real world problem solving examples

39 Best Problem-Solving Examples

Problem-solving is a process where you’re tasked with identifying an issue and coming up with the most practical and effective solution.

This indispensable skill is necessary in several aspects of life, from personal relationships to education to business decisions.

Problem-solving aptitude boosts rational thinking, creativity, and the ability to cooperate with others. It’s also considered essential in 21st Century workplaces.

If explaining your problem-solving skills in an interview, remember that the employer is trying to determine your ability to handle difficulties. Focus on explaining exactly how you solve problems, including by introducing your thoughts on some of the following frameworks and how you’ve applied them in the past.

Problem-Solving Examples

1. divergent thinking.

Divergent thinking refers to the process of coming up with multiple different answers to a single problem. It’s the opposite of convergent thinking, which would involve coming up with a singular answer .

The benefit of a divergent thinking approach is that it can help us achieve blue skies thinking – it lets us generate several possible solutions that we can then critique and analyze .

In the realm of problem-solving, divergent thinking acts as the initial spark. You’re working to create an array of potential solutions, even those that seem outwardly unrelated or unconventional, to get your brain turning and unlock out-of-the-box ideas.

This process paves the way for the decision-making stage, where the most promising ideas are selected and refined.

Go Deeper: Divervent Thinking Examples

2. Convergent Thinking

Next comes convergent thinking, the process of narrowing down multiple possibilities to arrive at a single solution.

This involves using your analytical skills to identify the best, most practical, or most economical solution from the pool of ideas that you generated in the divergent thinking stage.

In a way, convergent thinking shapes the “roadmap” to solve a problem after divergent thinking has supplied the “destinations.”

Have a think about which of these problem-solving skills you’re more adept at: divergent or convergent thinking?

Go Deeper: Convergent Thinking Examples

3. Brainstorming

Brainstorming is a group activity designed to generate a multitude of ideas regarding a specific problem. It’s divergent thinking as a group , which helps unlock even more possibilities.

A typical brainstorming session involves uninhibited and spontaneous ideation, encouraging participants to voice any possible solutions, no matter how unconventional they might appear.

It’s important in a brainstorming session to suspend judgment and be as inclusive as possible, allowing all participants to get involved.

By widening the scope of potential solutions, brainstorming allows better problem definition, more creative solutions, and helps to avoid thinking “traps” that might limit your perspective.

Go Deeper: Brainstorming Examples

4. Thinking Outside the Box

The concept of “thinking outside the box” encourages a shift in perspective, urging you to approach problems from an entirely new angle.

Rather than sticking to traditional methods and processes, it involves breaking away from conventional norms to cultivate unique solutions.

In problem-solving, this mindset can bypass established hurdles and bring you to fresh ideas that might otherwise remain undiscovered.

Think of it as going off the beaten track when regular routes present roadblocks to effective resolution.

5. Case Study Analysis

Analyzing case studies involves a detailed examination of real-life situations that bear relevance to the current problem at hand.

For example, if you’re facing a problem, you could go to another environment that has faced a similar problem and examine how they solved it. You’d then bring the insights from that case study back to your own problem.

This approach provides a practical backdrop against which theories and assumptions can be tested, offering valuable insights into how similar problems have been approached and resolved in the past.

See a Broader Range of Analysis Examples Here

6. Action Research

Action research involves a repetitive process of identifying a problem, formulating a plan to address it, implementing the plan, and then analyzing the results. It’s common in educational research contexts.

The objective is to promote continuous learning and improvement through reflection and action. You conduct research into your problem, attempt to apply a solution, then assess how well the solution worked. This becomes an iterative process of continual improvement over time.

For problem-solving, this method offers a way to test solutions in real-time and allows for changes and refinements along the way, based on feedback or observed outcomes. It’s a form of active problem-solving that integrates lessons learned into the next cycle of action.

Go Deeper: Action Research Examples

7. Information Gathering

Fundamental to solving any problem is the process of information gathering.

This involves collecting relevant data , facts, and details about the issue at hand, significantly aiding in the understanding and conceptualization of the problem.

In problem-solving, information gathering underpins every decision you make.

This process ensures your actions are based on concrete information and evidence, allowing for an informed approach to tackle the problem effectively.

8. Seeking Advice

Seeking advice implies turning to knowledgeable and experienced individuals or entities to gain insights on problem-solving.

It could include mentors, industry experts, peers, or even specialized literature.

The value in this process lies in leveraging different perspectives and proven strategies when dealing with a problem. Moreover, it aids you in avoiding pitfalls, saving time, and learning from others’ experiences.

9. Creative Thinking

Creative thinking refers to the ability to perceive a problem in a new way, identify unconventional patterns, or produce original solutions.

It encourages innovation and uniqueness, often leading to the most effective results.

When applied to problem-solving, creative thinking can help you break free from traditional constraints, ideal for potentially complex or unusual problems.

Go Deeper: Creative Thinking Examples

10. Conflict Resolution

Conflict resolution is a strategy developed to resolve disagreements and arguments, often involving communication, negotiation, and compromise.

When employed as a problem-solving technique, it can diffuse tension, clear bottlenecks, and create a collaborative environment.

Effective conflict resolution ensures that differing views or disagreements do not become roadblocks in the process of problem-solving.

Go Deeper: Conflict Resolution Examples

11. Addressing Bottlenecks

Bottlenecks refer to obstacles or hindrances that slow down or even halt a process.

In problem-solving, addressing bottlenecks involves identifying these impediments and finding ways to eliminate them.

This effort not only smooths the path to resolution but also enhances the overall efficiency of the problem-solving process.

For example, if your workflow is not working well, you’d go to the bottleneck – that one point that is most time consuming – and focus on that. Once you ‘break’ this bottleneck, the entire process will run more smoothly.

12. Market Research

Market research involves gathering and analyzing information about target markets, consumers, and competitors.

In sales and marketing, this is one of the most effective problem-solving methods. The research collected from your market (e.g. from consumer surveys) generates data that can help identify market trends, customer preferences, and competitor strategies.

In this sense, it allows a company to make informed decisions, solve existing problems, and even predict and prevent future ones.

13. Root Cause Analysis

Root cause analysis is a method used to identify the origin or the fundamental reason for a problem.

Once the root cause is determined, you can implement corrective actions to prevent the problem from recurring.

As a problem-solving procedure, root cause analysis helps you to tackle the problem at its source, rather than dealing with its surface symptoms.

Go Deeper: Root Cause Analysis Examples

14. Mind Mapping

Mind mapping is a visual tool used to structure information, helping you better analyze, comprehend and generate new ideas.

By laying out your thoughts visually, it can lead you to solutions that might not have been apparent with linear thinking.

In problem-solving, mind mapping helps in organizing ideas and identifying connections between them, providing a holistic view of the situation and potential solutions.

15. Trial and Error

The trial and error method involves attempting various solutions until you find one that resolves the problem.

It’s an empirical technique that relies on practical actions instead of theories or rules.

In the context of problem-solving, trial and error allows you the flexibility to test different strategies in real situations, gaining insights about what works and what doesn’t.

16. SWOT Analysis

SWOT is an acronym standing for Strengths, Weaknesses, Opportunities, and Threats.

It’s an analytic framework used to evaluate these aspects in relation to a particular objective or problem.

In problem-solving, SWOT Analysis helps you to identify favorable and unfavorable internal and external factors. It helps to craft strategies that make best use of your strengths and opportunities, whilst addressing weaknesses and threats.

Go Deeper: SWOT Analysis Examples

17. Scenario Planning

Scenario planning is a strategic planning method used to make flexible long-term plans.

It involves imagining, and then planning for, multiple likely future scenarios.

By forecasting various directions a problem could take, scenario planning helps manage uncertainty and is an effective tool for problem-solving in volatile conditions.

18. Six Thinking Hats

The Six Thinking Hats is a concept devised by Edward de Bono that proposes six different directions or modes of thinking, symbolized by six different hat colors.

Each hat signifies a different perspective, encouraging you to switch ‘thinking modes’ as you switch hats. This method can help remove bias and broaden perspectives when dealing with a problem.

19. Decision Matrix Analysis

Decision Matrix Analysis is a technique that allows you to weigh different factors when faced with several possible solutions.

After listing down the options and determining the factors of importance, each option is scored based on each factor.

Revealing a clear winner that both serves your objectives and reflects your values, Decision Matrix Analysis grounds your problem-solving process in objectivity and comprehensiveness.

20. Pareto Analysis

Also known as the 80/20 rule, Pareto Analysis is a decision-making technique.

It’s based on the principle that 80% of problems are typically caused by 20% of the causes, making it a handy tool for identifying the most significant issues in a situation.

Using this analysis, you’re likely to direct your problem-solving efforts more effectively, tackling the root causes producing most of the problem’s impact.

21. Critical Thinking

Critical thinking refers to the ability to analyze facts to form a judgment objectively.

It involves logical, disciplined thinking that is clear, rational, open-minded, and informed by evidence.

For problem-solving, critical thinking helps evaluate options and decide the most effective solution. It ensures your decisions are grounded in reason and facts, and not biased or irrational assumptions.

Go Deeper: Critical Thinking Examples

22. Hypothesis Testing

Hypothesis testing usually involves formulating a claim, testing it against actual data, and deciding whether to accept or reject the claim based on the results.

In problem-solving, hypotheses often represent potential solutions. Hypothesis testing provides verification, giving a statistical basis for decision-making and problem resolution.

Usually, this will require research methods and a scientific approach to see whether the hypothesis stands up or not.

Go Deeper: Types of Hypothesis Testing

23. Cost-Benefit Analysis

A cost-benefit analysis (CBA) is a systematic process of weighing the pros and cons of different solutions in terms of their potential costs and benefits.

It allows you to measure the positive effects against the negatives and informs your problem-solving strategy.

By using CBA, you can identify which solution offers the greatest benefit for the least cost, significantly improving efficacy and efficiency in your problem-solving process.

Go Deeper: Cost-Benefit Analysis Examples

24. Simulation and Modeling

Simulations and models allow you to create a simplified replica of real-world systems to test outcomes under controlled conditions.

In problem-solving, you can broadly understand potential repercussions of different solutions before implementation.

It offers a cost-effective way to predict the impacts of your decisions, minimizing potential risks associated with various solutions.

25. Delphi Method

The Delphi Method is a structured communication technique used to gather expert opinions.

The method involves a group of experts who respond to questionnaires about a problem. The responses are aggregated and shared with the group, and the process repeats until a consensus is reached.

This method of problem solving can provide a diverse range of insights and solutions, shaped by the wisdom of a collective expert group.

26. Cross-functional Team Collaboration

Cross-functional team collaboration involves individuals from different departments or areas of expertise coming together to solve a common problem or achieve a shared goal.

When you bring diverse skills, knowledge, and perspectives to a problem, it can lead to a more comprehensive and innovative solution.

In problem-solving, this promotes communal thinking and ensures that solutions are inclusive and holistic, with various aspects of the problem being addressed.

27. Benchmarking

Benchmarking involves comparing one’s business processes and performance metrics to the best practices from other companies or industries.

In problem-solving, it allows you to identify gaps in your own processes, determine how others have solved similar problems, and apply those solutions that have proven to be successful.

It also allows you to compare yourself to the best (the benchmark) and assess where you’re not as good.

28. Pros-Cons Lists

A pro-con analysis aids in problem-solving by weighing the advantages (pros) and disadvantages (cons) of various possible solutions.

This simple but powerful tool helps in making a balanced, informed decision.

When confronted with a problem, a pro-con analysis can guide you through the decision-making process, ensuring all possible outcomes and implications are scrutinized before arriving at the optimal solution. Thus, it helps to make the problem-solving process both methodical and comprehensive.

29. 5 Whys Analysis

The 5 Whys Analysis involves repeatedly asking the question ‘why’ (around five times) to peel away the layers of an issue and discover the root cause of a problem.

As a problem-solving technique, it enables you to delve into details that you might otherwise overlook and offers a simple, yet powerful, approach to uncover the origin of a problem.

For example, if your task is to find out why a product isn’t selling your first answer might be: “because customers don’t want it”, then you ask why again – “they don’t want it because it doesn’t solve their problem”, then why again – “because the product is missing a certain feature” … and so on, until you get to the root “why”.

30. Gap Analysis

Gap analysis entails comparing current performance with potential or desired performance.

You’re identifying the ‘gaps’, or the differences, between where you are and where you want to be.

In terms of problem-solving, a Gap Analysis can help identify key areas for improvement and design a roadmap of how to get from the current state to the desired one.

31. Design Thinking

Design thinking is a problem-solving approach that involves empathy, experimentation, and iteration.

The process focuses on understanding user needs, challenging assumptions , and redefining problems from a user-centric perspective.

In problem-solving, design thinking uncovers innovative solutions that may not have been initially apparent and ensures the solution is tailored to the needs of those affected by the issue.

32. Analogical Thinking

Analogical thinking involves the transfer of information from a particular subject (the analogue or source) to another particular subject (the target).

In problem-solving, you’re drawing parallels between similar situations and applying the problem-solving techniques used in one situation to the other.

Thus, it allows you to apply proven strategies to new, but related problems.

33. Lateral Thinking

Lateral thinking requires looking at a situation or problem from a unique, sometimes abstract, often non-sequential viewpoint.

Unlike traditional logical thinking methods, lateral thinking encourages you to employ creative and out-of-the-box techniques.

In solving problems, this type of thinking boosts ingenuity and drives innovation, often leading to novel and effective solutions.

Go Deeper: Lateral Thinking Examples

34. Flowcharting

Flowcharting is the process of visually mapping a process or procedure.

This form of diagram can show every step of a system, process, or workflow, enabling an easy tracking of the progress.

As a problem-solving tool, flowcharts help identify bottlenecks or inefficiencies in a process, guiding improved strategies and providing clarity on task ownership and process outcomes.

35. Multivoting

Multivoting, or N/3 voting, is a method where participants reduce a large list of ideas to a prioritized shortlist by casting multiple votes.

This voting system elevates the most preferred options for further consideration and decision-making.

As a problem-solving technique, multivoting allows a group to narrow options and focus on the most promising solutions, ensuring more effective and democratic decision-making.

