, this small adjustment can make a big difference in encouraging creativity.

8. Practice Design Thinking

Practicing design thinking can make you a more creative problem-solver. While commonly associated with the workplace, adopting a design thinking mentality can also improve your everyday life. Here are several ways you can practice design thinking:

• Learn from others: There are many examples of design thinking in business . Review case studies to learn from others’ successes, research problems companies haven't addressed, and consider alternative solutions using the design thinking process.
• Approach everyday problems with a design thinking mentality: One of the best ways to practice design thinking is to apply it to your daily life. Approach everyday problems using design thinking’s four-stage framework to uncover what solutions it yields.
• Study design thinking: While learning design thinking independently is a great place to start, taking an online course can offer more insight and practical experience. The right course can teach you important skills , increase your marketability, and provide valuable networking opportunities.

Ready to Become a Creative Problem-Solver?

Though creativity comes naturally to some, it's an acquired skill for many. Regardless of which category you're in, improving your ability to innovate is a valuable endeavor. Whether you want to bolster your creativity or expand your professional skill set, taking an innovation-based course can enhance your problem-solving.

If you're ready to become a more creative problem-solver, explore Design Thinking and Innovation , one of our online entrepreneurship and innovation courses . If you aren't sure which course is the right fit, download our free course flowchart to determine which best aligns with your goals.

About the Author

How to Use Creativity in Problem-Solving

Using creativity in problem-solving is a dynamic process that involves seeing challenges from unique perspectives, generating novel solutions , and redefining the status quo. It requires going beyond traditional methodologies and employing inventive thinking.

Table of Contents

Techniques such as brainstorming, lateral thinking, and mind mapping can help ignite your creative sparks. By cultivating a culture of creativity, you empower yourself and others to tackle issues innovatively, ensuring that the problem-solving process is effective but also exciting and rewarding.

What is the Role of Creativity in Problem-Solving?

Creative problem-solving is an approach that combines imagination, innovation, and a broad sense of flexibility to find solutions to problems. It’s about shunning the traditional mindset that restricts our thoughts to only known and accepted techniques and methods . Instead, it encourages thinking outside the box, leveraging all cognitive resources, and pushing beyond the boundaries of standard methodologies to arrive at unique and often more effective solutions.

At the heart of creative problem-solving is the understanding that problems are often not what they initially appear to be. An issue may seem like a stumbling block. Still, with creative problem-solving , it can be transformed into an opportunity for innovation and growth. It’s about not accepting the immediate, apparent problem at face value but delving deeper into uncovering the root cause and addressing that, often leading to a more comprehensive and long-lasting solution.

Stages of Creative Problem-Solving

To appreciate what is creative problem-solving, it is crucial to recognize its critical stages. First is problem identification, which involves understanding the problem from different angles and perspectives. This stage lays the groundwork for the creative process by opening up many possibilities.

Next comes idea generation. This stage is the crux of the creative process, where traditional thinking is left behind, and innovative ideas can flourish. Techniques like brainstorming, free writing, and mind mapping are commonly used to spur creativity and encourage various possible solutions.

Finally, there’s the evaluation and implementation of the solution. This stage involves critically assessing the proposed solutions, selecting the best one, and implementing them. It’s important to remember that the solution’s effectiveness should be evaluated and adjustments made, if necessary, to ensure the problem is resolved.

In essence, creative problem-solving is a process that welcomes innovation, embraces change, and turns problems into opportunities for creative growth. It’s not about finding a solution but about using creativity to discover the best solution. The beauty of creative problem-solving is that honing this skill is possible and can be developed, ultimately leading to better decision-making and problem-solving abilities in all areas of life.

How to Harness Creativity in Problem-Solving

Harnessing creativity is the cornerstone of innovative problem-solving. This involves challenging our usual thought patterns and opening ourselves to new ways of thinking. But how do we activate this creative engine within us? The answer lies in asking the right creative problem-solving questions.

Creative Problem-Solving Questions

Questions are the fuel that ignites the engine of creativity. They challenge our assumptions, expand our perspectives, and drive us to think outside the box. In problem-solving, creative questions can illuminate unseen possibilities and pathways toward innovative solutions.

The first step in harnessing creativity for problem-solving is understanding the problem in-depth. Questions such as “What is the core issue?” or “Why is this a problem?” can help identify the root cause rather than just dealing with symptoms. Understanding the problem at a granular level often reveals unique angles and opportunities for innovative solutions.

Once we deeply understand the problem, it’s time to generate ideas. Here, creative problem-solving questions are designed to push our thinking beyond usual boundaries. Questions like “What if the impossible were possible?” or “How would this problem be solved in a completely different context?” can spark unconventional ideas and unlock creative potential.

The next stage is about evaluating the solutions. Questions such as “What could be the potential impacts of this solution?” or “How can we improve this idea?” ensure we critically assess the proposed solutions from various angles. It’s vital to constructively challenge each idea’s viability, promoting further creativity and refinement.

Finally, we come to the implementation of the chosen solution. Questions like “What resources are needed to execute this solution?” and “What could be potential roadblocks, and how can we overcome them?” enable us to foresee any practical issues and address them proactively, thus ensuring a smooth execution of the solution.

Asking creative problem-solving questions can help unlock our inherent creative capabilities. By harnessing our creativity, we can drive innovative problem-solving and find solutions that are not just effective but also genuinely novel and groundbreaking. These questions are more than just tools; they are the catalysts that transform problems into opportunities for creative innovation.

What is the Connection between Creativity and Problem-Solving?

Creativity is an invaluable tool in the problem-solving process. It empowers us to develop unique solutions that resolve the issue and provide opportunities for growth and innovation. But how is creativity used in problem-solving? Let’s dive into the nuances of this connection.

At its core, problem-solving is about finding solutions to obstacles or challenges. Traditional problem-solving techniques often focus on logical reasoning and proven methodologies. However, these techniques may only sometimes be sufficient, especially when dealing with complex or unprecedented problems. This is where creativity steps in.

How is Creativity Used in Problem-Solving

Creativity in problem-solving starts with reframing the problem. It prompts us to see beyond the apparent and understand the problem from different perspectives. This is particularly helpful when dealing with intricate issues, as it helps identify underlying patterns and relationships that might not be immediately apparent.

Once the problem is reframed, the next step is idea generation. This is where the power of creativity truly shines. Creative thinking encourages us to break free from conventional thinking patterns and explore a broader spectrum of possibilities. Brainstorming, mind mapping, or even daydreaming can help stimulate creative thoughts and generate innovative ideas.

Creativity also plays a critical role in evaluating and selecting the best solution. It allows us to envision how each potential solution might play out, assess the risks and benefits, and choose the most effective and innovative option.

Finally, creativity is instrumental in the implementation of the solution. It encourages us to think on our feet, adapt to unexpected challenges, and continuously refine the solution until the problem is fully resolved.

Creativity fuels each stage of the problem-solving process, transforming it from a mundane task into an exciting journey of discovery and innovation. So, whether you’re dealing with a minor hiccup or a major hurdle, remember to tap into your creative side. You might be surprised at the great solutions that emerge.

How to Explore Techniques for Fostering Creativity in Problem-Solving

In the dynamic and competitive business world, a creative approach to problem-solving can be a significant differentiator. Now businesses require innovative solutions to keep up with rapidly changing environments and customer expectations. Here, we’ll explore techniques for fostering creative problem-solving in business.

How to Use Creative Problem-Solving in Business

Firstly, it’s crucial to cultivate an environment that encourages creativity. An open-minded culture supporting risk-taking and diverse perspectives can significantly enhance creative thinking. This includes welcoming all ideas during brainstorming sessions, regardless of how unconventional they seem, and celebrating successes and learning opportunities from failures.

Secondly, divergent thinking is a powerful tool for creative problem-solving. It involves generating multiple possible solutions to a problem rather than following a linear, logical path. Techniques like brainstorming or lateral thinking can stimulate divergent thinking, leading to more innovative problem-solving.

Another technique uses creative problem-solving frameworks, like the SCAMPER model (Substitute, Combine, Adapt, Modify, Put to another use, Eliminate, Reverse). These frameworks provide structured methods for thinking creatively and can be particularly useful in a business setting.

Also, fostering creativity requires constant learning and development . Encouraging continuous learning, such as attending seminars, workshops, or online courses on creativity and innovation, can significantly enhance creative problem-solving skills. Also, exposure to different industries, cultures, and ways of thinking can provide new perspectives and ideas.

Creativity can also be enhanced by embracing technology. AI and machine learning, for example, can provide insights and patterns that would be hard to spot otherwise, opening new avenues for creative solutions.

Lastly, it’s essential to recognize the power of rest in fostering creativity. Downtime, hobbies, or simple walks in nature can rejuvenate the mind and often lead to ‘Eureka’ moments when least expected.

Fostering creative problem-solving in business is not a one-size-fits-all process. It requires a blend of culture, techniques, learning, technology, and well-being that suits your team’s unique needs and dynamics. However, the rewards – innovative solutions, competitive advantage, and team satisfaction – make it an investment worth making.

What are Some Successful Implementations of Creativity in Problem-Solving?

Applying creativity in problem-solving has led to groundbreaking solutions in various fields. In this context, we will explore several instances of creative problem-solving that resulted in successful and innovative outcomes.

Examples of Creative Problem-Solving

Accommodation: Let’s look at a classic example from the business world: Airbnb. In its early days, the company needed help to gain traction. The founders identified a key issue: the quality of listing photos could have been better, deterring potential renters. In a creative problem-solving move, they hired professional photographers to take pictures of the rentals. This innovative approach significantly improved the appeal of the listings, and the rest is history. Airbnb’s success illustrates how a creative solution can transform a problem into an opportunity.

Motor Industry: Consider the example of the automobile industry’s Tesla Motors . Confronted with the problem of fossil fuel dependency and its environmental impact, Tesla disrupted the conventional solution of tweaking existing fuel technologies. Instead, they creatively focused on developing high-performance electric vehicles, changing the industry’s perception and leading towards sustainable transportation.

Healthcare: Another example can be found in healthcare, particularly in the fight against polio. In the 1950s, the ‘iron lung’ was the primary treatment for polio-induced respiratory failure. It was a cumbersome and expensive solution. Dr. Bjørn Aage Ibsen , confronted with a polio outbreak, creatively proposed a new method: positive pressure ventilation. This involved manually ventilating the patient with a tube inserted into their trachea. This became the precursor to modern mechanical ventilation, demonstrating the impact of creative problem-solving in healthcare.

Education: Lastly, consider the example from education: the Khan Academy . Recognizing that traditional classroom education could not cater to each student’s pace and learning style, Salman Khan saw an opportunity to teach differently. He used technology creatively to provide free online educational videos, fundamentally transforming the access and delivery of education on a global scale.

The Impact of Creative Problem-Solving

In these cases, the key to successful problem-solving was applying creative thinking. These examples of creative problem-solving underscore the power of innovative thinking in transforming challenges into opportunities for growth and advancement. The ability to think creatively in problem-solving is a valuable skill and, in many cases, a game-changer.

How to Overcome Obstacles in Creativity in Problem-Solving

While creative problem-solving offers incredible potential for innovative solutions, it’s not without its challenges. However, these obstacles can often be overcome with a structured approach, such as the creative problem-solving model (CPS).

Creative Problem-Solving Model

The CPS model, initially developed by Alex Osborn and Sidney Parnes, provides a clear framework for navigating challenges that can arise during creative problem-solving. This model consists of four main steps: Clarify, Ideate, Develop, and Implement.

The first step, ‘Clarify,’ involves identifying the problem accurately and comprehensively. It’s easy to rush into solving a problem based on initial perceptions, which often results in treating symptoms rather than addressing the underlying issue. The CPS model emphasizes the importance of dedicating time to deeply understand the problem before jumping to solutions.

The second step, ‘Ideate,’ is generating various possible solutions. It’s common to experience blocks during this stage, such as sticking to familiar ideas or fearing judgment for unconventional thoughts. This step encourages divergent thinking, pushing past the initial, most apparent ideas to reach more unique and creative solutions.

Next, the ‘Develop’ stage involves converging on the most promising ideas and fleshing them into actionable solutions. Sometimes, the most creative ideas can seem risky or unrealistic. This stage, however, reminds us that these ideas often hold the most potential for innovative solutions and should be explored and developed rather than dismissed.

Finally, ‘Implement’ is about turning the solution into reality. Implementation can face many obstacles, from resistance to change, lack of resources, or unforeseen challenges. But the CPS model treats these not as dead ends but as parts of the problem-solving journey to be creatively overcome.

The creative problem-solving model provides a powerful tool to deal with the challenges of creative thinking. It offers a structured approach that fosters creativity, keeps the problem-solving process on track, and ultimately leads to innovative and effective solutions.

What are Some Tools and Strategies for Enhancing Creativity in Problem-Solving?

Creative problem-solving is a critical skill in today’s dynamic and complex world. It helps us navigate challenges with innovative and effective solutions. Various tools and strategies can enhance this process. Here, we delve into some of these creative problem-solving tools.

Creative Problem-Solving Tools

Brainstorming.

Brainstorming is the most familiar tool. It’s a freewheeling method to generate many ideas without immediate judgment or criticism. It invites and encourages wild and divergent thoughts, which are later sifted and refined. This tool is particularly effective in groups where diverse perspectives can spark unique ideas.

Mind Mapping

Mind Mapping, another powerful tool, visually represents thoughts and their interconnections. You can reveal unexpected connections by mapping the problem and related ideas and fostering innovative solutions. It’s an excellent tool for complex problems that involve multiple dimensions or for situations where a holistic view is needed.

The SCAMPER Method

The SCAMPER method (Substitute, Combine, Adapt, Modify, Put to another use, Eliminate, Reverse) prompts users to ask specific questions about the problem. Each word in the acronym poses a different way to manipulate and think about the problem, leading to fresh insights and solutions.

Six Thinking Hats Technique

Then there’s the Six Thinking Hats technique by Edward de Bono. This tool urges users to assume different ‘hats’ or roles (like the optimist, devil’s advocate, creative, etc.) during problem-solving. This strategy ensures a comprehensive approach, capturing different perspectives and reducing bias in decision-making.

Alongside these tools, specific strategies can cultivate creativity in problem-solving. Encouraging a culture of openness, where diverse thoughts are valued, can lead to more prosperous, more creative problem-solving. Creating a safe space where risks are welcomed is beneficial, and failures are seen as learning opportunities rather than setbacks.

Moreover, taking regular breaks and engaging in different activities can stimulate creativity. Often, stepping away from a problem allows our subconscious minds to work on it, leading to unexpected insights.

Regularly practicing and using these tools and strategies can dramatically improve creative problem-solving abilities. They stimulate innovative thinking and help structure the process, making it more effective and efficient. By leveraging these creative problem-solving tools, we can transform how we approach problems, turning challenges into opportunities for innovation.

What is the Future of Creativity in Problem-Solving?