36. Force Field Analysis

Force Field Analysis is a decision-making technique that identifies the forces for and against change when contemplating a decision.

The ‘forces’ represent the differing factors that can drive or hinder change.

In problem-solving, Force Field Analysis allows you to understand the entirety of the context, favoring a balanced view over a one-sided perspective. A comprehensive view of all the forces at play can lead to better-informed problem-solving decisions.

TRIZ, which stands for “The Theory of Inventive Problem Solving,” is a problem-solving, analysis, and forecasting methodology.

It focuses on finding contradictions inherent in a scenario. Then, you work toward eliminating the contraditions through finding innovative solutions.

So, when you’re tackling a problem, TRIZ provides a disciplined, systematic approach that aims for ideal solutions and not just acceptable ones. Using TRIZ, you can leverage patterns of problem-solving that have proven effective in different cases, pivoting them to solve the problem at hand.

38. A3 Problem Solving

A3 Problem Solving, derived from Lean Management, is a structured method that uses a single sheet of A3-sized paper to document knowledge from a problem-solving process.

Named after the international paper size standard of A3 (or 11-inch by 17-inch paper), it succinctly records all key details of the problem-solving process from problem description to the root cause and corrective actions.

Used in problem-solving, this provides a straightforward and logical structure for addressing the problem, facilitating communication between team members, ensuring all critical details are included, and providing a record of decisions made.

39. Scenario Analysis

Scenario Analysis is all about predicting different possible future events depending upon your decision.

To do this, you look at each course of action and try to identify the most likely outcomes or scenarios down the track if you take that course of action.

This technique helps forecast the impacts of various strategies, playing each out to their (logical or potential) end. It’s a good strategy for project managers who need to keep a firm eye on the horizon at all times.

When solving problems, Scenario Analysis assists in preparing for uncertainties, making sure your solution remains viable, regardless of changes in circumstances.

How to Answer “Demonstrate Problem-Solving Skills” in an Interview

When asked to demonstrate your problem-solving skills in an interview, the STAR method often proves useful. STAR stands for Situation, Task, Action, and Result.

Situation: Begin by describing a specific circumstance or challenge you encountered. Make sure to provide enough detail to allow the interviewer a clear understanding. You should select an event that adequately showcases your problem-solving abilities.

For instance, “In my previous role as a project manager, we faced a significant issue when our key supplier abruptly went out of business.”

Task: Explain what your responsibilities were in that situation. This serves to provide context, allowing the interviewer to understand your role and the expectations placed upon you.

For instance, “It was my task to ensure the project remained on track despite this setback. Alternative suppliers needed to be found without sacrificing quality or significantly increasing costs.”

Action: Describe the steps you took to manage the problem. Highlight your problem-solving process. Mention any creative approaches or techniques that you used.

For instance, “I conducted thorough research to identify potential new suppliers. After creating a shortlist, I initiated contact, negotiated terms, assessed samples for quality and made a selection. I also worked closely with the team to re-adjust the project timeline.”

Result: Share the outcomes of your actions. How did the situation end? Did your actions lead to success? It’s particularly effective if you can quantify these results.

For instance, “As a result of my active problem solving, we were able to secure a new supplier whose costs were actually 10% cheaper and whose quality was comparable. We adjusted the project plan and managed to complete the project just two weeks later than originally planned, despite the major vendor setback.”

Remember, when you’re explaining your problem-solving skills to an interviewer, what they’re really interested in is your approach to handling difficulties, your creativity and persistence in seeking a resolution, and your ability to carry your solution through to fruition. Tailoring your story to highlight these aspects will help exemplify your problem-solving prowess.

Go Deeper: STAR Interview Method Examples

Benefits of Problem-Solving

Problem-solving is beneficial for the following reasons (among others):

• It can help you to overcome challenges, roadblocks, and bottlenecks in your life.
• It can save a company money.
• It can help you to achieve clarity in your thinking.
• It can make procedures more efficient and save time.
• It can strengthen your decision-making capacities.
• It can lead to better risk management.

Whether for a job interview or school, problem-solving helps you to become a better thinking, solve your problems more effectively, and achieve your goals. Build up your problem-solving frameworks (I presented over 40 in this piece for you!) and work on applying them in real-life situations.

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 5 Top Tips for Succeeding at University
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 50 Durable Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 100 Consumer Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 30 Globalization Pros and Cons

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Practical Guide: Solving Problems Examples in Real-World Scenarios

In today’s fast-paced world, problem-solving is an essential skill that can help individuals navigate various challenges. However, merely possessing this skill is not enough. It is crucial to have practical examples of problem-solving techniques and strategies that can be applied to real-life scenarios.

This guide aims to provide a comprehensive overview of problem-solving skills and techniques that can be implemented in different contexts. It explores various problem-solving strategies, including brainstorming, root cause analysis, decision-making frameworks, and creative problem-solving methods.

Furthermore, this guide showcases practical examples of problem-solving in business and personal settings. It features in-depth case studies of real-life scenarios, highlighting the challenges faced, the strategies employed, and the outcomes achieved.

By the end of this guide, readers will have a deeper understanding of problem-solving techniques and strategies. They will also have the knowledge and tools to apply these skills effectively in different scenarios, both in personal and professional life.

Understanding Different Problem-Solving Techniques

The ability to solve problems is a critical skill in both personal and professional life. It involves identifying and analyzing an issue, generating possible solutions, and selecting the best course of action. There are several problem-solving techniques that can be applied to different situations, including:

Brainstorming

Brainstorming involves generating ideas in a group setting without criticism or judgment. This technique encourages creativity and diversity of thought, allowing individuals to approach a problem from different angles.

Root Cause Analysis

Root cause analysis involves identifying the underlying cause of a problem. This technique involves asking “why” multiple times to determine the primary reason for the issue. By addressing the root cause, individuals can develop more effective solutions.

Decision-Making Frameworks

Decision-making frameworks involve using a set of criteria to evaluate different options and make an informed decision. These frameworks can be simple or complex and involve weighing the pros and cons of each alternative.

Creative Problem-Solving Methods

Creative problem-solving methods involve using non-traditional approaches to generate innovative solutions. These techniques can include mind mapping, lateral thinking, or the use of analogies.

By understanding and using different problem-solving techniques, individuals can approach challenges with a more comprehensive and effective approach. These techniques can be applied in both personal and professional settings, enhancing critical thinking and decision-making skills.

Problem-Solving Examples in Business Settings

In today’s competitive business environment, companies face numerous challenges that require effective problem-solving skills. Successful businesses employ problem-solving strategies that help them overcome obstacles and achieve their goals. Here are some real-life examples of companies that used problem-solving to overcome challenges:

Example 1: Improving Customer Service

A telecommunications company noticed a decline in customer satisfaction ratings. Through surveys and customer feedback, they discovered that customers were frustrated with the company’s long wait times and unresponsive customer service representatives. The company implemented a new customer service training program for their representatives, which included active listening, problem-solving, and conflict resolution skills. As a result, the company’s customer satisfaction ratings improved, and they gained a competitive advantage in the industry.

Example 2: Reducing Production Costs

A manufacturing company was struggling with high production costs due to inefficient processes and materials. The company conducted a thorough analysis of their production line and identified areas where they could cut costs. They implemented new production methods and materials that were more efficient and cost-effective. As a result, the company was able to reduce their production costs, increase their profit margins, and remain competitive in the market.

These examples demonstrate the importance of problem-solving skills in the business world. By identifying challenges, analyzing the root causes, and implementing effective solutions, companies can achieve their goals and remain competitive in their respective industries.

Problem-Solving Strategies in Personal Life

Effective problem-solving skills aren’t just essential in professional settings. They’re equally crucial in personal life too. Whether it’s making a tough decision, dealing with unexpected challenges, or resolving conflicts, problem-solving is critical to achieving desired outcomes. Here are some practical problem-solving strategies to apply in personal situations:

1. Breakdown the problem:

When you encounter a problem, start by breaking it down into smaller parts. This approach will help you identify the root cause and develop a step-by-step plan to address the issue.

2. Evaluate your options:

Once you have a clear understanding of the problem, evaluate your options objectively. Consider the pros and cons of each alternative and analyze their potential outcomes.

3. Seek advice:

Don’t hesitate to ask for advice from those you trust and respect. Getting an outside perspective can help you gain a new insight into the problem at hand.

4. Use creative problem-solving techniques:

Applying creative problem-solving techniques like brainstorming, mind-mapping, and reverse-thinking can help you explore innovative solutions to complex problems. It’s essential to think outside the box.

5. Learn from failures:

Failure is a part of life, and it’s okay to make mistakes. The key is to learn from these experiences and use them as an opportunity to grow and develop your problem-solving skills further.

By applying these practical problem-solving strategies in your everyday life, you’ll develop a strong problem-solving mindset that enables you to tackle any challenge with confidence and ease.

Case Studies: Real-Life Problem-Solving Examples

In this section, we will explore real-life examples of problem-solving in different industries. These case studies showcase effective problem-solving strategies and provide insights into how challenges can be overcome using a structured approach.

Airbnb: Breaking Through Regulatory Barriers

When Airbnb was expanding into cities around the world, it faced regulatory barriers that threatened to derail its growth. In New York City, for example, hosts were required to register with the city and rent their apartments for a minimum of 30 days at a time.

To overcome these barriers, Airbnb worked with city officials to develop a new regulatory framework that allowed hosts to rent their homes for shorter periods of time. The company also implemented a host education program to ensure compliance with local laws.

Through this problem-solving approach, Airbnb was able to break through regulatory barriers and continue its expansion into new markets.

Toyota: Improving Quality Control

Toyota faced a massive recall of millions of vehicles due to safety concerns related to its accelerator pedals. In response, the company implemented a problem-solving strategy known as “5 Whys,” which involves asking why a problem occurred five times to identify the root cause.

Through this process, Toyota discovered that a faulty design led to the accelerator pedal becoming stuck, which led to the recall. The company then implemented a new quality control process to prevent similar issues from occurring in the future.

By using a structured problem-solving methodology, Toyota was able to identify the root cause of the issue and implement an effective solution to prevent future recalls.

Microsoft: Adapting to Changing Markets

Microsoft faced significant challenges in the early 2010s as the market shifted towards mobile devices and away from personal computers. The company responded by shifting its focus to cloud-based services and mobile devices.

To do this, Microsoft implemented a problem-solving strategy known as “design thinking,” which involves empathizing with users and designing products that meet their needs. By focusing on the needs of its customers, Microsoft was able to adapt to the changing market and remain a leading player in the tech industry.

These case studies demonstrate the power of effective problem-solving strategies in real-world scenarios. By utilizing structured problem-solving methodologies and focusing on the needs of their customers, these companies were able to overcome challenges and achieve success.

Developing Problem-Solving Skills through Exercises

Problem-solving is a skill that can be developed and honed through practice. By engaging in specific exercises and activities, individuals can enhance their problem-solving abilities and become more effective in real-life scenarios.

Here are a few exercises and activities that can help individuals develop their problem-solving skills:

One of the most popular problem-solving techniques is brainstorming. This exercise involves generating multiple ideas in a short amount of time, without evaluating the quality of each idea. It can be used to solve both personal and professional problems. To conduct a brainstorming session, gather a group of individuals and pose a problem or challenge. Encourage everyone to share as many ideas as possible towards a potential solution.

Mock Scenarios

Mock scenarios are another effective way to practice problem-solving. This exercise involves creating a hypothetical scenario and asking individuals to solve it. The scenario can be related to personal or professional challenges and should require critical thinking and decision-making skills. By practicing in a risk-free environment, individuals can experiment with different problem-solving techniques and strategies, and evaluate the effectiveness of each approach.

Gamification

Gamification involves using game-like elements to engage individuals and motivate problem-solving efforts. This exercise can be particularly effective for younger individuals or those who prefer a more interactive approach. Gamification can involve using puzzles, quizzes, or other game formats to solve problems. These activities offer a fun and engaging way to develop problem-solving skills.

Remember that while exercises can be helpful, problem-solving is ultimately a skill that is developed through practice and experience in real-life scenarios. Continually seeking opportunities to engage in problem-solving can improve abilities and build confidence in making informed decisions.

Implementing Problem-Solving Methods in Real-Time

Problem-solving is not a one-time event but an ongoing process. It requires adaptability, critical thinking, and decision-making abilities to achieve desired outcomes. Here are some practical methods for implementing problem-solving in real-time situations:

Stay Focused on the Problem

When faced with a problem, it’s essential to stay focused on the issue at hand. Avoid getting sidetracked by unrelated details, emotions, or distractions. Keep a clear understanding of the problem and the desired outcome.

Brainstorm Possible Solutions

Engage in brainstorming sessions to generate possible solutions to the problem. Encourage everyone’s participation and have an open mind to new ideas. Use a whiteboard or sticky notes to collect and organize ideas for evaluation.

Prioritize Possible Solutions

After generating possible solutions, evaluate and prioritize them based on their potential impact, feasibility, and cost. Choose the most appropriate solution based on these factors, and consider the potential risks and drawbacks associated with it.

Monitor and Adjust the Solution

Implement the chosen solution and monitor its progress. Check if it’s being executed as planned and if it’s achieving the desired outcomes. Be open to making adjustments to the solution if necessary and continue to monitor its progress.

Document the Problem-Solving Process

Keep a record of the problem-solving process, including the problem, the chosen solution, the implementation process, and the results achieved. Use this information to evaluate the success of the problem-solving process, identify areas for improvement, and apply what you’ve learned to future challenges.

Implementing problem-solving methods in real-time requires focus, creativity, and persistence. With the right approach and mindset, you can successfully overcome challenges and achieve your desired outcomes.

Strategies for Overcoming Common Problem-Solving Challenges

Problem-solving can be a challenging and complex process, and it’s not uncommon to encounter roadblocks along the way. Here are some strategies for overcoming common problem-solving challenges:

Managing ambiguity

Often, problems can be vague and ill-defined, making it difficult to know exactly what to do. To overcome this challenge, it can be helpful to break down the problem into smaller, more manageable pieces. Identifying the root cause of the issue and defining clear objectives can also help reduce ambiguity and provide direction.

Dealing with complexity

Complex problems can be overwhelming, and it’s easy to get bogged down in the details. To tackle complexity, it’s important to step back and take a broader view of the situation. Looking at all the relevant factors and considering different perspectives can help identify potential solutions.