As we navigate through a world that is becoming progressively more complex and unpredictable, the importance of creativity in problem-solving cannot be overstated. While still valuable, traditional problem-solving methods often must catch up when dealing with unprecedented challenges. Creativity injects flexibility, innovation, and adaptability into problem-solving, making it a vital skill for the future. Here, we explore some trends and predictions of creativity in problem-solving.

Growing Creative Problem-Solving

Firstly, we will likely see greater recognition of the role of creativity in problem-solving across various sectors. From businesses to education systems, there’s a growing understanding that generating and implementing innovative solutions to problems for survival and growth is crucial. We can see more emphasis on fostering creativity in leadership roles and at all levels.

Tech-Enhanced Creative Solutions

Secondly, technology will continue to play a significant role in enhancing creativity in problem-solving. Advanced technologies like AI and machine learning can provide us with more data and insights, enabling us to understand problems better and develop more creative solutions. At the same time, technology can facilitate the creative problem-solving process through tools that stimulate creative thinking and collaboration.

However, as we increasingly rely on technology, there’s also a danger that we might limit our creativity by depending too much on algorithms and predefined solutions. Therefore, balancing technology and human creativity will be essential to future problem-solving.

Additionally, we expect to see more integration of diverse perspectives in problem-solving. As we face global problems across various fields and cultures, it’s becoming clear that the most creative and effective solutions often come from interdisciplinary and diverse teams.

Dynamic Problem Adaptation

Finally, resilience and adaptability in problem-solving will be emphasized as we move toward a more uncertain future. Creative problem-solving will be less about finding the correct answer and more about continuous learning and adapting to evolving situations.

The future of creativity in problem-solving looks bright, promising, and exciting. By recognizing the importance of creativity and harnessing it effectively, we can equip ourselves to navigate future challenges with innovative and effective solutions.

What is the role of creativity in problem-solving?

Creativity in problem-solving allows for the generation of unique, practical solutions. It involves thinking outside the box, challenging traditional assumptions, and viewing the problem from various perspectives. Creativity is crucial in problem-solving as it fosters innovation and adaptability.

How can creativity be harnessed in problem-solving?

Creativity can be harnessed in problem-solving by promoting a culture that supports risk-taking and values diverse perspectives, employing techniques like divergent thinking and creative problem-solving frameworks, engaging in continuous learning and development, embracing technology, and prioritizing well-being and rest.

What is the connection between creativity and effective problem-solving?

Creativity contributes to effective problem-solving by enabling the generation of numerous possible solutions, encouraging novel perspectives, and fostering flexibility and adaptability. These aspects, in turn, lead to more comprehensive and innovative solutions.

What challenges might one encounter in creative problem-solving?

Challenges in creative problem-solving include rushing to solve the problem without fully understanding it, experiencing blocks during the ideation stage, dismissing seemingly unrealistic or risky ideas, and encountering resistance or unforeseen challenges during the implementation stage.

How might the future of creativity in problem-solving look like?

The future will likely see greater recognition of the role of creativity in problem-solving across various sectors. Technology will play a significant role in enhancing creativity, but maintaining a balance with human creativity will be necessary. Integrating diverse perspectives and emphasis on resilience and adaptability will also characterize future problem-solving.

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Understanding the Psychology of Creativity

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

Michael H / DigitalVision / Getty Images

What Is Creativity?

When does creativity happen, types of creativity, what does it take to be creative, creativity and the big five, how to increase creativity, frequently asked questions.

What is creativity? Creativity involves the ability to develop new ideas or utilize objects or information in novel ways. It can involve large-scale ideas that have the potential to change the world, such as inventing tools that impact how people live, or smaller acts of creation such as figuring out a new way to accomplish a task in your daily life.

This article explores what creativity is and when it is most likely to happen. It also covers some of the steps that you can take to improve your own creativity.

Studying creativity can be a tricky process. Not only is creativity a complex topic in and of itself, but there is also no clear consensus on how exactly to define creativity. Many of the most common definitions suggest that creativity is the tendency to solve problems or create new things in novel ways.

Two of the primary components of creativity include:

• Originality: The idea should be something new that is not simply an extension of something else that already exists.
• Functionality: The idea needs to actually work or possess some degree of usefulness.

In his book Creativity: Flow and the Psychology of Discovery and Invention , psychologist Mihaly Csikszentmihalyi suggested that creativity can often be seen in a few different situations.  

• People who seem stimulating, interesting, and have a variety of unusual thoughts.
• People who perceive the world with a fresh perspective, have insightful ideas and make important personal discoveries. These individuals make creative discoveries that are generally known only to them.
• People who make great creative achievements that become known to the entire world. Inventors and artists such as Thomas Edison and Pablo Picasso would fall into this category.

Experts also tend to distinguish between different types of creativity. The “four c” model of creativity suggests that there are four different types:

• “Mini-c” creativity involves personally meaningful ideas and insights that are known only to the self.
• “ Little-c” creativity involves mostly everyday thinking and problem-solving. This type of creativity helps people solve everyday problems they face and adapt to changing environments.
• “Pro-C” creativity takes place among professionals who are skilled and creative in their respective fields. These individuals are creative in their vocation or profession but do not achieve eminence for their works.
• “Big-C” creativity involves creating works and ideas that are considered great in a particular field. This type of creativity leads to eminence and acclaim and often leads to world-changing creations such as medical innovations, technological advances, and artistic achievements.

Csikszentmihalyi suggests that creative people tend to possess are ​a variety of traits that contribute to their innovative thinking. Some of these key traits include:

• Energy: Creative people tend to possess a great deal of both physical and mental energy. However, they also tend to spend a great deal of time quietly thinking and reflecting.
• Intelligence: Psychologists have long believed that intelligence plays a critical role in creativity. In Terman’s famous longitudinal study of gifted children, researchers found that while high IQ was necessary for great creativity, not all people with high IQs are creative. Csikszentmihalyi believes that creative people must be smart, but they must be capable of looking at things in fresh, even naïve, ways.
• Discipline: Creative people do not just sit around waiting for inspiration to strike. They ​are playful, yet they are also disciplined in the pursuit of their work and passions.

Certain personality traits are also connected to creativity. According to the big five theory of personality , human personality is made up of five broad dimensions:

• Conscientiousness
• Extroversion
• Agreeableness
• Neuroticism

Each dimension represents a continuum, so for each trait, people can be either high, low, or somewhere between the two. 

Openness to experience is a big five trait that is correlated with creativity. People who are high on this trait are more open to new experiences and ideas. They tend to seek novelty and enjoy trying new things, meeting new people, and considering different perspectives. 

However, other personality traits and characteristics can also play a role in creativity. For example, intrinsic motivation , curiosity, and persistence can all determine how much people tend to pursue new ideas and look for novel solutions.

While some people seem to come by creativity naturally, there are things that you can do to increase your own creativity .

Some strategies that can be helpful for improving creativity include: 

• Being open to new ideas : Openness to experience is the personality trait that is most closely correlated with creativity. Focus on being willing to try new things and explore new ideas.
• Be persistent : Creativity is not just about sitting around waiting for inspiration to strike. Creative people spend time working to produce new things. Their efforts don't always work out, but continued practice builds skills that contribute to creativity.
• Make time for creativity : In addition to being persistent, you also need to devote time specifically toward creative efforts. This might mean setting aside a little time each day or each week specifically to brainstorm, practice, learn, or create.

Csikszentmihalyi has noted that creativity requires both a fresh perspective combined with discipline. As Thomas Edison famously suggested, genius is 1% inspiration and 99% perspiration.

A Word From Verywell

Creativity is a complex subject and researchers are still working to understand exactly what factors contribute to the ability to think creatively. While some people seem to come by creativity naturally, there are also things you can do to build and strengthen this ability.

The late Maya Angelou also suggested that thinking creativity helps foster even greater creativity, "The important thing is to use it. You can’t use up creativity. The more you use it, the more you have," she suggested.

Creativity does not reside in one single area of the brain; many areas are actually involved. The frontal cortex of the brain is responsible for many of the functions that play a part in creativity.

However, other parts of the brain impact creativity as well, including the hippocampus (which is important to memory) and the basal ganglia (which is essential in the memory of how to perform tasks). The white matter of the brain, which keeps the various parts of the brain connected, is also essential for creative thinking.

Research suggests that people can train their brains to be more creative. Engaging in cognitively stimulating tasks, going on a walk, finding sources of inspiration, and meditating are a few strategies that may help boost creative thinking abilities. 

The "big five" are the broad categories of traits that make up personality. The five dimensions are openness, conscientiousness, extroversion, agreeableness, and neuroticism. Each trait involves a range between two extremes, and people can be either at each end or somewhere in the middle.

American Psychological Association. The science of creativity .

Csikszentmihalyi M. Creativity: Flow and the Psychology of Discovery and Invention .   New York: HarperCollins; 2013.

Kaufman J, Beghetto R. Beyond big and little: The four C model of creativity .  Review of General Psychology . 2009;13(1):1-12. doi:10.1037/a0013688

Kaufman SB, Quilty LC, Grazioplene RG, et al. Openness to experience and intellect differentially predict creative achievement in the arts and sciences .  J Pers . 2016;84(2):248-258. doi:10.1111/jopy.12156

Elliot J.  Conversations With Maya Angelou . Jackson, Miss.: University Press of Mississippi; 1998.

Cavdarbasha D, Kurczek J. Connecting the dots: your brain and creativity . Front Young Minds . 2017;5:19. doi:10.3389/frym.2017.00019

Sun J, Chen Q, Zhang Q, Li Y, Li H, Wei D, Yang W, Qiu J.  Training your brain to be more creative: brain functional and structural changes induced by divergent thinking training .  Hum Brain Mapp . 2016;37(10):3375-87. doi:10.1002/hbm.23246

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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A Cognitive Trick for Solving Problems Creatively

• Theodore Scaltsas

Mental biases can actually help.

Many experts argue that creative thinking requires people to challenge their preconceptions and assumptions about the way the world works. One common claim, for example, is that the mental shortcuts we all rely on to solve problems get in the way of creative thinking. How can you innovate if your thinking is anchored in past experience?

• TS Theodore Scaltsas is a Chaired Professor in Classical Philosophy at the University of Edinburgh in Scotland.

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48 Problem Solving

Department of Psychological and Brain Sciences, University of California, Santa Barbara

• Published: 03 June 2013
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Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or nonroutine, and as well defined or ill defined. The major cognitive processes in problem solving are representing, planning, executing, and monitoring. The major kinds of knowledge required for problem solving are facts, concepts, procedures, strategies, and beliefs. Classic theoretical approaches to the study of problem solving are associationism, Gestalt, and information processing. Current issues and suggested future issues include decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific thinking, everyday thinking, and the cognitive neuroscience of problem solving. Common themes concern the domain specificity of problem solving and a focus on problem solving in authentic contexts.

The study of problem solving begins with defining problem solving, problem, and problem types. This introduction to problem solving is rounded out with an examination of cognitive processes in problem solving, the role of knowledge in problem solving, and historical approaches to the study of problem solving.

Definition of Problem Solving

Problem solving refers to cognitive processing directed at achieving a goal for which the problem solver does not initially know a solution method. This definition consists of four major elements (Mayer, 1992 ; Mayer & Wittrock, 2006 ):

Cognitive —Problem solving occurs within the problem solver’s cognitive system and can only be inferred indirectly from the problem solver’s behavior (including biological changes, introspections, and actions during problem solving). Process —Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of a new mental representation. Directed —Problem solving is aimed at achieving a goal. Personal —Problem solving depends on the existing knowledge of the problem solver so that what is a problem for one problem solver may not be a problem for someone who already knows a solution method.

The definition is broad enough to include a wide array of cognitive activities such as deciding which apartment to rent, figuring out how to use a cell phone interface, playing a game of chess, making a medical diagnosis, finding the answer to an arithmetic word problem, or writing a chapter for a handbook. Problem solving is pervasive in human life and is crucial for human survival. Although this chapter focuses on problem solving in humans, problem solving also occurs in nonhuman animals and in intelligent machines.

How is problem solving related to other forms of high-level cognition processing, such as thinking and reasoning? Thinking refers to cognitive processing in individuals but includes both directed thinking (which corresponds to the definition of problem solving) and undirected thinking such as daydreaming (which does not correspond to the definition of problem solving). Thus, problem solving is a type of thinking (i.e., directed thinking).

Reasoning refers to problem solving within specific classes of problems, such as deductive reasoning or inductive reasoning. In deductive reasoning, the reasoner is given premises and must derive a conclusion by applying the rules of logic. For example, given that “A is greater than B” and “B is greater than C,” a reasoner can conclude that “A is greater than C.” In inductive reasoning, the reasoner is given (or has experienced) a collection of examples or instances and must infer a rule. For example, given that X, C, and V are in the “yes” group and x, c, and v are in the “no” group, the reasoning may conclude that B is in “yes” group because it is in uppercase format. Thus, reasoning is a type of problem solving.

Definition of Problem

A problem occurs when someone has a goal but does not know to achieve it. This definition is consistent with how the Gestalt psychologist Karl Duncker ( 1945 , p. 1) defined a problem in his classic monograph, On Problem Solving : “A problem arises when a living creature has a goal but does not know how this goal is to be reached.” However, today researchers recognize that the definition should be extended to include problem solving by intelligent machines. This definition can be clarified using an information processing approach by noting that a problem occurs when a situation is in the given state, the problem solver wants the situation to be in the goal state, and there is no obvious way to move from the given state to the goal state (Newell & Simon, 1972 ). Accordingly, the three main elements in describing a problem are the given state (i.e., the current state of the situation), the goal state (i.e., the desired state of the situation), and the set of allowable operators (i.e., the actions the problem solver is allowed to take). The definition of “problem” is broad enough to include the situation confronting a physician who wishes to make a diagnosis on the basis of preliminary tests and a patient examination, as well as a beginning physics student trying to solve a complex physics problem.

Types of Problems

It is customary in the problem-solving literature to make a distinction between routine and nonroutine problems. Routine problems are problems that are so familiar to the problem solver that the problem solver knows a solution method. For example, for most adults, “What is 365 divided by 12?” is a routine problem because they already know the procedure for long division. Nonroutine problems are so unfamiliar to the problem solver that the problem solver does not know a solution method. For example, figuring out the best way to set up a funding campaign for a nonprofit charity is a nonroutine problem for most volunteers. Technically, routine problems do not meet the definition of problem because the problem solver has a goal but knows how to achieve it. Much research on problem solving has focused on routine problems, although most interesting problems in life are nonroutine.

Another customary distinction is between well-defined and ill-defined problems. Well-defined problems have a clearly specified given state, goal state, and legal operators. Examples include arithmetic computation problems or games such as checkers or tic-tac-toe. Ill-defined problems have a poorly specified given state, goal state, or legal operators, or a combination of poorly defined features. Examples include solving the problem of global warming or finding a life partner. Although, ill-defined problems are more challenging, much research in problem solving has focused on well-defined problems.