Approaching problems from different perspectives

It can be easy to get stuck in a rut and approach problems in the same way every time. To overcome this challenge, try approaching problems from different angles. Considering multiple perspectives can help uncover new solutions and shed light on potential blind spots.

Building resilience

Problem-solving can be a tough and sometimes frustrating process. It’s important to develop resilience and the ability to persist in the face of obstacles. Practicing mindfulness techniques, maintaining a positive attitude, and taking breaks when needed can all help build resilience.

Maintaining a positive problem-solving mindset

It can be easy to get discouraged when things don’t go as planned. To maintain a positive problem-solving mindset, focus on the progress made, rather than the setbacks encountered. Celebrating small wins along the way can help keep momentum going and boost motivation.

Frequently Asked Questions (FAQ) about Problem-Solving

In this section, we address some of the commonly asked questions related to problem-solving. These FAQ’s aim to provide guidance and clarify doubts on various aspects of problem-solving methods and techniques.

What are the different problem-solving techniques?

There are several problem-solving techniques that individuals and businesses can apply to resolve any challenges they face. Popular strategies include brainstorming, root cause analysis, decision-making frameworks, and creative problem-solving methods.

How can problem-solving skills be developed?

Problem-solving skills can be honed by practicing exercises and activities designed to enhance critical thinking and decision-making processes. Continuous learning and development are also crucial for building effective problem-solving skills.

What are the essential qualities for effective problem-solving?

Effective problem-solving requires critical thinking, adaptability, decision-making skills, a positive mindset, and the ability to manage ambiguity and complexity. Communication and collaboration skills are also important, as problem-solving often involves working with others.

What are some common challenges encountered during problem-solving processes, and how can they be addressed?

Common challenges during problem-solving include managing ambiguity, dealing with complexity, and approaching problems from different perspectives. To overcome these challenges, it is essential to remain flexible, stay focused on the end goal, and break problems down into smaller, more manageable parts. Taking breaks and seeking feedback from others can also be beneficial.

How can problem-solving methods be effectively applied in real-time situations?

Effective problem-solving in real-time situations requires critical thinking, analytical skills, and decision-making abilities. It is important to remain adaptable and flexible, consider multiple options, and prioritize actions based on their potential impact. Communication and collaboration with others can also aid in effective problem-solving.

What are some additional resources for learning about problem-solving?

There are several additional resources available for further learning about problem-solving. Books, online courses, and workshops can provide valuable insights and practical guidance for developing problem-solving skills. Networking with others in similar fields and seeking mentorship can also be beneficial for problem-solving growth and development.

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October 31, 2022

Creative problem solving examples that solved real world problems, by jordan nottrodt.

Not all problems have simple, straightforward solutions. And the more we try to solve these problems with basic techniques, the worse the problems get. Real-world problems are messy and complicated, and they require a creative approach to problem solving. In this post, we’ll share a range of real-world creative problem solving examples from the human-centred design work of Overlap Associates.

When there isn’t a straightforward answer, it’s time for another approach—one that puts all of the people involved at the forefront of decision making.

What is Creative Problem Solving?

Creative problem solving applies human-centred design principles, practices, and tools to complex problems, enabling individuals, teams, and organizations to unlock innovation and navigate uncertainty in a rapidly changing world. It’s all about tapping into the unknown to uncover brand new solutions—ones you’ve never thought of before or didn’t know were possible.

The more complex a problem is , the more nuanced and layered the solution needs to be. Creative problem solving requires that you separate divergent thinking ( idea generation and brainstorming ) from convergent thinking (idea evaluation and decision making) as opposed to trying to do both at once. 

Creative problem solving involves gathering observations, asking questions, and considering a wide range of perspectives.

Let’s discuss complex, real-world problems that were solved using creative problem solving and human-centred design techniques. 

Creative Problem Solving Examples

Example #1: adapting customer service to evolving customer expectations and needs.

The Complex Problem:

Customer service always has room for improvement, and the insurance industry is no exception. Tensions run high when receiving claims, and it is critical that customers feel both comfortable and satisfied with the claims experience. Gore Mutual was at a standstill with a 97% customer satisfaction rating, but the company wanted to do more. As customer expectations and needs continue to evolve, how can customer service continue to improve?

Creative Problem Solving Methods:

In order to improve customer satisfaction, Gore Mutual first needed to understand the experiences of all relevant stakeholders in the claims process, which included customers, brokers, and service providers. Acknowledging the role of each group in the overall claims experience would create a clear customer journey.

Overlap led a series of engagement sessions and gathered feedback from all groups involved in the customer journey to better understand where the journey could be improved. Methods of information gathering included in-person interviews, interactive Stakeholder Lab workshops, and observational research of spaces, such as dispatch centres, digital platforms, contractors’ shops, and customer meetings. 

This thorough approach went beyond simple satisfaction surveys to paint a detailed picture of the entire customer journey. A Journey Map , a design tool for capturing new ways of looking at someone’s experience, was used to guide research collection. 

In the end, a nuanced insights report was created to outline the current and ideal future state of navigating the claims process. With this ideal claims journey in mind, Gore Mutual established ClaimCare, a new approach to claims processing, which included improvements such as a Concierge for inquiries, a Mobile Response Team, and a Mobile Response Centre for catastrophes.

Learn more about the Service Design Project

Gore Mutual Insurance .

Example #2: Developing Inclusive Online Facilitation in the Midst of a Pandemic

The Complex Problem: 

The beginning of the pandemic left businesses scrambling to find inventive ways to hold in-person meetings and events. How do you create engaging facilitation without experiencing the intangible moments that come with face-to-face, in-person connection? How do you develop online facilitation that’s engaging and accessible to everyone in the midst of overwhelming Zoom fatigue? How do you implement technology in order to be effective while also not alienating those who are unfamiliar or struggle with new technology? 

Like many businesses, The Schlegel-UW Research Institute for Aging (RIA) was caught in the dramatic shift to online methods that occurred in the early days of the pandemic. They knew they needed to adopt new technology in order to thrive—or even survive—but they didn’t want engagement to suffer or for those less technologically inclined to be left behind. 

Using the lens of creative problem solving and human-centred design techniques, RIA was able to translate all they previously knew about facilitation into an adaptive and inclusive online approach. It was essential to find tools and solutions that were simple to navigate and accessible to everyone on the RIA team, as well as those RIA works with. 

Overlap provided these tools and the training required to implement online facilitation quickly and effectively while sharing insight into how to spot unconscious bias, how to lead an accessible session, and how to apply diversity, equity, and inclusion across all online communication. Keeping human-centred design principles top-of-mind ensured all voices were heard, and no one was left behind in the transition. 

Learn more about Developing New Training for Great Online Facilitation .

Example #3: Improving the Experiences of Aging Adults

Aging is a deeply personal and challenging experience. How can caregivers better understand the experiences of older adults? Instead of grouping every senior together, how can care be designed to meet the needs of all subgroups of aging adults? For example, newcomers, people who identify as LGBTQ+, and people with dementia may require or prefer different methods of service.

To solve this complex problem, Overlap deployed design teams to complete high-touch, day-long ethnography as well as low-touch, three-minute surveys to gather a wealth of data that could inform decision making. Overlap used the findings and insights to develop a thorough and wide-ranging set of design principles for serving older adults.

A comprehensive toolkit was designed to help service providers co-design alongside older adults. The toolkit included practical, creative problem solving techniques and guided design thinking practices to ensure everyone affected was involved in the process. In addition to the toolkit, training was provided directly to caregivers to ensure all gaps in service and understanding were bridged.

Directly involving aging adults from all walks of life, their loved ones, and their caregivers meant the decision making process was thoroughly informed, which enabled care to be adapted to meet the needs of all individuals. 

Learn more about the Aging By Design Project in New York State .

Learning More About the Creative Problem Solving Process

Overlap’s Creative Problem Solving School has a suite of courses that have been carefully designed to bring design thinking training to anyone ready to learn. We share tools and strategies that will help you and your team make better decisions. 

Our wide range of courses include practical and engaging materials that will help you work better together, understand your customers, and navigate complex challenges. 

The Exploring Complex Problems (201) course focuses on how to solve complex, real world problems using creative problem solving methods. It’s a deep dive into the Define and Research phases of the human-centred design cycle and demonstrates why remaining in the problem space and iterating between these two phases creates a strong foundation for ideation. 

Learn more: Why Every Team Needs Human-Centred Design Training .

If you want to continue developing your creative problem solving skills, follow us on social media and sign up for our monthly newsletter to stay informed about our latest training schedule, new courses, and free resources!

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STEM learning is largely about designing creative solutions for real-world problems. When students learn within the context of authentic, problem-based STEM design, they can more clearly see the genuine impact of their learning. That kind of authenticity builds engagement, taking students from groans of “When will I ever use this?” to a genuine connection between skills and application.

Using STEM to promote critical thinking and innovation

“Educational outcomes in traditional settings focus on how many answers a student knows. We want students to learn how to develop a critical stance with their work: inquiring, editing, thinking flexibly, and learning from another person’s perspective,” says Arthur L. Costa in his book Learning and Leading with Habits of Mind . “The critical attribute of intelligent human beings is not only having information but also knowing how to act on it.”

Invention and problem-solving aren’t just for laboratory thinkers hunkered down away from the classroom. Students from elementary to high school can wonder, design, and invent a real product that solves real problems. “ Problem-solving involves finding answers to questions and solutions for undesired effects. STEM lessons revolve around the engineering design process (EDP) — an organized, open-ended approach to investigation that promotes creativity, invention, and prototype design, along with testing and analysis,” says Ann Jolly in her book STEM by Design . “These iterative steps will involve your students in asking critical questions about the problem, and guide them through creating and testing actual prototypes to solve that problem.”

STEM projects that use real-world problems

Here are some engaging projects that get your students thinking about how to solve real-world problems.

Preventing soil erosion

In this project, meant for sixth – 12th grade, students learn to build a seawall to protest a coastline from erosion, calculating wave energy to determine the best materials for the job.  See the project.

Growing food during a flood

A natural disaster that often devastates communities, floods can make it difficult to grow food. In this project, students explore “a problem faced by farmers in Bangladesh and how to grow food even when the land floods.”  See the project .

Solving a city’s design needs

Get your middle or high school students involved in some urban planning. Students can identify a city’s issues, relating to things like transportation, the environment, or overcrowding — and design solutions. See the project here or this Lego version for younger learners.

Creating clean water

Too many areas of the world — including cities in our own country — do not have access to clean water. In this STEM project, teens will learn how to build and test their own water filtration systems.  See the project here .

Improving the lives of those with disabilities

How can someone with crutches or a wheelchair carry what they need? Through some crafty designs! This project encourages middle school students to think creatively  and  to participate in civic engagement.   See the project here .

Cleaning up an oil spill

We’ve all seen images of beaches and wildlife covered in oil after a disastrous spill. This project gets elementary to middle school students designing and testing oil spill clean-up kits. See the project here .

Building earthquake-resistant structures

With the ever-increasing amount of devastating earthquakes around the world, this project solves some major problems. Elementary students can learn to create earthquake resistant structures in their classroom. See the project here .

Constructing solar ovens

In remote places or impoverished areas, it’s possible to make solar ovens to safely cook food. In this project, elementary students construct solar ovens to learn all about how they work and their environmental and societal impact.  See the project here .

Stopping apple oxidization

Stop those apples from turning brown with this oxidation-based project. Perfect for younger learners, students can predict, label, count, and experiment! See the project here .

Advancing as a STEAM educator

The push for STEM has evolved into the STEAM movement, adding the arts for further enrichment and engagement. There are so many ways to embed STEM or STEAM lessons in your curriculum, but doing it well requires foundational knowledge and professional development. Imagine what type of impact you could have on your students and your community if you were supported by a theoretical framework, a variety of strategies, and a wealth of ideas and resources.

You may also like to read

• Teaching STEM: Challenging Students to Think Through Tough Problems
• Professional Development Resources for STEM Teachers
• What is the Washington State STEM Lighthouse Program?
• Characteristics of a Great STEAM Program
• Building a Partnership Between Your School and a STEAM Organization
• The Art of Inquiry in STEAM Education

Categorized as: Tips for Teachers and Classroom Resources

Tagged as: Art ,  Educational Technology ,  Engaging Activities ,  Math and Science ,  Science ,  STEAM

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5 Strategies for Aligning PBL to Real-World Problem-Solving

The closer project-based learning comes to the messy, complicated problems of our world today, the more students benefit.

In March 2020, I faced a number of challenges as a school superintendent. Earlier in the month, I had read about a virus that was sweeping the world, and while American schools had not shuttered, the challenge seemed both eminent and far off.

Over the next several weeks, months, and years, I, and every other leader, faced a series of problems, including closing schools, redesigning in-person instruction, developing virtual learning programs, and working in partnership with public health organizations.

Interestingly, I learned that authentic, real-world problem-solving has a few key features:

• I was never given one problem but was presented with a number of problem situations in which I and my team needed to derive key questions that drove our decision-making.
• The problems we faced continued to change, requiring us to go back and learn new content, prepare for multiple contingencies, and communicate up-to-date information and our plans for multiple scenarios.

Contemporary learning frameworks and related methodologies can learn a lot from what we are experiencing with Covid-19. Applying the two features above to project-based learning (PBL) by using a more fluid rather than static, linear model may best prepare students for what the future of learning and work actually looks and feels like.

5 Strategies to Make PBL More Authentic

1: Students derive the driving question from multiple contexts or multiple issues within a context. In one third-grade class, students read the book We Are Water Protectors and discuss the challenges Native Americans face with the introduction of the Keystone pipeline. Next, the teacher presents two problems:

• The extraction of cobalt to build electric cars and the negative impact on rural African communities
• The development of wind farms and the decline of the golden eagle

Students then work together in this strategy to determine the key challenges facing Indigenous people and native species. Next, they develop core questions they want to answer and determine what they need to learn to answer those questions.

2: Students face changes in the problem(s) they are contemplating. Problem environments are fluid, not static. In an AP economics class, students are analyzing supply and demand of a new video game system and preparing to advise the company on what it should do to improve profits.