Cognitive Processes in Problem Solving

The process of problem solving can be broken down into two main phases: problem representation , in which the problem solver builds a mental representation of the problem situation, and problem solution , in which the problem solver works to produce a solution. The major subprocess in problem representation is representing , which involves building a situation model —that is, a mental representation of the situation described in the problem. The major subprocesses in problem solution are planning , which involves devising a plan for how to solve the problem; executing , which involves carrying out the plan; and monitoring , which involves evaluating and adjusting one’s problem solving.

For example, given an arithmetic word problem such as “Alice has three marbles. Sarah has two more marbles than Alice. How many marbles does Sarah have?” the process of representing involves building a situation model in which Alice has a set of marbles, there is set of marbles for the difference between the two girls, and Sarah has a set of marbles that consists of Alice’s marbles and the difference set. In the planning process, the problem solver sets a goal of adding 3 and 2. In the executing process, the problem solver carries out the computation, yielding an answer of 5. In the monitoring process, the problem solver looks over what was done and concludes that 5 is a reasonable answer. In most complex problem-solving episodes, the four cognitive processes may not occur in linear order, but rather may interact with one another. Although some research focuses mainly on the execution process, problem solvers may tend to have more difficulty with the processes of representing, planning, and monitoring.

Knowledge for Problem Solving

An important theme in problem-solving research is that problem-solving proficiency on any task depends on the learner’s knowledge (Anderson et al., 2001 ; Mayer, 1992 ). Five kinds of knowledge are as follows:

Facts —factual knowledge about the characteristics of elements in the world, such as “Sacramento is the capital of California” Concepts —conceptual knowledge, including categories, schemas, or models, such as knowing the difference between plants and animals or knowing how a battery works Procedures —procedural knowledge of step-by-step processes, such as how to carry out long-division computations Strategies —strategic knowledge of general methods such as breaking a problem into parts or thinking of a related problem Beliefs —attitudinal knowledge about how one’s cognitive processing works such as thinking, “I’m good at this”

Although some research focuses mainly on the role of facts and procedures in problem solving, complex problem solving also depends on the problem solver’s concepts, strategies, and beliefs (Mayer, 1992 ).

Historical Approaches to Problem Solving

Psychological research on problem solving began in the early 1900s, as an outgrowth of mental philosophy (Humphrey, 1963 ; Mandler & Mandler, 1964 ). Throughout the 20th century four theoretical approaches developed: early conceptions, associationism, Gestalt psychology, and information processing.

Early Conceptions

The start of psychology as a science can be set at 1879—the year Wilhelm Wundt opened the first world’s psychology laboratory in Leipzig, Germany, and sought to train the world’s first cohort of experimental psychologists. Instead of relying solely on philosophical speculations about how the human mind works, Wundt sought to apply the methods of experimental science to issues addressed in mental philosophy. His theoretical approach became structuralism —the analysis of consciousness into its basic elements.

Wundt’s main contribution to the study of problem solving, however, was to call for its banishment. According to Wundt, complex cognitive processing was too complicated to be studied by experimental methods, so “nothing can be discovered in such experiments” (Wundt, 1911/1973 ). Despite his admonishments, however, a group of his former students began studying thinking mainly in Wurzburg, Germany. Using the method of introspection, subjects were asked to describe their thought process as they solved word association problems, such as finding the superordinate of “newspaper” (e.g., an answer is “publication”). Although the Wurzburg group—as they came to be called—did not produce a new theoretical approach, they found empirical evidence that challenged some of the key assumptions of mental philosophy. For example, Aristotle had proclaimed that all thinking involves mental imagery, but the Wurzburg group was able to find empirical evidence for imageless thought .

Associationism

The first major theoretical approach to take hold in the scientific study of problem solving was associationism —the idea that the cognitive representations in the mind consist of ideas and links between them and that cognitive processing in the mind involves following a chain of associations from one idea to the next (Mandler & Mandler, 1964 ; Mayer, 1992 ). For example, in a classic study, E. L. Thorndike ( 1911 ) placed a hungry cat in what he called a puzzle box—a wooden crate in which pulling a loop of string that hung from overhead would open a trap door to allow the cat to escape to a bowl of food outside the crate. Thorndike placed the cat in the puzzle box once a day for several weeks. On the first day, the cat engaged in many extraneous behaviors such as pouncing against the wall, pushing its paws through the slats, and meowing, but on successive days the number of extraneous behaviors tended to decrease. Overall, the time required to get out of the puzzle box decreased over the course of the experiment, indicating the cat was learning how to escape.

Thorndike’s explanation for how the cat learned to solve the puzzle box problem is based on an associationist view: The cat begins with a habit family hierarchy —a set of potential responses (e.g., pouncing, thrusting, meowing, etc.) all associated with the same stimulus (i.e., being hungry and confined) and ordered in terms of strength of association. When placed in the puzzle box, the cat executes its strongest response (e.g., perhaps pouncing against the wall), but when it fails, the strength of the association is weakened, and so on for each unsuccessful action. Eventually, the cat gets down to what was initially a weak response—waving its paw in the air—but when that response leads to accidentally pulling the string and getting out, it is strengthened. Over the course of many trials, the ineffective responses become weak and the successful response becomes strong. Thorndike refers to this process as the law of effect : Responses that lead to dissatisfaction become less associated with the situation and responses that lead to satisfaction become more associated with the situation. According to Thorndike’s associationist view, solving a problem is simply a matter of trial and error and accidental success. A major challenge to assocationist theory concerns the nature of transfer—that is, where does a problem solver find a creative solution that has never been performed before? Associationist conceptions of cognition can be seen in current research, including neural networks, connectionist models, and parallel distributed processing models (Rogers & McClelland, 2004 ).

Gestalt Psychology

The Gestalt approach to problem solving developed in the 1930s and 1940s as a counterbalance to the associationist approach. According to the Gestalt approach, cognitive representations consist of coherent structures (rather than individual associations) and the cognitive process of problem solving involves building a coherent structure (rather than strengthening and weakening of associations). For example, in a classic study, Kohler ( 1925 ) placed a hungry ape in a play yard that contained several empty shipping crates and a banana attached overhead but out of reach. Based on observing the ape in this situation, Kohler noted that the ape did not randomly try responses until one worked—as suggested by Thorndike’s associationist view. Instead, the ape stood under the banana, looked up at it, looked at the crates, and then in a flash of insight stacked the crates under the bananas as a ladder, and walked up the steps in order to reach the banana.

According to Kohler, the ape experienced a sudden visual reorganization in which the elements in the situation fit together in a way to solve the problem; that is, the crates could become a ladder that reduces the distance to the banana. Kohler referred to the underlying mechanism as insight —literally seeing into the structure of the situation. A major challenge of Gestalt theory is its lack of precision; for example, naming a process (i.e., insight) is not the same as explaining how it works. Gestalt conceptions can be seen in modern research on mental models and schemas (Gentner & Stevens, 1983 ).

Information Processing

The information processing approach to problem solving developed in the 1960s and 1970s and was based on the influence of the computer metaphor—the idea that humans are processors of information (Mayer, 2009 ). According to the information processing approach, problem solving involves a series of mental computations—each of which consists of applying a process to a mental representation (such as comparing two elements to determine whether they differ).

In their classic book, Human Problem Solving , Newell and Simon ( 1972 ) proposed that problem solving involved a problem space and search heuristics . A problem space is a mental representation of the initial state of the problem, the goal state of the problem, and all possible intervening states (based on applying allowable operators). Search heuristics are strategies for moving through the problem space from the given to the goal state. Newell and Simon focused on means-ends analysis , in which the problem solver continually sets goals and finds moves to accomplish goals.

Newell and Simon used computer simulation as a research method to test their conception of human problem solving. First, they asked human problem solvers to think aloud as they solved various problems such as logic problems, chess, and cryptarithmetic problems. Then, based on an information processing analysis, Newell and Simon created computer programs that solved these problems. In comparing the solution behavior of humans and computers, they found high similarity, suggesting that the computer programs were solving problems using the same thought processes as humans.

An important advantage of the information processing approach is that problem solving can be described with great clarity—as a computer program. An important limitation of the information processing approach is that it is most useful for describing problem solving for well-defined problems rather than ill-defined problems. The information processing conception of cognition lives on as a keystone of today’s cognitive science (Mayer, 2009 ).

Classic Issues in Problem Solving

Three classic issues in research on problem solving concern the nature of transfer (suggested by the associationist approach), the nature of insight (suggested by the Gestalt approach), and the role of problem-solving heuristics (suggested by the information processing approach).

Transfer refers to the effects of prior learning on new learning (or new problem solving). Positive transfer occurs when learning A helps someone learn B. Negative transfer occurs when learning A hinders someone from learning B. Neutral transfer occurs when learning A has no effect on learning B. Positive transfer is a central goal of education, but research shows that people often do not transfer what they learned to solving problems in new contexts (Mayer, 1992 ; Singley & Anderson, 1989 ).

Three conceptions of the mechanisms underlying transfer are specific transfer , general transfer , and specific transfer of general principles . Specific transfer refers to the idea that learning A will help someone learn B only if A and B have specific elements in common. For example, learning Spanish may help someone learn Latin because some of the vocabulary words are similar and the verb conjugation rules are similar. General transfer refers to the idea that learning A can help someone learn B even they have nothing specifically in common but A helps improve the learner’s mind in general. For example, learning Latin may help people learn “proper habits of mind” so they are better able to learn completely unrelated subjects as well. Specific transfer of general principles is the idea that learning A will help someone learn B if the same general principle or solution method is required for both even if the specific elements are different.

In a classic study, Thorndike and Woodworth ( 1901 ) found that students who learned Latin did not subsequently learn bookkeeping any better than students who had not learned Latin. They interpreted this finding as evidence for specific transfer—learning A did not transfer to learning B because A and B did not have specific elements in common. Modern research on problem-solving transfer continues to show that people often do not demonstrate general transfer (Mayer, 1992 ). However, it is possible to teach people a general strategy for solving a problem, so that when they see a new problem in a different context they are able to apply the strategy to the new problem (Judd, 1908 ; Mayer, 2008 )—so there is also research support for the idea of specific transfer of general principles.

Insight refers to a change in a problem solver’s mind from not knowing how to solve a problem to knowing how to solve it (Mayer, 1995 ; Metcalfe & Wiebe, 1987 ). In short, where does the idea for a creative solution come from? A central goal of problem-solving research is to determine the mechanisms underlying insight.

The search for insight has led to five major (but not mutually exclusive) explanatory mechanisms—insight as completing a schema, insight as suddenly reorganizing visual information, insight as reformulation of a problem, insight as removing mental blocks, and insight as finding a problem analog (Mayer, 1995 ). Completing a schema is exemplified in a study by Selz (Fridja & de Groot, 1982 ), in which people were asked to think aloud as they solved word association problems such as “What is the superordinate for newspaper?” To solve the problem, people sometimes thought of a coordinate, such as “magazine,” and then searched for a superordinate category that subsumed both terms, such as “publication.” According to Selz, finding a solution involved building a schema that consisted of a superordinate and two subordinate categories.

Reorganizing visual information is reflected in Kohler’s ( 1925 ) study described in a previous section in which a hungry ape figured out how to stack boxes as a ladder to reach a banana hanging above. According to Kohler, the ape looked around the yard and found the solution in a flash of insight by mentally seeing how the parts could be rearranged to accomplish the goal.

Reformulating a problem is reflected in a classic study by Duncker ( 1945 ) in which people are asked to think aloud as they solve the tumor problem—how can you destroy a tumor in a patient without destroying surrounding healthy tissue by using rays that at sufficient intensity will destroy any tissue in their path? In analyzing the thinking-aloud protocols—that is, transcripts of what the problem solvers said—Duncker concluded that people reformulated the goal in various ways (e.g., avoid contact with healthy tissue, immunize healthy tissue, have ray be weak in healthy tissue) until they hit upon a productive formulation that led to the solution (i.e., concentrating many weak rays on the tumor).

Removing mental blocks is reflected in classic studies by Duncker ( 1945 ) in which solving a problem involved thinking of a novel use for an object, and by Luchins ( 1942 ) in which solving a problem involved not using a procedure that had worked well on previous problems. Finding a problem analog is reflected in classic research by Wertheimer ( 1959 ) in which learning to find the area of a parallelogram is supported by the insight that one could cut off the triangle on one side and place it on the other side to form a rectangle—so a parallelogram is really a rectangle in disguise. The search for insight along each of these five lines continues in current problem-solving research.

Heuristics are problem-solving strategies, that is, general approaches to how to solve problems. Newell and Simon ( 1972 ) suggested three general problem-solving heuristics for moving from a given state to a goal state: random trial and error , hill climbing , and means-ends analysis . Random trial and error involves randomly selecting a legal move and applying it to create a new problem state, and repeating that process until the goal state is reached. Random trial and error may work for simple problems but is not efficient for complex ones. Hill climbing involves selecting the legal move that moves the problem solver closer to the goal state. Hill climbing will not work for problems in which the problem solver must take a move that temporarily moves away from the goal as is required in many problems.

Means-ends analysis involves creating goals and seeking moves that can accomplish the goal. If a goal cannot be directly accomplished, a subgoal is created to remove one or more obstacles. Newell and Simon ( 1972 ) successfully used means-ends analysis as the search heuristic in a computer program aimed at general problem solving, that is, solving a diverse collection of problems. However, people may also use specific heuristics that are designed to work for specific problem-solving situations (Gigerenzer, Todd, & ABC Research Group, 1999 ; Kahneman & Tversky, 1984 ).

Current and Future Issues in Problem Solving

Eight current issues in problem solving involve decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific problem solving, everyday thinking, and the cognitive neuroscience of problem solving.

Decision Making

Decision making refers to the cognitive processing involved in choosing between two or more alternatives (Baron, 2000 ; Markman & Medin, 2002 ). For example, a decision-making task may involve choosing between getting $240 for sure or having a 25% change of getting $1000. According to economic theories such as expected value theory, people should chose the second option, which is worth $250 (i.e., .25 x $1000) rather than the first option, which is worth $240 (1.00 x $240), but psychological research shows that most people prefer the first option (Kahneman & Tversky, 1984 ).

Research on decision making has generated three classes of theories (Markman & Medin, 2002 ): descriptive theories, such as prospect theory (Kahneman & Tversky), which are based on the ideas that people prefer to overweight the cost of a loss and tend to overestimate small probabilities; heuristic theories, which are based on the idea that people use a collection of short-cut strategies such as the availability heuristic (Gigerenzer et al., 1999 ; Kahneman & Tversky, 2000 ); and constructive theories, such as mental accounting (Kahneman & Tversky, 2000 ), in which people build a narrative to justify their choices to themselves. Future research is needed to examine decision making in more realistic settings.