Every day at the beginning of class, their teacher asks them to scan reliable news sources to report any changes to supply chains, governmental restrictions such as embargoes, or any other factor that would influence their solutions to the client.

The students found out that there were major supply chain issues with essential parts needed to create the video game console. Moreover, some of the ships carrying current consoles are sitting in Asia awaiting passage to the United States because of a political dispute.

The students worked together in small groups and discussed the key factors that were impacting the company they were advising, along with what the students needed to learn and understand before meeting with the client, and finally developed multiple recommendations based on multiple contingencies.

The general strategy looks like this:

• Students learn about changes to the problem content (this could be via reading multiple news reports, listening to daily podcasts, or engaging with actual people in the field).
• In small groups, students share their key understanding of the changes and how that impacts their current understanding and strategy.
• Students determine key “need-to-knows” they have and work with the teacher and peers to gain competencies.
• Students plan for multiple contingencies and tentative solutions.

3: Presentations are short bursts of what students think and propose during the project with dollops of feedback to make adjustments. Seventh-grade students are sending in their persuasive essay on one of a number of topics (e.g., addressing the homelessness crisis, engaging with politicians on critical race theory).

As they are drafting their papers, students are randomly assigned to present their ideas and current drafts to other students and receive feedback on their writing as well as their persuasiveness to opposing views.

The strategy looks like this:

• Students have a mid-lesson stop in which they have 5 minutes to prepare to present their current work.
• Students conduct a feedback protocol (tuning or critical friends) in which one or two students receive feedback.
• Students who received feedback share what they have changed in a reflective journal or exit ticket.
• This process is repeated daily.

4: Authentic audiences engage with students throughout the project rather than just at the beginning and/or end. In a fifth-grade art class, students have been commissioned by the local town council to paint murals that represent voices that are largely marginalized in their community. During their work, students meet with a number of artists and community members who share their stories, offer feedback, and address questions.

In this strategy, students engage with people outside the classroom at the beginning, middle, and end of a project to hear stories that relate to the problem context, receive guidance on the technical aspects of the content they are learning, and ask questions.

5: Groups work together in small bursts of time to solve problems. Students in Algebra II are working with logarithms to solve a number of problems related to stomach acid, algae-filled hot tubs, soil composition, and buffalo teeth.

While each student may be solving a different problem, students form small groups to share their learning, evaluate the connections between each context, and give each other feedback. After approximately two weeks of solving complex math tasks, the teacher presents three new problems and forms new groups for students to solve the problem in one or two days.

In this strategy, students form temporary groups of two to three to solve a new challenge and work together for one to two days without forming task-specific roles.

• ⋮⋮⋮ ×

Use Real World Examples to Teach Sustainability

Pedagogic guidance for teaching using real world examples

Multiple pedagogic strategies can be used to incorporate real examples into the classroom. These include teaching with case studies or with investigative cases , field experiences such as field labs or student research, and using local data and examples to teach about issues. Connecting local examples with global challenges can also be beneficial for expanding the context of larger scale issues (e.g. water quality and quantity could be both a local issue as well as a global issue) or those that are non-local, but may still affect students (e.g. drought in California affects local food prices).

Engaging Students

Real world problems are inherently engaging since they tend to be meaningful and applicable to students' lives, either directly or indirectly (e.g. through the media or social networks). If you're not sure where to begin, the tips below can get you started. These tips were compiled from small group discussions among workshop participants at multiple InTeGrate workshops .

• Introduce students to your research - make it personal. It inspires students.
• Task students with bringing examples of real-world experiences and problems to the class.
• Bring experience into the classroom through guest speakers, engaging students in case studies, or field work
• Engage students in community work, such as service learning. Learn more about service learning .
• Bring in ethics (e.g. Hurricane Sandy preparedness and subsequent lawsuits): this makes connections between disciplines and is centered around current events. Ethics also broaches topics related to responsibilities: What are your responsibilities as a citizen, property owner, or professional?
• Remember to maintain hope and agency in the face of long-lasting complex challenges related to sustainability. Studying success stories, people who have made a difference, and actions that give hope can be effective. There is a tension between maintaining hope, and understanding the full extent of how complex and deeply entrenched the problems are.
• While we all desire our students to become actors in making our civilization more environmentally just, there are a variety of strategies for approaching this in different instructional settings. They range from developing empathy and awareness to requiring students to engage in service or advocacy. In all cases, faculty should be careful not to dictate the students perspective or approach. The frame is to learn how to act, not to be told to act in a certain way.
• There is a strong tension between educating and engaging students in Environmental Justice and respecting the affected communities. This requires attention, preparation and skill. Anthropologists and sociologists have experience with these issues that can be brought to bear. Listening, sensitivity to context, and reflexivity are essential. While we have expertise to offer, we must refrain from removing agency to ourselves.
• Having to make and negotiate decisions in a group takes patience, time, and skill, and is something that environmental justice communities have to do under exceptionally "high-stakes" problems.

Effective strategies for teaching using real world problems

As discussed above, there are many ways to incorporate examples into the classroom. Exploring case studies, using the local environment and data, and service learning are three popular strategies. Ideas for using case studies are presented below. For a more in-depth look at using the local environment and service learning, including examples for implementing each, see these pages on Using Local Examples and Data and Service Learning .

Case Studies

• Remember to consider your audience: local hazards might be more effective to consider and timeliness may be an issue (e.g. Loma Prieta, Mt. St. Helens may bring blank stares).   
• Bring in professional reports. Where possible, incorporate more of the history of the project. Also, there are public domain reports that could be incorporated into instruction and activities.
• If teaching about mineral resources, look for case studies for mineral resources of geologic interest that have already been exploited. These are more likely to have data, geologic maps, etc. in the public domain and thus are more widely accessible. (E.g. Yerington batholith, Nevada).
• Utilize models such as sea level rise and other natural hazard risks common to an area (e.g. earthquakes, landslides, flooding) and have students assess risk and prepare management plans to address the risks. If assessing a local hazard, you could set up a community debriefing as a service learning opportunity.  
• Tie it to life choices students will make in the future: have students pick a city where they would want to move and assess the risk of living there and the level of preparedness for the risks that exist.
• Sea Level Rise in Fort Lauderdale, Florida case study,
• Southern California Earthquakes case study,
• Red tide and harmful algal blooms site guide, or
• Choose from a variety of real examples you can use in the classroom. Most of these examples lend themselves to discussion starters or role-play activities.  

Opportunities to strengthen the use of real world examples  

Utilize the opportunity to apply classroom knowledge to real, tangible problems. Below are some ideas to get you started, or see browseable collections of examples :

• Engage students in thinking about the natural hazards in their local environ, such as is done in this activity: Evaluating natural hazards data to assess the risk to your California home by Corrie Neighbors, UC Riverside. Take this a step further and have students think about preparing for natural hazard situations before crises occur, such as done in this activity: Developing a Multi-Hazard Mitigation Strategy by Rebekah Green, Western Washington University.
• Start a discussion or role play using a specific real world example, such as Sea Level Rise in Fort Lauderdale, Florida by Alana Edwards, Mary Beth Hartman, and Leonard Berry, Florida Atlantic University, Southern California Earthquakes, prepared by John Taber, and other examples , submitted by participants at the 2014 Teaching about Risk and Resilience workshop.  
• Usefulness of Google Earth/Wikimapia as risk predictor and damage/ resilience assessment tools by Charlene Sharpe, Rutgers University.
• Using Google Earth to Measure Seacliff Erosion Rates by Alfred Hochstaedter, Monterey Peninsula College.
• Hurricane Tracks and Energy , by Lisa Gilbert (Williams College), Josh Galster (Montclair State University), Joan Ramage (Lehigh University), is part of a larger InTeGrate module Natural Hazards and Risks: Hurricanes .
• Mapping Environmental Justice: The Geography of Population and Pollution by Christopher Cusack.
• Using Media to Document Public Attitudes on Waste by Sya Buryn Kedzior.
• Hazardous Waste and Toxics: Real Data for Real Places by Richard Kujawa.
• Assessing Water Resource Demand in New York City , by Kyle M. Monahan, adapted from an original activity by Richard F. Bopp.
• Delve into the complexities of sustainability and the impacts of climate change, e.g.: Impact of climate change on endangered fish population in Pyramid Lake .
• Encountering Geoscience Issues in the Popular Press by Marian Buzon, University of Idaho   
• Presenting Science to the Public: The ethics of communicating potential environmental impacts of industrial projects by Joy Branlund, Southwestern Illinois College.  
• Case of GMOs in Environmental Cleanup by Daniel Vallero, Duke University.  

Materials and Resources for Teaching with Real World Examples  

See how other faculty are using real-world examples with these examples from a range of disciplines and learning environments. Example Activities

• Real world example collection from Teaching about Risk and Resilience 2014 workshop participants.
• Environmental justice activities from Teaching about Environmental Justice 2013 workshop participants.
• Hazard event pages , from On the Cutting Edge, compile visualizations, activities, and resources to explore particular natural hazard events.  
• Environmental justice Case studies from the University of Michigan.
• Environmental justice Native Case Studies from Evergreen.

Related Links

• Teaching with Investigative Cases
• Using Socioscientific Issues
• Teaching with Current Research and Data site guide connects you to a variety of resources that incorporate data into the classroom.  

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Getting smart collective, impact update, 7 real-world issues that can allow students to tackle big challenges.

Ever since I started teaching in 1990, I have been a student voice advocate. Whether it was as a media/English teacher, student leadership advisor or a site leader. I have always believed that students not only have good ideas, but that they may just have new, unique or even better ones. In an effort to find their own voice and place in the world, they may see things that we don’t see or have long been paralyzed to do anything about. In 1999, I saw students address a school’s racial divide and cultural issues by creating a school-wide learning experience (see Harmony at Buchanan High School ). Ever since then, I have believed that projects with real-world outcomes hold some of the greatest potential for helping students become driven, empathetic and engaged citizens. The outpouring of student voice  in the wake of the recent tragedy in Parkland, Florida, is a great example.

When we begin the project design process in PBL, we can start either with a challenging problem or question and then tie it to our standards, or we can start with our standards and connect them to a real-world challenge. This second approach is more foundational to project based learning, for many reasons, including student engagement, student voice, relevance and authenticity. But beyond that, we also do it because this is where jobs are. Jobs are created and grown as we work to address the real problems facing our world and peoples. Our students are ready to tackle the problems facing our world. They have a voice. They have the tools and resources. And they are not afraid to collaborate and form new communities poised for the problem-solving work that needs to be done.

As an educator, parent and advocate for an engaged/empowered citizenry, I could not be prouder of how the students in Parkland, Florida – along with their peers across the nation – have both found their voice, as well as changed the narrative. These students, as well as many others across the nation, are not afraid to collaborate, and use new technologies and form new professional networks in order to address our current and future challenges. Let’s be honest, our best hope of improving the status of our planet’s many issues truly lie with our youth.

With all of this in mind, there are a number of current and ongoing real-world challenges that we currently face (and probably will for a long time). I don’t like the term “problem-solving” in this context, as it implies that we can fix, cure or eradicate a problem or challenge, but by going after our problems with new solutions, we can certainly move progress forward. And in that movement, there is magic. There is innovation. There is change. There is our collective human mission: how can we creatively collaborate, critically think and communicate in ways that make our world a better place to live.

Our students are ready to exercise their collective voices and create calls to action. The following seven ideas are not ranked, but are rather my go to “top seven” that naturally lend themselves to projects that excite student interest, rely on available resources, and maintain relevance and authenticity. Moreover, they are not subject-specific. Indeed, there are many opportunities for English, science, social science, math and others to connect to these project challenges. They are:

1) Climate Change – Climate Change will have a significant impact on our students’ lives. Indeed, there may not be one issue that will impact them more comprehensively. Students have seen the data and witnessed the changes, and are listening to the science community. They know that this an urgent issue that will affect almost everything, including, but not limited to, weather, sea levels, food security, water quality, air quality, sustainability and much more. Many organizations – such as NASA , The National Park Service , National Center for Science Education , National Oceanic Atmospheric Association  and SOCAN  to name a few – are working to bring climate change curriculum and projects to teachers and students.

2) Health Care  – Since this has become a prominent topic in the national debate, students are becoming aware of the issues in our country related to rising costs, access, quality and equity. They are beginning to understand the importance both individually and societally. Like the aforementioned topic of climate change, students are also (and unfortunately) learning that we are not necessarily leading the world in this area. They know that this problem is connected to profits, insurance, bureaucracy and more, but they also have a fresher sense of how it could be different, and how we could learn from others around the world. The work on this topic, like many others, is being led by our universities. Institutions such as University of Michigan , Johns Hopkins  and Stanford are leading the way.

3) Food Insecurity   – as our students become more aware of their surrounding communities, as well as the peers they interact with daily, they begin to see differences. Differences in socioeconomic status, opportunities for growth, housing, security, support services and more. And since 13 million young people live in food-insecure homes, almost all of our students, as well as educators, know someone who is hungry on a daily basis. This may often start with service-based projects, but can also lead to high quality project based learning complete with research, data analysis, diverse solutions and ultimately a variety of calls to action. If you want to see how one teacher and his students transformed not only their school, but entire community related to food insecurity, check out Power Of A Plant author Stephen Ritz and the Green Bronx Machine .

4) Violence  – This is a natural given current events taking the nation by storm. However, the related topics and issues here are not new. And yes, they are politically charged, but young people care about these issues . They care about their collective safety and futures, but also know something can be done. In addition to the specifics related to school violence and safety, students can study details of how to advocate, organize, campaign and solicit support, learn that this is a complex problem that has many plausible causes, and, perhaps most importantly, hope for progress. They also know that although they are concerned about attending school in safe environments, our society and culture have violence-related problems and issues that they want to see addressed. Following the recent incident in Florida and the subsequent response from students, the New York Times has compiled a list of resources  for educators on this topic.