Intelligence and Creativity

Although researchers do not have complete consensus on the definition of intelligence (Sternberg, 1990 ), it is reasonable to view intelligence as the ability to learn or adapt to new situations. Fluid intelligence refers to the potential to solve problems without any relevant knowledge, whereas crystallized intelligence refers to the potential to solve problems based on relevant prior knowledge (Sternberg & Gregorenko, 2003 ). As people gain more experience in a field, their problem-solving performance depends more on crystallized intelligence (i.e., domain knowledge) than on fluid intelligence (i.e., general ability) (Sternberg & Gregorenko, 2003 ). The ability to monitor and manage one’s cognitive processing during problem solving—which can be called metacognition —is an important aspect of intelligence (Sternberg, 1990 ). Research is needed to pinpoint the knowledge that is needed to support intelligent performance on problem-solving tasks.

Creativity refers to the ability to generate ideas that are original (i.e., other people do not think of the same idea) and functional (i.e., the idea works; Sternberg, 1999 ). Creativity is often measured using tests of divergent thinking —that is, generating as many solutions as possible for a problem (Guilford, 1967 ). For example, the uses test asks people to list as many uses as they can think of for a brick. Creativity is different from intelligence, and it is at the heart of creative problem solving—generating a novel solution to a problem that the problem solver has never seen before. An important research question concerns whether creative problem solving depends on specific knowledge or creativity ability in general.

Teaching of Thinking Skills

How can people learn to be better problem solvers? Mayer ( 2008 ) proposes four questions concerning teaching of thinking skills:

What to teach —Successful programs attempt to teach small component skills (such as how to generate and evaluate hypotheses) rather than improve the mind as a single monolithic skill (Covington, Crutchfield, Davies, & Olton, 1974 ). How to teach —Successful programs focus on modeling the process of problem solving rather than solely reinforcing the product of problem solving (Bloom & Broder, 1950 ). Where to teach —Successful programs teach problem-solving skills within the specific context they will be used rather than within a general course on how to solve problems (Nickerson, 1999 ). When to teach —Successful programs teaching higher order skills early rather than waiting until lower order skills are completely mastered (Tharp & Gallimore, 1988 ).

Overall, research on teaching of thinking skills points to the domain specificity of problem solving; that is, successful problem solving depends on the problem solver having domain knowledge that is relevant to the problem-solving task.

Expert Problem Solving

Research on expertise is concerned with differences between how experts and novices solve problems (Ericsson, Feltovich, & Hoffman, 2006 ). Expertise can be defined in terms of time (e.g., 10 years of concentrated experience in a field), performance (e.g., earning a perfect score on an assessment), or recognition (e.g., receiving a Nobel Prize or becoming Grand Master in chess). For example, in classic research conducted in the 1940s, de Groot ( 1965 ) found that chess experts did not have better general memory than chess novices, but they did have better domain-specific memory for the arrangement of chess pieces on the board. Chase and Simon ( 1973 ) replicated this result in a better controlled experiment. An explanation is that experts have developed schemas that allow them to chunk collections of pieces into a single configuration.

In another landmark study, Larkin et al. ( 1980 ) compared how experts (e.g., physics professors) and novices (e.g., first-year physics students) solved textbook physics problems about motion. Experts tended to work forward from the given information to the goal, whereas novices tended to work backward from the goal to the givens using a means-ends analysis strategy. Experts tended to store their knowledge in an integrated way, whereas novices tended to store their knowledge in isolated fragments. In another study, Chi, Feltovich, and Glaser ( 1981 ) found that experts tended to focus on the underlying physics concepts (such as conservation of energy), whereas novices tended to focus on the surface features of the problem (such as inclined planes or springs). Overall, research on expertise is useful in pinpointing what experts know that is different from what novices know. An important theme is that experts rely on domain-specific knowledge rather than solely general cognitive ability.

Analogical Reasoning

Analogical reasoning occurs when people solve one problem by using their knowledge about another problem (Holyoak, 2005 ). For example, suppose a problem solver learns how to solve a problem in one context using one solution method and then is given a problem in another context that requires the same solution method. In this case, the problem solver must recognize that the new problem has structural similarity to the old problem (i.e., it may be solved by the same method), even though they do not have surface similarity (i.e., the cover stories are different). Three steps in analogical reasoning are recognizing —seeing that a new problem is similar to a previously solved problem; abstracting —finding the general method used to solve the old problem; and mapping —using that general method to solve the new problem.

Research on analogical reasoning shows that people often do not recognize that a new problem can be solved by the same method as a previously solved problem (Holyoak, 2005 ). However, research also shows that successful analogical transfer to a new problem is more likely when the problem solver has experience with two old problems that have the same underlying structural features (i.e., they are solved by the same principle) but different surface features (i.e., they have different cover stories) (Holyoak, 2005 ). This finding is consistent with the idea of specific transfer of general principles as described in the section on “Transfer.”

Mathematical and Scientific Problem Solving

Research on mathematical problem solving suggests that five kinds of knowledge are needed to solve arithmetic word problems (Mayer, 2008 ):

Factual knowledge —knowledge about the characteristics of problem elements, such as knowing that there are 100 cents in a dollar Schematic knowledge —knowledge of problem types, such as being able to recognize time-rate-distance problems Strategic knowledge —knowledge of general methods, such as how to break a problem into parts Procedural knowledge —knowledge of processes, such as how to carry our arithmetic operations Attitudinal knowledge —beliefs about one’s mathematical problem-solving ability, such as thinking, “I am good at this”

People generally possess adequate procedural knowledge but may have difficulty in solving mathematics problems because they lack factual, schematic, strategic, or attitudinal knowledge (Mayer, 2008 ). Research is needed to pinpoint the role of domain knowledge in mathematical problem solving.

Research on scientific problem solving shows that people harbor misconceptions, such as believing that a force is needed to keep an object in motion (McCloskey, 1983 ). Learning to solve science problems involves conceptual change, in which the problem solver comes to recognize that previous conceptions are wrong (Mayer, 2008 ). Students can be taught to engage in scientific reasoning such as hypothesis testing through direct instruction in how to control for variables (Chen & Klahr, 1999 ). A central theme of research on scientific problem solving concerns the role of domain knowledge.

Everyday Thinking

Everyday thinking refers to problem solving in the context of one’s life outside of school. For example, children who are street vendors tend to use different procedures for solving arithmetic problems when they are working on the streets than when they are in school (Nunes, Schlieman, & Carraher, 1993 ). This line of research highlights the role of situated cognition —the idea that thinking always is shaped by the physical and social context in which it occurs (Robbins & Aydede, 2009 ). Research is needed to determine how people solve problems in authentic contexts.

Cognitive Neuroscience of Problem Solving

The cognitive neuroscience of problem solving is concerned with the brain activity that occurs during problem solving. For example, using fMRI brain imaging methodology, Goel ( 2005 ) found that people used the language areas of the brain to solve logical reasoning problems presented in sentences (e.g., “All dogs are pets…”) and used the spatial areas of the brain to solve logical reasoning problems presented in abstract letters (e.g., “All D are P…”). Cognitive neuroscience holds the potential to make unique contributions to the study of problem solving.

Problem solving has always been a topic at the fringe of cognitive psychology—too complicated to study intensively but too important to completely ignore. Problem solving—especially in realistic environments—is messy in comparison to studying elementary processes in cognition. The field remains fragmented in the sense that topics such as decision making, reasoning, intelligence, expertise, mathematical problem solving, everyday thinking, and the like are considered to be separate topics, each with its own separate literature. Yet some recurring themes are the role of domain-specific knowledge in problem solving and the advantages of studying problem solving in authentic contexts.