5) Homelessness  – We often hear the expression “think globally, act locally.” The topic of homelessness has garnered more attention than ever as more and more communities wrestle with a growing homeless population. In addition to opportunities for our students and schools to partner with local non-profit organizations dealing with homelessness, this topic, like others, is also a great way to elicit empathy in our students. We often hear from educators, employers and others that we want to raise adults that are able to solve problems, improve our communities, and have the ability to see beyond themselves. This topic can provide a number of options for helping students develop those skills. Finally, we also have a growing population of homeless students. So, the relevancy and urgency are all there. Many have laid the groundwork for us to address this within our curriculum. Organizations like Bridge Communities , National Coalition For The Homeless , Homeless Hub  and Learning To Give  are some of the many leading the way.

6) Sustainability  – This is an extremely global issue that affects everything from energy, to food, to resources, economics, health, wellness and more. Students are becoming more and more aware that our very future as a species depends on how we address sustainability challenges. They are aware that this challenge requires new ways of thinking, new priorities, new standards and new ways of doing things. Sustainability is all about future innovation. Students have tremendous opportunities to collaborate, think critically, communicate, and be creative when questioning if a current practice, method, resource or even industry is sustainable without dramatic change and shifts. Students who tackle these challenges will be our leaders – business, political and cultural – of the future. Educators and students can find almost infinite resources and partners. A few of these are Green Education Foundation , Green Schools Initiative , Strategic Energy Innovations , Facing the Future  and Teach For America .

7) Education  – It seems that each and every day, more and more of us (though maybe still not enough) are moving closer to realizing that our educational systems are seemingly unprepared to make the big shifts needed to truly address the learning needs of 21st-century students. The related challenges are many – new literacies, skills, economic demands, brain research, technology, outcomes and methodologies. It’s a good thing that more and more people – both inside and outside of education – are both demanding and implementing change. However, one of the continued ironies within education is that we (and I recognize that this is a generalization) rarely ask the primary customer (students) what they think their education should look, feel and sound like. We have traditionally underestimated their ability to articulate what they need and what would benefit them for their individual and collective futures. One of the many foundational advantages of project based learning is that we consult and consider the student in project design and implementation. Student “voice & choice” creates opportunities for students to have input on and make decisions regarding everything from the final product, to focus area within a topic or challenge, and even whom they may partner with from peers to professionals. It’s this choice that not only helps elicit engagement and ownership of learning, but offers opportunities for students to enhance all of the skills that we want in our ideal graduates. As one might guess, there is not a lot of formal curriculum being developed for teachers to lead students through the issue of education reform. This may need to be an organic thing that happens class by class and school by school. It can start as easily as one teacher asking students about what they want out of their education. Some other entry points are The Buck Institute for Education , Edutopia’s Five Ways To Give Your Students More Voice & Choice , Barbara Bray’s Rethinking Learning  and reDesign .

This is not intended to be an exhaustive or comprehensive list. However, these seven broad topics present hundreds of relevant challenges that our students can and should have opportunities to address. If they do, they will not only be more prepared for their futures, but also poised to positively impact all of our futures.

For more, see:

• High Quality PBL Case Study: School21
• In Broward County, Student Voice Impacts the Classroom and Beyond
• Introducing a Framework for High Quality Project Based Learning

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Real World Problem-Solving

Real world problem-solving (RWPS) is what we do every day. It requires flexibility, resilience, resourcefulness, and a certain degree of creativity. A crucial feature of RWPS is that it involves continuous interaction with the environment during the problem-solving process. In this process, the environment can be seen as not only a source of inspiration for new ideas but also as a tool to facilitate creative thinking. The cognitive neuroscience literature in creativity and problem-solving is extensive, but it has largely focused on neural networks that are active when subjects are not focused on the outside world, i.e., not using their environment. In this paper, I attempt to combine the relevant literature on creativity and problem-solving with the scattered and nascent work in perceptually-driven learning from the environment. I present my synthesis as a potential new theory for real world problem-solving and map out its hypothesized neural basis. I outline some testable predictions made by the model and provide some considerations and ideas for experimental paradigms that could be used to evaluate the model more thoroughly.

1. Introduction

In the Apollo 13 space mission, astronauts together with ground control had to overcome several challenges to bring the team safely back to Earth (Lovell and Kluger, 2006 ). One of these challenges was controlling carbon dioxide levels onboard the space craft: “For 2 days straight [they] had worked on how to jury-rig the Odysseys canisters to the Aquarius's life support system. Now, using materials known to be available onboard the spacecraft—a sock, a plastic bag, the cover of a flight manual, lots of duct tape, and so on—the crew assembled a strange contraption and taped it into place. Carbon dioxide levels immediately began to fall into the safe range” (Team, 1970 ; Cass, 2005 ).

The success of Apollo 13's recovery from failure is often cited as a glowing example of human resourcefulness and inventiveness alongside more well-known inventions and innovations over the course of human history. However, this sort of inventive capability is not restricted to a few creative geniuses, but an ability present in all of us, and exemplified in the following mundane example. Consider a situation when your only suit is covered in lint and you do not own a lint remover. You see a roll of duct tape, and being resourceful you reason that it might be a good substitute. You then solve the problem of lint removal by peeling a full turn's worth of tape and re-attaching it backwards onto the roll to expose the sticky side all around the roll. By rolling it over your suit, you can now pick up all the lint.

In both these examples (historic as well as everyday), we see evidence for our innate ability to problem-solve in the real world. Solving real world problems in real time given constraints posed by one's environment are crucial for survival. At the core of this skill is our mental capability to get out of “sticky situations” or impasses, i.e., difficulties that appear unexpectedly as impassable roadblocks to solving the problem at hand. But, what are the cognitive processes that enable a problem solver to overcome such impasses and arrive at a solution, or at least a set of promising next steps?

A central aspect of this type of real world problem solving, is the role played by the solver's surrounding environment during the problem-solving process. Is it possible that interaction with one's environment can facilitate creative thinking? The answer to this question seems somewhat obvious when one considers the most famous anecdotal account of creative problem solving, namely that of Archimedes of Syracuse. During a bath, he found a novel way to check if the King's crown contained non-gold impurities. The story has traditionally been associated with the so-called “Eureka moment,” the sudden affective experience when a solution to a particularly thorny problem emerges. In this paper, I want to temporarily turn our attention away from the specific “aha!” experience itself and take particular note that Archimedes made this discovery, not with his eyes closed at a desk, but in a real-world context of a bath 1 . The bath was not only a passive, relaxing environment for Archimedes, but also a specific source of inspiration. Indeed it was his noticing the displacement of water that gave him a specific methodology for measuring the purity of the crown; by comparing how much water a solid gold bar of the same weight would displace as compared with the crown. This sort of continuous environmental interaction was present when the Apollo 13 engineers discovered their life-saving solution, and when you solved the suit-lint-removal problem with duct tape.

The neural mechanisms underlying problem-solving have been extensively studied in the literature, and there is general agreement about the key functional networks and nodes involved in various stages of problem-solving. In addition, there has been a great deal of work in studying the neural basis for creativity and insight problem solving, which is associated with the sudden emergence of solutions. However, in the context of problem-solving, creativity, and insight have been researched as largely an internal process without much interaction with and influence from the external environment (Wegbreit et al., 2012 ; Abraham, 2013 ; Kounios and Beeman, 2014 ) 2 . Thus, there are open questions of what role the environment plays during real world problem-solving (RWPS) and how the brain enables the assimilation of novel items during these external interactions.

In this paper, I synthesize the literature on problem-solving, creativity and insight, and particularly focus on how the environment can inform RWPS. I explore three environmentally-informed mechanisms that could play a critical role: (1) partial-cue driven context-shifting, (2) heuristic prototyping and learning novel associations, and (3) learning novel physical inferences. I begin first with some intuitions about real world problem solving, that might help ground this discussion and providing some key distinctions from more traditional problem solving research. Then, I turn to a review of the relevant literature on problem-solving, creativity, and insight first, before discussing the three above-mentioned environmentally-driven mechanisms. I conclude with a potential new model and map out its hypothesized neural basis.

2. Problem solving, creativity, and insight

2.1. what is real world problem-solving.

Archimedes was embodied in the real world when he found his solution. In fact, the real world helped him solve the problem. Whether or not these sorts of historic accounts of creative inspiration are accurate 3 , they do correlate with some of our own key intuitions about how problem solving occurs “in the wild.” Real world problem solving (RWPS) is different from those that occur in a classroom or in a laboratory during an experiment. They are often dynamic and discontinuous, accompanied by many starts and stops. Solvers are never working on just one problem. Instead, they are simultaneously juggling several problems of varying difficulties and alternating their attention between them. Real world problems are typically ill-defined, and even when they are well-defined, often have open-ended solutions. Coupled with that is the added aspect of uncertainty associated with the solver's problem solving strategies. As introduced earlier, an important dimension of RWPS is the continuous interaction between the solver and their environment. During these interactions, the solver might be inspired or arrive at an “aha!” moment. However, more often than not, the solver experiences dozens of minor discovery events— “hmmm, interesting…” or “wait, what?…” moments. Like discovery events, there's typically never one singular impasse or distraction event. The solver must iterate through the problem solving process experiencing and managing these sorts of intervening events (including impasses and discoveries). In summary, RWPS is quite messy and involves a tight interplay between problem solving, creativity, and insight. Next, I explore each of these processes in more detail and explicate a possible role of memory, attention, conflict management and perception.

2.2. Analytical problem-solving

In psychology and neuroscience, problem-solving broadly refers to the inferential steps taken by an agent 4 that leads from a given state of affairs to a desired goal state (Barbey and Barsalou, 2009 ). The agent does not immediately know how this goal can be reached and must perform some mental operations (i.e., thinking) to determine a solution (Duncker, 1945 ).

The problem solving literature divides problems based on clarity (well-defined vs. ill-defined) or on the underlying cognitive processes (analytical, memory retrieval, and insight) (Sprugnoli et al., 2017 ). While memory retrieval is an important process, I consider it as a sub-process to problem solving more generally. I first focus on analytical problem-solving process, which typically involves problem-representation and encoding, and the process of forming and executing a solution plan (Robertson, 2016 ).

2.2.1. Problem definition and representation

An important initial phase of problem-solving involves defining the problem and forming a representation in the working memory. During this phase, components of the prefrontal cortex (PFC), default mode network (DMN), and the dorsal anterior cingulate cortex (dACC) have been found to be activated. If the problem is familiar and well-structured, top-down executive control mechanisms are engaged and the left prefrontal cortex including the frontopolar, dorso-lateral (dlPFC), and ventro-lateral (vlPFC) are activated (Barbey and Barsalou, 2009 ). The DMN along with the various structures in the medial temporal lobe (MTL) including the hippocampus (HF), parahippocampal cortex, perirhinal and entorhinal cortices are also believed to have limited involvement, especially in episodic memory retrieval activities during this phase (Beaty et al., 2016 ). The problem representation requires encoding problem information for which certain visual and parietal areas are also involved, although the extent of their involvement is less clear (Anderson and Fincham, 2014 ; Anderson et al., 2014 ).

2.2.1.1. Working memory

An important aspect of problem representation is the engagement and use of working memory (WM). The WM allows for the maintenance of relevant problem information and description in the mind (Gazzaley and Nobre, 2012 ). Research has shown that WM tasks consistently recruit the dlPFC and left inferior frontal cortex (IC) for encoding an manipulating information; dACC for error detection and performance adjustment; and vlPFC and the anterior insula (AI) for retrieving, selecting information and inhibitory control (Chung and Weyandt, 2014 ; Fang et al., 2016 ).

2.2.1.2. Representation

While we generally have a sense for the brain regions that are functionally influential in problem definition, less is known about how exactly events are represented within these regions. One theory for how events are represented in the PFC is the structured event complex theory (SEC), in which components of the event knowledge are represented by increasingly higher-order convergence zones localized within the PFC, akin to the convergence zones (from posterior to anterior) that integrate sensory information in the brain (Barbey et al., 2009 ). Under this theory, different zones in the PFC (left vs. right, anterior vs. posterior, lateral vs. medial, and dorsal vs. ventral) represent different aspects of the information contained in the events (e.g., number of events to be integrated together, the complexity of the event, whether planning, and action is needed). Other studies have also suggested the CEN's role in tasks requiring cognitive flexibility, and functions to switch thinking modes, levels of abstraction of thought and consider multiple concepts simultaneously (Miyake et al., 2000 ).

Thus, when the problem is well-structured, problem representation is largely an executive control activity coordinated by the PFC in which problem information from memory populates WM in a potentially structured representation. Once the problem is defined and encoded, planning and execution of a solution can begin.

2.2.2. Planning

The central executive network (CEN), particularly the PFC, is largely involved in plan formation and in plan execution. Planning is the process of generating a strategy to advance from the current state to a goal state. This in turn involves retrieving a suitable solution strategy from memory and then coordinating its execution.

2.2.2.1. Plan formation

The dlPFC supports sequential planning and plan formation, which includes the generation of hypothesis and construction of plan steps (Barbey and Barsalou, 2009 ). Interestingly, the vlPFC and the angular gyrus (AG), implicated in a variety of functions including memory retrieval, are also involved in plan formation (Anderson et al., 2014 ). Indeed, the AG together with the regions in the MTL (including the HF) and several other regions form a what is known as the “core” network. The core network is believed to be activated when recalling past experiences, imagining fictitious, and future events and navigating large-scale spaces (Summerfield et al., 2010 ), all key functions for generating plan hypotheses. A recent study suggests that the AG is critical to both episodic simulation, representation, and episodic memory (Thakral et al., 2017 ). One possibility for how plans are formulated could involve a dynamic process of retrieving an optimal strategy from memory. Research has shown significant interaction between striatal and frontal regions (Scimeca and Badre, 2012 ; Horner et al., 2015 ). The striatum is believed to play a key role in declarative memory retrieval, and specifically helping retrieve optimal (or previously rewarded) memories (Scimeca and Badre, 2012 ). Relevant to planning and plan formation, Scimeca & Badre have suggested that the striatum plays two important roles: (1) in mapping acquired value/utility to action selection, and thereby helping plan formation, and (2) modulation and re-encoding of actions and other plan parameters. Different types of problems require different sets of specialized knowledge. For example, the knowledge needed to solve mathematical problems might be quite different (albeit overlapping) from the knowledge needed to select appropriate tools in the environment.

Thus far, I have discussed planning and problem representation as being domain-independent, which has allowed me to outline key areas of the PFC, MTL, and other regions relevant to all problem-solving. However, some types of problems require domain-specific knowledge for which other regions might need to be recruited. For example, when planning for tool-use, the superior parietal lobe (SPL), supramarginal gyrus (SMG), anterior inferior parietal lobe (AIPL), and certain portions of the temporal and occipital lobe involved in visual and spatial integration have been found to be recruited (Brandi et al., 2014 ). It is believed that domain-specific information stored in these regions is recovered and used for planning.

2.2.2.2. Plan execution

Once a solution plan has been recruited from memory and suitably tuned for the problem on hand, the left-rostral PFC, caudate nucleus (CN), and bilateral posterior parietal cortices (PPC) are responsible for translating the plan into executable form (Stocco et al., 2012 ). The PPC stores and maintains “mental template” of the executable form. Hemispherical division of labor is particularly relevant in planning where it was shown that when planning to solve a Tower of Hanoi (block moving) problem, the right PFC is involved in plan construction whereas the left PFC is involved in controlling processes necessary to supervise the execution of the plan (Newman and Green, 2015 ). On a separate note and not the focus of this paper, plan execution and problem-solving can require the recruitment of affective and motivational processing in order to supply the agent with the resolve to solve problems, and the vmPFC has been found to be involved in coordinating this process (Barbey and Barsalou, 2009 ).

2.3. Creativity

During the gestalt movement in the 1930s, Maier noted that “most instances of “real” problem solving involves creative thinking” (Maier, 1930 ). Maier performed several experiments to study mental fixation and insight problem solving. This close tie between insight and creativity continues to be a recurring theme, one that will be central to the current discussion. If creativity and insight are linked to RWPS as noted by Maier, then it is reasonable to turn to the creativity and insight literature for understanding the role played by the environment. A large portion of the creativity literature has focused on viewing creativity as an internal process, one in which the solvers attention is directed inwards, and toward internal stimuli, to facilitate the generation of novel ideas and associations in memory (Beaty et al., 2016 ). Focusing on imagination, a number of researchers have looked at blinking, eye fixation, closing eyes, and looking nowhere behavior and suggested that there is a shift of attention from external to internal stimuli during creative problem solving (Salvi and Bowden, 2016 ). The idea is that shutting down external stimuli reduces cognitive load and focuses attention internally. Other experiments studying sleep behavior have also noted the beneficial role of internal stimuli in problem solving. The notion of ideas popping into ones consciousness, suddenly, during a shower is highly intuitive for many and researchers have attempted to study this phenomena through the lens of incubation, and unconscious thought that is internally-driven. There have been several theories and counter-theories proposed to account specifically for the cognitive processes underlying incubation (Ritter and Dijksterhuis, 2014 ; Gilhooly, 2016 ), but none of these theories specifically address the role of the external environment.

The neuroscience of creativity has also been extensively studied and I do not focus on an exhaustive literature review in this paper (a nice review can be found in Sawyer, 2011 ). From a problem-solving perspective, it has been found that unlike well-structured problems, ill-structured problems activate the right dlPFC. Most of the past work on creativity and creative problem-solving has focused on exploring memory structures and performing internally-directed searches. Creative idea generation has primarily been viewed as internally directed attention (Jauk et al., 2012 ; Benedek et al., 2016 ) and a primary mechanism involved is divergent thinking , which is the ability to produce a variety of responses in a given situation (Guilford, 1962 ). Divergent thinking is generally thought to involve interactions between the DMN, CEN, and the salience network (Yoruk and Runco, 2014 ; Heinonen et al., 2016 ). One psychological model of creative cognition is the Geneplore model that considers two major phases of generation (memory retrieval and mental synthesis) and exploration (conceptual interpretation and functional inference) (Finke et al., 1992 ; Boccia et al., 2015 ). It has been suggested that the associative mode of processing to generate new creative association is supported by the DMN, which includes the medial PFC, posterior cingulate cortex (PCC), tempororparietal juntion (TPJ), MTL, and IPC (Beaty et al., 2014 , 2016 ).

That said, the creativity literature is not completely devoid of acknowledging the role of the environment. In fact, it is quite the opposite. Researchers have looked closely at the role played by externally provided hints from the time of the early gestalt psychologists and through to present day studies (Öllinger et al., 2017 ). In addition to studying how hints can help problem solving, researchers have also looked at how directed action can influence subsequent problem solving—e.g., swinging arms prior to solving the two-string puzzle, which requires swinging the string (Thomas and Lleras, 2009 ). There have also been numerous studies looking at how certain external perceptual cues are correlated with creativity measures. Vohs et al. suggested that untidiness in the environment and the increased number of potential distractions helps with creativity (Vohs et al., 2013 ). Certain colors such as blue have been shown to help with creativity and attention to detail (Mehta and Zhu, 2009 ). Even environmental illumination, or lack thereof, have been shown to promote creativity (Steidle and Werth, 2013 ). However, it is important to note that while these and the substantial body of similar literature show the relationship of the environment to creative problem solving, they do not specifically account for the cognitive processes underlying the RWPS when external stimuli are received.

2.4. Insight problem solving

Analytical problem solving is believed to involve deliberate and conscious processing that advances step by step, allowing solvers to be able to explain exactly how they solved it. Inability to solve these problems is often associated with lack of required prior knowledge, which if provided, immediately makes the solution tractable. Insight, on the other hand, is believed to involve a sudden and unexpected emergence of an obvious solution or strategy sometimes accompanied by an affective aha! experience. Solvers find it difficult to consciously explain how they generated a solution in a sequential manner. That said, research has shown that having an aha! moment is neither necessary nor sufficient to insight and vice versa (Danek et al., 2016 ). Generally, it is believed that insight solvers acquire a full and deep understanding of the problem when they have solved it (Chu and Macgregor, 2011 ). There has been an active debate in the problem solving community about whether insight is something special. Some have argued that it is not, and that there are no special or spontaneous processes, but simply a good old-fashioned search of a large problem space (Kaplan and Simon, 1990 ; MacGregor et al., 2001 ; Ash and Wiley, 2006 ; Fleck, 2008 ). Others have argued that insight is special and suggested that it is likely a different process (Duncker, 1945 ; Metcalfe, 1986 ; Kounios and Beeman, 2014 ). This debate lead to two theories for insight problem solving. MacGregor et al. proposed the Criterion for Satisfactory Progress Theory (CSPT), which is based on Newell and Simons original notion of problem solving as being a heuristic search through the problem space (MacGregor et al., 2001 ). The key aspect of CSPT is that the solver is continually monitoring their progress with some set of criteria. Impasses arise when there is a criterion failure, at which point the solver tries non-maximal but promising states. The representational change theory (RCT) proposed by Ohlsson et al., on the other hand, suggests that impasses occur when the goal state is not reachable from an initial problem representation (which may have been generated through unconscious spreading activation) (Ohlsson, 1992 ). In order to overcome an impasse, the solver needs to restructure the problem representation, which they can do by (1) elaboration (noticing new features of a problem), (2) re-encoding fixing mistaken or incomplete representations of the problem, and by (3) changing constraints. Changing constraints is believed to involve two sub-processes of constraint relaxation and chunk-decomposition.

The current position is that these two theories do not compete with each other, but instead complement each other by addressing different stages of problem solving: pre- and post-impasse. Along these lines, Ollinger et al. proposed an extended RCT (eRCT) in which revising the search space and using heuristics was suggested as being a dynamic and iterative and recursive process that involves repeated instances of search, impasse and representational change (Öllinger et al., 2014 , 2017 ). Under this theory, a solver first forms a problem representation and begins searching for solutions, presumably using analytical problem solving processes as described earlier. When a solution cannot be found, the solver encounters an impasse, at which point the solver must restructure or change the problem representation and once again search for a solution. The model combines both analytical problem solving (through heuristic searches, hill climbing and progress monitoring), and creative mechanisms of constraint relaxation and chunk decomposition to enable restructuring.

Ollingers model appears to comprehensively account for both analytical and insight problem solving and, therefore, could be a strong candidate to model RWPS. However, while compelling, it is nevertheless an insufficient model of RWPS for many reasons, of which two are particularly significant for the current paper. First, the model does explicitly address mechanisms by which external stimuli might be assimilated. Second, the model is not sufficiently flexible to account for other events (beyond impasse) occurring during problem solving, such as distraction, mind-wandering and the like.

So, where does this leave us? I have shown the interplay between problem solving, creativity and insight. In particular, using Ollinger's proposal, I have suggested (maybe not quite explicitly up until now) that RWPS involves some degree of analytical problem solving as well as the post-impasse more creative modes of problem restructuring. I have also suggested that this model might need to be extended for RWPS along two dimensions. First, events such as impasses might just be an instance of a larger class of events that intervene during problem solving. Thus, there needs to be an accounting of the cognitive mechanisms that are potentially influenced by impasses and these other intervening events. It is possible that these sorts of events are crucial and trigger a switch in attentional focus, which in turn facilitates switching between different problem solving modes. Second, we need to consider when and how externally-triggered stimuli from the solver's environment can influence the problem solving process. I detail three different mechanisms by which external knowledge might influence problem solving. I address each of these ideas in more detail in the next two sections.

3. Event-triggered mode switching during problem-solving

3.1. impasse.

When solving certain types of problems, the agent might encounter an impasse, i.e., some block in its ability to solve the problem (Sprugnoli et al., 2017 ). The impasse may arise because the problem may have been ill-defined to begin with causing incomplete and unduly constrained representations to have been formed. Alternatively, impasses can occur when suitable solution strategies cannot be retrieved from memory or fail on execution. In certain instances, the solution strategies may not exist and may need to be generated from scratch. Regardless of the reason, an impasse is an interruption in the problem solving process; one that was running conflict-free up until the point when a seemingly unresolvable issue or an error in the predicted solution path was encountered. Seen as a conflict encountered in the problem-solving process it activates the anterior cingulate cortex (ACC). It is believed that the ACC not only helps detect the conflict, but also switch modes from one of “exploitation” (planning) to “exploration” (search) (Quilodran et al., 2008 ; Tang et al., 2012 ), and monitors progress during resolution (Chu and Macgregor, 2011 ). Some mode switching duties are also found to be shared with the AI (the ACC's partner in the salience network), however, it is unclear exactly the extent of this function-sharing.

Even though it is debatable if impasses are a necessary component of insight, they are still important as they provide a starting point for the creativity (Sprugnoli et al., 2017 ). Indeed, it is possible that around the moment of impasse, the AI and ACC together, as part of the salience network play a crucial role in switching thought modes from analytical planning mode to creative search and discovery mode. In the latter mode, various creative mechanisms might be activated allowing for a solution plan to emerge. Sowden et al. and many others have suggested that the salience network is potentially a candidate neurobiological mechanism for shifting between thinking processes, more generally (Sowden et al., 2015 ). When discussing various dual-process models as they relate to creative cognition, Sowden et al. have even noted that the ACC activation could be useful marker to identify shifting as participants work creative problems.

3.2. Defocused attention

As noted earlier, in the presence of an impasse there is a shift from an exploitative (analytical) thinking mode to an exploratory (creative) thinking mode. This shift impacts several networks including, for example, the attention network. It is believed attention can switch between a focused mode and a defocused mode. Focused attention facilitates analytic thought by constraining activation such that items are considered in a compact form that is amenable to complex mental operations. In the defocused mode, agents expand their attention allowing new associations to be considered. Sowden et al. ( 2015 ) note that the mechanism responsible for adjustments in cognitive control may be linked to the mechanisms responsible for attentional focus. The generally agreed position is that during generative thinking, unconscious cognitive processes activated through defocused attention are more prevalent, whereas during exploratory thinking, controlled cognition activated by focused attention becomes more prevalent (Kaufman, 2011 ; Sowden et al., 2015 ).

Defocused attention allows agents to not only process different aspects of a situation, but to also activate additional neural structures in long term memory and find new associations (Mendelsohn, 1976 ; Yoruk and Runco, 2014 ). It is believed that cognitive material attended to and cued by positive affective state results in defocused attention, allowing for more complex cognitive contexts and therefore a greater range of interpretation and integration of information (Isen et al., 1987 ). High attentional levels are commonly considered a typical feature of highly creative subjects (Sprugnoli et al., 2017 ).

4. Role of the environment

In much of the past work the focus has been on treating creativity as largely an internal process engaging the DMN to assist in making novel connections in memory. The suggestion has been that “individual needs to suppress external stimuli and concentrate on the inner creative process during idea generation” (Heinonen et al., 2016 ). These ideas can then function as seeds for testing and problem-solving. While true of many creative acts, this characterization does not capture how creative ideas arise in many real-world creative problems. In these types of problems, the agent is functioning and interacting with its environment before, during and after problem-solving. It is natural then to expect that stimuli from the environment might play a role in problem-solving. More specifically, it can be expected that through passive and active involvement with the environment, the agent is (1) able to trigger an unrelated, but potentially useful memory relevant for problem-solving, (2) make novel connections between two events in memory with the environmental cue serving as the missing link, and (3) incorporate a completely novel information from events occuring in the environment directly into the problem-solving process. I explore potential neural mechanisms for these three types of environmentally informed creative cognition, which I hypothesize are enabled by defocused attention.

4.1. Partial cues trigger relevant memories through context-shifting

I have previously discussed the interaction between the MTL and PFC in helping select task-relevant and critical memories for problem-solving. It is well-known that pattern completion is an important function of the MTL and one that enables memory retrieval. Complementary Learning Theory (CLS) and its recently updated version suggest that the MTL and related structures support initial storage as well as retrieval of item and context-specific information (Kumaran et al., 2016 ). According to CLS theory, the dentate gyrus (DG) and the CA3 regions of the HF are critical to selecting neural activity patterns that correspond to particular experiences (Kumaran et al., 2016 ). These patterns might be distinct even if experiences are similar and are stabilized through increases in connection strengths between the DG and CA3. Crucially, because of the connection strengths, reactivation of part of the pattern can activate the rest of it (i.e., pattern completion). Kumaran et al. have further noted that if consistent with existing knowledge, these new experiences can be quickly replayed and interleaved into structured representations that form part of the semantic memory.