Future Directions

Some important issues for future research include the three classic issues examined in this chapter—the nature of problem-solving transfer (i.e., How are people able to use what they know about previous problem solving to help them in new problem solving?), the nature of insight (e.g., What is the mechanism by which a creative solution is constructed?), and heuristics (e.g., What are some teachable strategies for problem solving?). In addition, future research in problem solving should continue to pinpoint the role of domain-specific knowledge in problem solving, the nature of cognitive ability in problem solving, how to help people develop proficiency in solving problems, and how to provide aids for problem solving.

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Further Reading

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Weisberg, R. W. ( 2006 ). Creativity . New York: Wiley.

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Creativity in problem solving: integrating two different views of insight

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

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

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

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1 Introduction

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

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

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

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

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

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

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

1.1 Problem solving models

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

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

The cognitive-metacognitive model (Lester, 1985 )

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

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

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

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

1.2 Creativity models

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

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

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

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

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

1.3 Expert and novice problem solvers

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

Knowledge for understanding and representing problems (Orientation).

Strategic knowledge (Organization).

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

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

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

2.1 Data collection and materials

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

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

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

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

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

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

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

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

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

which boils down to

and finally

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

2.2 Data analysis

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

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

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

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

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

3.1 Problem 1: the Roman inheritance problem

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

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

Experts’ equation solution to the Roman problem

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

Novice students We identified three approaches for the novice groups.

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

Example of novices’ model solution for the Roman problem

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

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

3.2 Problem 2: wrong arithmetic, but correct result

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

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

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

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

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

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

3.3 Problem solving model

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

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

3.4 Creativity model

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

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

3.5 How students gained insight

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

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

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

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

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

4 Final thoughts

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

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

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

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

• Problem-solving techniques to identify and analyze problems
• Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

• Six Thinking Hats
• Lightning Decision Jam
• Problem Definition Process
• Discovery & Action Dialogue

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

• The Creativity Dice
• Fishbone Analysis
• Problem Tree
• SWOT Analysis
• Agreement-Certainty Matrix
• The Journalistic Six
• LEGO Challenge
• What, So What, Now What?
• Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

• Improved Solutions
• Four-Step Sketch
• 15% Solutions
• How-Now-Wow matrix
• Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

• Check-in/Check-out
• Doodling Together
• Show and Tell
• Constellations
• Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

• One Breath Feedback
• Who What When Matrix
• Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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Critical Thinking Definition, Skills, and Examples

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Critical thinking refers to the ability to analyze information objectively and make a reasoned judgment. It involves the evaluation of sources, such as data, facts, observable phenomena, and research findings.

Good critical thinkers can draw reasonable conclusions from a set of information, and discriminate between useful and less useful details to solve problems or make decisions. Employers prioritize the ability to think critically—find out why, plus see how you can demonstrate that you have this ability throughout the job application process. 

Why Do Employers Value Critical Thinking Skills?

Employers want job candidates who can evaluate a situation using logical thought and offer the best solution.

 Someone with critical thinking skills can be trusted to make decisions independently, and will not need constant handholding.

Hiring a critical thinker means that micromanaging won't be required. Critical thinking abilities are among the most sought-after skills in almost every industry and workplace. You can demonstrate critical thinking by using related keywords in your resume and cover letter, and during your interview.

Examples of Critical Thinking

The circumstances that demand critical thinking vary from industry to industry. Some examples include:

• A triage nurse analyzes the cases at hand and decides the order by which the patients should be treated.
• A plumber evaluates the materials that would best suit a particular job.
• An attorney reviews evidence and devises a strategy to win a case or to decide whether to settle out of court.
• A manager analyzes customer feedback forms and uses this information to develop a customer service training session for employees.

Promote Your Skills in Your Job Search

If critical thinking is a key phrase in the job listings you are applying for, be sure to emphasize your critical thinking skills throughout your job search.

Add Keywords to Your Resume

You can use critical thinking keywords (analytical, problem solving, creativity, etc.) in your resume. When describing your  work history , include top critical thinking skills that accurately describe you. You can also include them in your  resume summary , if you have one.

For example, your summary might read, “Marketing Associate with five years of experience in project management. Skilled in conducting thorough market research and competitor analysis to assess market trends and client needs, and to develop appropriate acquisition tactics.”

Mention Skills in Your Cover Letter

Include these critical thinking skills in your cover letter. In the body of your letter, mention one or two of these skills, and give specific examples of times when you have demonstrated them at work. Think about times when you had to analyze or evaluate materials to solve a problem.

Show the Interviewer Your Skills

You can use these skill words in an interview. Discuss a time when you were faced with a particular problem or challenge at work and explain how you applied critical thinking to solve it.

Some interviewers will give you a hypothetical scenario or problem, and ask you to use critical thinking skills to solve it. In this case, explain your thought process thoroughly to the interviewer. He or she is typically more focused on how you arrive at your solution rather than the solution itself. The interviewer wants to see you analyze and evaluate (key parts of critical thinking) the given scenario or problem.

Of course, each job will require different skills and experiences, so make sure you read the job description carefully and focus on the skills listed by the employer.

Top Critical Thinking Skills

Keep these in-demand critical thinking skills in mind as you update your resume and write your cover letter. As you've seen, you can also emphasize them at other points throughout the application process, such as your interview. 

Part of critical thinking is the ability to carefully examine something, whether it is a problem, a set of data, or a text. People with  analytical skills  can examine information, understand what it means, and properly explain to others the implications of that information.

• Asking Thoughtful Questions
• Data Analysis
• Interpretation
• Questioning Evidence
• Recognizing Patterns

Communication

Often, you will need to share your conclusions with your employers or with a group of colleagues. You need to be able to  communicate with others  to share your ideas effectively. You might also need to engage in critical thinking in a group. In this case, you will need to work with others and communicate effectively to figure out solutions to complex problems.

• Active Listening
• Collaboration
• Explanation
• Interpersonal
• Presentation
• Verbal Communication
• Written Communication

Critical thinking often involves creativity and innovation. You might need to spot patterns in the information you are looking at or come up with a solution that no one else has thought of before. All of this involves a creative eye that can take a different approach from all other approaches.

• Flexibility
• Conceptualization
• Imagination
• Drawing Connections
• Synthesizing

Open-Mindedness

To think critically, you need to be able to put aside any assumptions or judgments and merely analyze the information you receive. You need to be objective, evaluating ideas without bias.

• Objectivity
• Observation

Problem Solving

Problem-solving is another critical thinking skill that involves analyzing a problem, generating and implementing a solution, and assessing the success of the plan. Employers don’t simply want employees who can think about information critically. They also need to be able to come up with practical solutions.

• Attention to Detail
• Clarification
• Decision Making
• Groundedness
• Identifying Patterns

More Critical Thinking Skills

• Inductive Reasoning
• Deductive Reasoning
• Noticing Outliers
• Adaptability
• Emotional Intelligence
• Brainstorming
• Optimization
• Restructuring
• Integration
• Strategic Planning
• Project Management
• Ongoing Improvement
• Causal Relationships
• Case Analysis
• Diagnostics
• SWOT Analysis
• Business Intelligence
• Quantitative Data Management
• Qualitative Data Management
• Risk Management
• Scientific Method
• Consumer Behavior

Key Takeaways

• Demonstrate that you have critical thinking skills by adding relevant keywords to your resume.
• Mention pertinent critical thinking skills in your cover letter, too, and include an example of a time when you demonstrated them at work.
• Finally, highlight critical thinking skills during your interview. For instance, you might discuss a time when you were faced with a challenge at work and explain how you applied critical thinking skills to solve it.

University of Louisville. " What is Critical Thinking ."

American Management Association. " AMA Critical Skills Survey: Workers Need Higher Level Skills to Succeed in the 21st Century ."

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