Cues in the environment provided by these experiences hold partial information about past stimuli or events and this partial information converges in the MTL. CLS accounts for how these cues might serve to reactivate partial patterns, thereby triggering pattern completion. When attention is defocused I hypothesize that (1) previously unnoticed partial cues are considered, and (2) previously noticed partial cues are decomposed to produce previously unnoticed sub-cues, which in turn are considered. Zabelina et al. ( 2016 ) have shown that real-world creativity and creative achievement is associated with “leaky attention,” i.e., attention that allows for irrelevant information to be noticed. In two experiments they systematically explored the relationship between two notions of creativity— divergent thinking and real-world creative achievement—and the use of attention. They found that attentional use is associated in different ways for each of the two notions of creativity. While divergent thinking was associated with flexible attention, it does not appear to be leaky. Instead, selective focus and inhibition components of attention were likely facilitating successful performance on divergent thinking tasks. On the other hand, real-world creative achievement was linked to leaky attention. RWPS involves elements of both divergent thinking and of real-world creative achievement, thus I would expect some amount of attentional leaks to be part of the problem solving process.

Thus, it might be the case that a new set of cues or sub-cues “leak” in and activate memories that may not have been previously considered. These cues serve to reactivate a diverse set of patterns that then enable accessing a wide range of memories. Some of these memories are extra-contextual, in that they consider the newly noticed cues in several contexts. For example, when unable to find a screwdriver, we might consider using a coin. It is possible that defocused attention allows us to consider the coin's edge as being a potentially relevant cue that triggers uses for the thin edge outside of its current context in a coin. The new cues (or contexts) may allow new associations to emerge with cues stored in memory, which can occur during incubation. Objects and contexts are integrated into memory automatically into a blended representation and changing contexts disrupts this recognition (Hayes et al., 2007 ; Gabora, 2016 ). Cue-triggered context shifting allows an agent to break-apart a memory representation, which can then facilitate problem-solving in new ways.

4.2. Heuristic prototyping facilitates novel associations

It has long been the case that many scientific innovations have been inspired by events in nature and the surrounding environment. As noted earlier, Archimedes realized the relationship between the volume of an irregularly shaped object and the volume of water it displaced. This is an example of heuristic prototyping where the problem-solver notices an event in the environment, which then triggers the automatic activation of a heuristic prototype and the formation of novel associations (between the function of the prototype and the problem) which they can then use to solve the problem (Luo et al., 2013 ). Although still in its relative infancy, there has been some recent research into the neural basis for heuristic prototyping. Heuristic prototype has generally been defined as an enlightening prototype event with a similar element to the current problem and is often composed of a feature and a function (Hao et al., 2013 ). For example, in designing a faster and more efficient submarine hull, a heuristic prototype might be a shark's skin, while an unrelated prototype might be a fisheye camera (Dandan et al., 2013 ).

Research has shown that activating the feature function of the right heuristic prototype and linking it by way of semantic similarity to the required function of the problem was the key mechanism people used to solve several scienitific insight problems (Yang et al., 2016 ). A key region activated during heuristic prototyping is the dlPFC and it is believed to be generally responsible for encoding the events into memory and may play an important role in selecting and retrieving the matched unsolved technical problem from memory (Dandan et al., 2013 ). It is also believed that the precuneus plays a role in automatic retrieval of heuristic information allowing the heuristic prototype and the problem to combine (Luo et al., 2013 ). In addition to semantic processing, certain aspects of visual imagery have also been implicated in heuristic prototyping leading to the suggestion of the involvement of Broadman's area BA 19 in the occipital cortex.

There is some degree of overlap between the notions of heuristic prototyping and analogical transfer (the mapping of relations from one domain to another). Analogical transfer is believed to activate regions in the left medial fronto-parietal system (dlPFC and the PPC) (Barbey and Barsalou, 2009 ). I suggest here that analogical reasoning is largely an internally-guided process that is aided by heuristic prototyping which is an externally-guided process. One possible way this could work is if heuristic prototyping mechanisms help locate the relevant memory with which to then subsequently analogize.

4.3. Making physical inferences to acquire novel information

The agent might also be able to learn novel facts about their environment through passive observation as well as active experimentation. There has been some research into the neural basis for causal reasoning (Barbey and Barsalou, 2009 ; Operskalski and Barbey, 2016 ), but beyond its generally distributed nature, we do not know too much more. Beyond abstract causal reasoning, some studies looked into the cortical regions that are activated when people watch and predict physical events unfolding in real-time and in the real-world (Fischer et al., 2016 ). It was found that certain regions were associated with representing types of physical concepts, with the left intraparietal sulcus (IPS) and left middle frontal gyrus (MFG) shown to play a role in attributing causality when viewing colliding objects (Mason and Just, 2013 ). The parahippocampus (PHC) was associated with linking causal theory to observed data and the TPJ was involved in visualizing movement of objects and actions in space (Mason and Just, 2013 ).

5. Proposed theory

I noted earlier that Ollinger's model for insight problem solving, while serving as a good candidate for RWPS, requires extension. In this section, I propose a candidate model that includes some necessary extensions to Ollinger's framework. I begin by laying out some preliminary notions that underlie the proposed model.

5.1. Dual attentional modes

I propose that the attention-switching mechanism described earlier is at the heart of RWPS and enables two modes of operation: focused and defocused mode. In the focused mode, the problem representation is more or less fixed, and problem solving proceeds in a focused and goal directed manner through search, planning, and execution mechanisms. In the defocused mode, problem solving is not necessarily goal directed, but attempts to generate ideas, driven by both internal and external items.

At first glance, these modes might seem similar to convergent and divergent thinking modes postulated by numerous others to account for creative problem solving. Divergent thinking allows for the generation of new ideas and convergent thinking allows for verification and selection of generated ideas. So, it might seem that focused mode and convergent thinking are similar and likewise divergent and defocused mode. They are, however, quite different. The modes relate less to idea generation and verification, and more to the specific mechanisms that are operating with regard to a particular problem at a particular moment in time. Convergent and divergent processes may be occurring during both defocused and focused modes. Some degree of divergent processes may be used to search and identify specific solution strategies in focused mode. Also, there might be some degree of convergent idea verification occuring in defocused mode as candidate items are evaluated for their fit with the problem and goal. Thus, convergent and divergent thinking are one amongst many mechanisms that are utilized in focused and defocused mode. Each of these two modes has to do with degree of attention placed on a particular problem.

There have been numerous dual-process and dual-systems models of cognition proposed over the years. To address criticisms raised against these models and to unify some of the terminology, Evans & Stanovich proposed a dual-process model comprising Type 1 and Type 2 thought (Evans and Stanovich, 2013 ; Sowden et al., 2015 ). Type 1 processes are those that are believed to be autonomous and do not require working memory. Type 2 processes, on the other hand, are believed to require working memory and are cognitively decoupled to prevent real-world representations from becoming confused with mental simulations (Sowden et al., 2015 ). While acknowledging various other attributes that are often used to describe dual process models (e.g., fast/slow, associative/rule-based, automatic/controlled), Evans & Stanovich note that these attributes are merely frequent correlates and not defining characteristics of Type 1 or Type 2 processes. The proposed dual attentional modes share some similarities with the Evans & Stanovich Type 1 and 2 models. Specifically, Type 2 processes might occur in focused attentional mode in the proposed model as they typically involve the working memory and certain amount of analytical thought and planning. Similarly, Type 1 processes are likely engaged in defocused attentional mode as there are notions of associative and generative thinking that might be facilitated when attention has been defocused. The crucial difference between the proposed model and other dual-process models is that the dividing line between focused and defocused attentional modes is the degree of openness to internal and external stimuli (by various networks and functional units in the brain) when problem solving. Many dual process models were designed to classify the “type” of thinking process or a form of cognitive processing. In some sense, the “processes” in dual process theories are characterized by the type of mechanism of operation or the type of output they produced. Here, I instead characterize and differentiate the modes of thinking by the receptivity of different functional units in the brain to input during problem solving.

This, however, raises a different question of the relationship between these attentional modes and conscious vs. unconscious thinking. It is clear that both the conscious and unconscious are involved in problem solving, as well as in RWPS. Here, I claim that a problem being handled is, at any given point in time, in either a focused mode or in a defocused mode. When in the focused mode, problem solving primarily proceeds in a manner that is available for conscious deliberation. More specifically, problem space elements and representations are tightly managed and plans and strategies are available in the working memory and consciously accessible. There are, however, secondary unconscious operations in the focused modes that includes targeted memory retrieval and heuristic-based searches. In the defocused mode, the problem is primarily managed in an unconscious way. The problem space elements are broken apart and loosely managed by various mechanisms that do not allow for conscious deliberation. That said, it is possible that some problem parameters remain accessible. For example, it is possible that certain goal information is still maintained consciously. It is also possible that indexes to all the problems being considered by the solver are maintained and available to conscious awareness.

5.2. RWPS model

Returning to Ollinger's model for insight problem solving, it now becomes readily apparent how this model can be modified to incorporate environmental effects as well as generalizing the notion of intervening events beyond that of impasses. I propose a theory for RWPS that begins with standard analytical problem-solving process (See Figures ​ Figures1, 1 , ​ ,2 2 ).

Summary of neural activations during focused problem-solving (Left) and defocused problem-solving (Right) . During defocused problem-solving, the salience network (insula and ACC) coordinates the switching of several networks into a defocused attention mode that permits the reception of a more varied set of stimuli and interpretations via both the internally-guided networks (default mode network DMN) and externally guided networks (Attention). PFC, prefrontal cortex; ACC, anterior cingulate cortex; PCC, posterior cingulate cortex; IPC, inferior parietal cortex; PPC, posterior parietal cortex; IPS, intra-parietal sulcus; TPJ, temporoparietal junction; MTL, medial temporal lobe; FEF, frontal eye field.

Proposed Model for Real World Problem Solving (RWPS). The corresponding neural correlates are shown in italics. During problem-solving, an initial problem representation is formed based on prior knowledge and available perceptual information. The problem-solving then proceeds in a focused, goal-directed mode until the goal is achieved or a defocusing event (e.g., impasse or distraction) occurs. During focused mode operation, the solver interacts with the environment in directed manner, executing focused plans, and allowing for predicted items to be activated by the environment. When a defocusing event occurs, the problem-solving then switches into a defocused mode until a focusing event (e.g., discovery) occurs. In defocused mode, the solver performs actions unrelated to the problem (or is inactive) and is receptive to a set of environmental triggers that activate novel aspects using the three mechanisms discussed in this paper. When a focusing event occurs, the diffused problem elements cohere into a restructured representation and problem-solving returns into a focused mode.

5.2.1. Focused problem solving mode

Initially, both prior knowledge and perceptual entities help guide the creation of problem representations in working memory. Prior optimal or rewarding solution strategies are obtained from LTM and encoded in the working memory as well. This process is largely analytical and the solver interacts with their environment through focused plan or idea execution, targeted observation of prescribed entities, and estimating prediction error of these known entities. More specifically, when a problem is presented, the problem representations are activated and populated into working memory in the PFC, possibly in structured representations along convergence zones. The PFC along with the Striatum and the MTL together attempt at retrieving an optimal or previously rewarded solution strategy from long term memory. If successfully retrieved, the solution strategy is encoded into the PPC as a mental template, which then guides relevant motor control regions to execute the plan.

5.2.2. Defocusing event-triggered mode switching

The search and solve strategy then proceeds analytically until a “defocusing event” is encountered. The salience network (AI and ACC) monitor for conflicts and attempt to detect any such events in the problem-solving process. As long as no conflicts are detected, the salience network focuses on recruiting networks to achieve goals and suppresses the DMN (Beaty et al., 2016 ). If the plan execution or retrieval of the solution strategy fails, then a defocusing event is detected and the salience network performs mode switching. The salience network dynamically switches from the focused problem-solving mode to a defocused problem-solving mode (Menon, 2015 ). Ollinger's current model does not account for other defocusing events beyond an impasse, but it is not inconceivable that there could be other such events triggered by external stimuli (e.g., distraction or an affective event) or by internal stimuli (e.g., mind wandering).

5.2.3. Defocused problem solving mode

In defocused mode, the problem is operated on by mechanisms that allow for the generation and testing of novel ideas. Several large-scale brain networks are recruited to explore and generate new ideas. The search for novel ideas is facilitated by generally defocused attention, which in turn allows for creative idea generation from both internal as well as external sources. The salience network switches operations from defocused event detection to focused event or discovery detection, whereby for example, environmental events or ideas that are deemed interesting can be detected. During this idea exploration phase, internally, the DMN is no longer suppressed and attempts to generate new ideas for problem-solving. It is known that the IPC is involved in the generation of new ideas (Benedek et al., 2014 ) and together with the PPC in coupling different information together (Simone Sandkühler, 2008 ; Stocco et al., 2012 ). Beaty et al. ( 2016 ) have proposed that even this internal idea-generation process can be goal directed, thereby allowing for a closer working relationship between the CEN and the DMN. They point to neuroimaging evidence that support the possibility that the executive control network (comprising the lateral prefrontal and inferior parietal regions) can constrain and direct the DMN in its process of generating ideas to meet task-specific goals via top down monitoring and executive control (Beaty et al., 2016 ). The control network is believed to maintain an “internal train of thought” by keeping the task goal activated, thereby allowing for strategic and goal-congruent searches for ideas. Moreover, they suggest that the extent of CEN involvement in the DMN idea-generation may depend on the extent to which the creative task is constrained. In the RWPS setting, I would suspect that the internal search for creative solutions is not entirely unconstrained, even in the defocused mode. Instead, the solver is working on a specified problem and thus, must maintain the problem-thread while searching for solutions. Moreover, self-generated ideas must be evaluated against the problem parameters and thereby might need some top-down processing. This would suggest that in such circumstances, we would expect to see an increased involvement of the CEN in constraining the DMN.

On the external front, several mechanisms are operating in this defocused mode. Of particular note are the dorsal attention network, composed of the visual cortex (V), IPS and the frontal eye field (FEF) along with the precuneus and the caudate nucleus allow for partial cues to be considered. The MTL receives synthesized cue and contextual information and populates the WM in the PFC with a potentially expanded set of information that might be relevant for problem-solving. The precuneus, dlPFC and PPC together trigger the activation and use of a heuristic prototype based on an event in the environment. The caudate nucleus facilitates information routing between the PFC and PPC and is involved in learning and skill acquisition.

5.2.4. Focusing event-triggered mode switching

The problem's life in this defocused mode continues until a focusing event occurs, which could be triggered by either external (e.g., notification of impending deadline, discovery of a novel property in the environment) or internal items (e.g., goal completion, discovery of novel association or updated relevancy of a previously irrelevant item). As noted earlier, an internal train of thought may be maintained that facilitates top-down evaluation of ideas and tracking of these triggers (Beaty et al., 2016 ). The salience network switches various networks back to the focused problem-solving mode, but not without the potential for problem restructuring. As noted earlier, problem space elements are maintained somewhat loosely in the defocused mode. Thus, upon a focusing event, a set or subset of these elements cohere into a tight (restructured) representation suitable for focused mode problem solving. The process then repeats itself until the goal has been achieved.

5.3. Model predictions

5.3.1. single-mode operation.

The proposed RWPS model provides several interesting hypotheses, which I discuss next. First, the model assumes that any given problem being worked on is in one mode or another, but not both. Thus, the model predicts that there cannot be focused plan execution on a problem that is in defocused mode. The corollary prediction is that novel perceptual cues (as those discussed in section 4) cannot help the solver when in focused mode. The corollary prediction, presumably has some support from the inattentional blindness literature. Inattentional blindness is when perceptual cues are not noticed during a task (e.g., counting the number of basketball passes between several people, but not noticing a gorilla in the scene) (Simons and Chabris, 1999 ). It is possible that during focused problem solving, that external and internally generated novel ideas are simply not considered for problem solving. I am not claiming that these perceptual cues are always ignored, but that they are not considered within the problem. Sometimes external cues (like distracting occurrences) can serve as defocusing events, but the model predicts that the actual content of these cues are not themselves useful for solving the specific problem at hand.

When comparing dual-process models Sowden et al. ( 2015 ) discuss shifting from one type of thinking to another and explore how this shift relates to creativity. In this regard, they weigh the pros and cons of serial vs. parallel shifts. In dual-process models that suggest serial shifts, it is necessary to disengage one type of thought prior to engaging the other or to shift along a continuum. Whereas, in models that suggest parallel shifts, each of the thinking types can operate in parallel. Per this construction, the proposed RWPS model is serial, however, not quite in the same sense. As noted earlier, the RWPS model is not a dual-process model in the same sense as other dual process model. Instead, here, the thrust is on when the brain is receptive or not receptive to certain kinds of internal and external stimuli that can influence problem solving. Thus, while the modes may be serial with respect to a certain problem, it does not preclude the possibility of serial and parallel thinking processes that might be involved within these modes.

5.3.2. Event-driven transitions

The model requires an event (defocusing or focusing) to transition from one mode to another. After all why else would a problem that is successfully being resolved in the focused mode (toward completion) need to necessarily be transferred to defocused mode? These events are interpreted as conflicts in the brain and therefore the mode-switching is enabled by the saliency network and the ACC. Thus, the model predicts that there can be no transition from one mode to another without an event. This is a bit circular, as an event is really what triggers the transition in the first place. But, here I am suggesting that an external or internal cue triggered event is what drives the transition, and that transitions cannot happen organically without such an event. In some sense, the argument is that the transition is discontinuous, rather than a smooth one. Mind-wandering is good example of when we might drift into defocused mode, which I suggest is an example of an internally driven event caused by an alternative thought that takes attention away from the problem.

A model assumption underlying RWPS is that events such as impasses have a similar effect to other events such as distraction or mind wandering. Thus, it is crucial to be able to establish that there exists of class of such events and they have a shared effect on RWPS, which is to switch attentional modes.

5.3.3. Focused mode completion

The model also predicts that problems cannot be solved (i.e., completed) within the defocused mode. A problem can be considered solved when a goal is reached. However, if a goal is reached and a problem is completed in the defocused mode, then there must have not been any converging event or coherence of problem elements. While it is possible that the solver arbitrarily arrived at the goal in a diffused problem space and without conscious awareness of completing the task or even any converging event or problem recompiling, it appears somewhat unlikely. It is true that there are many tasks that we complete without actively thinking about it. We do not think about what foot to place in front of another while walking, but this is not an instance of problem solving. Instead, this is an instance of unconscious task completion.

5.3.4. Restructuring required

The model predicts that a problem cannot return to a focused mode without some amount of restructuring. That is, once defocused, the problem is essentially never the same again. The problem elements begin interacting with other internally and externally-generated items, which in turn become absorbed into the problem representation. This prediction can potentially be tested by establishing some preliminary knowledge, and then showing one group of subjects the same knowledge as before, while showing the another group of subjects different stimuli. If the model's predictions hold, the problem representation will be restructured in some way for both groups.

There are numerous other such predictions, which are beyond the scope of this paper. One of the biggest challenges then becomes evaluating the model to set up suitable experiments aimed at testing the predictions and falsifying the theory, which I address next.

6. Experimental challenges and paradigms

One of challenges in evaluating the RWPS is that real world factors cannot realistically be accounted for and sufficiently controlled within a laboratory environment. So, how can one controllably test the various predictions and model assumptions of “real world” problem solving, especially given that by definition RWPS involves the external environment and unconscious processing? At the expense of ecological validity, much of insight problem solving research has employed an experimental paradigm that involves providing participants single instances of suitably difficult problems as stimuli and observing various physiological, neurological and behavioral measures. In addition, through verbal protocols, experimenters have been able to capture subjective accounts and problem solving processes that are available to the participants' conscious. These experiments have been made more sophisticated through the use of timed-hints and/or distractions. One challenge with this paradigm has been the selection of a suitable set of appropriately difficult problems. The classic insight problems (e.g., Nine-dot, eight-coin) can be quite difficult, requiring complicated problem solving processes, and also might not generalize to other problems or real world problems. Some in the insight research community have moved in the direction of verbal tasks (e.g., riddles, anagrams, matchstick rebus, remote associates tasks, and compound remote associates tasks). Unfortunately, these puzzles, while providing a great degree of controllability and repeatability, are even less realistic. These problems are not entirely congruent with the kinds of problems that humans are solving every day.

The other challenge with insight experiments is the selection of appropriate performance and process tracking measures. Most commonly, insight researchers use measures such as time to solution, probability of finding solution, and the like for performance measures. For process tracking, verbal protocols, coded solution attempts, and eye tracking are increasingly common. In neuroscientific studies of insight various neurological measures using functional magnetic resonance imaging (fMRI), electroencephalography (EEGs), transcranial direct current stimulation (tDCS), and transcranial magnetic stimulation (tMS) are popular and allow for spatially and temporally localizing an insight event.

Thus, the challenge for RWPS is two-fold: (1) selection of stimuli (real world problems) that are generalizable, and (2) selection of measures (or a set of measures) that can capture key aspects of the problem solving process. Unfortunately, these two challenges are somewhat at odds with each other. While fMRI and various neuroscientific measures can capture the problem solving process in real time, it is practically difficult to provide participants a realistic scenario while they are laying flat on their back in an fMRI machine and allowed to move nothing more than a finger. To begin addressing this conundrum, I suggest returning to object manipulation problems (not all that different from those originally introduced by Maier and Duncker nearly a century ago), but using modern computing and user-interface technologies.

One pseudo-realistic approach is to generate challenging object manipulation problems in Virtual Reality (VR). VR has been used to describe 3-D environment displays that allows participants to interact with artificially projected, but experientially realistic scenarios. It has been suggested that virtual environments (VE) invoke the same cognitive modules as real equivalent environmental experience (Foreman, 2010 ). Crucially, since VE's can be scaled and designed as desired, they provide a unique opportunity to study pseudo-RWPS. However, a VR-based research approach has its limitations, one of which is that it is nearly impossible to track participant progress through a virtual problem using popular neuroscientific measures such as fMRI because of the limited mobility of connected participants.

Most of the studies cited in this paper utilized an fMRI-based approach in conjunction with a verbal or visual task involving problem-solving or creative thinking. Very few, if any, studies involved the use physical manipulation, and those physical manipulations were restricted to limited finger movements. Thus, another pseudo-realistic approach is allowing subjects to teleoperate robotic arms and legs from inside the fMRI machine. This paradigm has seen limited usage in psychology and robotics, in studies focused on Human-Robot interaction (Loth et al., 2015 ). It could be an invaluable tool in studying real-time dynamic problem-solving through the control of a robotic arm. In this paradigm a problem solving task involving physical manipulation is presented to the subject via the cameras of a robot. The subject (in an fMRI) can push buttons to operate the robot and interact with its environment. While the subjects are not themselves moving, they can still manipulate objects in the real world. What makes this paradigm all the more interesting is that the subject's manipulation-capabilities can be systematically controlled. Thus, for a particular problem, different robotic perceptual and manipulation capabilities can be exposed, allowing researchers to study solver-problem dynamics in a new way. For example, even simple manipulation problems (e.g., re-arranging and stacking blocks on a table) can be turned into challenging problems when the robotic movements are restricted. Here, the problem space restrictions are imposed not necessarily on the underlying problem, but on the solver's own capabilities. Problems of this nature, given their simple structure, may enable studying everyday practical creativity without the burden of devising complex creative puzzles. Crucial to note, both these pseudo-realistic paradigms proposed demonstrate a tight interplay between the solver's own capabilities and their environment.

7. Conclusion

While the neural basis for problem-solving, creativity and insight have been studied extensively in the past, there is still a lack of understanding of the role of the environment in informing the problem-solving process. Current research has primarily focused on internally-guided mental processes for idea generation and evaluation. However, the type of real world problem-solving (RWPS) that is often considered a hallmark of human intelligence has involved both a dynamic interaction with the environment and the ability to handle intervening and interrupting events. In this paper, I have attempted to synthesize the literature into a unified theory of RWPS, with a specific focus on ways in which the environment can help problem-solve and the key neural networks involved in processing and utilizing relevant and useful environmental information. Understanding the neural basis for RWPS will allow us to be better situated to solve difficult problems. Moreover, for researchers in computer science and artificial intelligence, clues into the neural underpinnings of the computations taking place during creative RWPS, can inform the design the next generation of helper and exploration robots which need these capabilities in order to be resourceful and resilient in the open-world.

Author contributions

The author confirms being the sole contributor of this work and approved it for publication.

Conflict of interest statement

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

Acknowledgments

I am indebted to Professor Matthias Scheutz, Professor Elizabeth Race, Professor Ayanna Thomas, and Professor. Shaun Patel for providing guidance with the research and the manuscript. I am also grateful for the facilities provided by Tufts University, Medford, MA, USA.

1 My intention is not to ignore the benefits of a concentrated internal thought process which likely occurred as well, but merely to acknowledge the possibility that the environment might have also helped.

2 The research in insight does extensively use “hints” which are, arguably, a form of external influence. But these hints are highly targeted and might not be available in this explicit form when solving problems in the real world.

3 The accuracy of these accounts has been placed in doubt. They often are recounted years later, with inaccuracies, and embellished for dramatic effect.

4 I use the term “agent” to refer to the problem-solver. The term agent is more general than “creature” or “person” or “you" and is intentionally selected to broadly reference humans, animals as well as artificial agents. I also selectively use the term “solver.”

Funding. The research for this Hypothesis/Theory Article was funded by the authors private means. Publication costs will be covered by my institution: Tufts University, Medford, MA, USA.

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Praxis Core Math

Course: praxis core math   >   unit 1.

• Algebraic properties | Lesson
• Algebraic properties | Worked example
• Solution procedures | Lesson
• Solution procedures | Worked example
• Equivalent expressions | Lesson
• Equivalent expressions | Worked example
• Creating expressions and equations | Lesson
• Creating expressions and equations | Worked example

Algebraic word problems | Lesson

• Algebraic word problems | Worked example
• Linear equations | Lesson
• Linear equations | Worked example
• Quadratic equations | Lesson
• Quadratic equations | Worked example

What are algebraic word problems?

What skills are needed.

• Translating sentences to equations
• Solving linear equations with one variable
• Evaluating algebraic expressions
• Solving problems using Venn diagrams

How do we solve algebraic word problems?

• Define a variable.
• Write an equation using the variable.
• Solve the equation.
• If the variable is not the answer to the word problem, use the variable to calculate the answer.

What's a Venn diagram?

• 7 + 10 − 13 = 4 ‍   brought both food and drinks.
• 7 − 4 = 3 ‍   brought only food.
• 10 − 4 = 6 ‍   brought only drinks.
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
• (Choice A)   $ 4 ‍   A $ 4 ‍  
• (Choice B)   $ 5 ‍   B $ 5 ‍  
• (Choice C)   $ 9 ‍   C $ 9 ‍  
• (Choice D)   $ 14 ‍   D $ 14 ‍  
• (Choice E)   $ 20 ‍   E $ 20 ‍  
• (Choice A)   10 ‍   A 10 ‍  
• (Choice B)   12 ‍   B 12 ‍  
• (Choice C)   24 ‍   C 24 ‍  
• (Choice D)   30 ‍   D 30 ‍  
• (Choice E)   32 ‍   E 32 ‍  
• (Choice A)   4 ‍   A 4 ‍  
• (Choice B)   10 ‍   B 10 ‍  
• (Choice C)   14 ‍   C 14 ‍  
• (Choice D)   18 ‍   D 18 ‍  
• (Choice E)   22 ‍   E 22 ‍  

Things to remember

Want to join the conversation.

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

• Good to Great Schools Australia Pilot Program
• Online teaching and learning resources to support mathematics and numeracy
• Support for Arts and Languages
• Support for Humanities and Social Sciences
• Support for Literacy and Numeracy
• National STEM School Education Strategy 2016–2026
• STEM Education Resources Toolkit
• STEM program evaluations in the early years and schooling 
• Research into Best Practice Models in mathematics teaching and learning
• Support for Social Cohesion
• Year 1 Phonics Check

Real-world problem-solving

On this page:, what is it.

Real-world problem-solving is more than demonstrating examples in a classroom. It’s about moving away from the textbooks to connect the concepts to the real world.  Teachers apply contemporary STEM knowledge to guide students through investigating and tackling an existing challenge or need. For example, it could be designing a greenhouse for the school garden, working with industry or designing a solution to a local council problem.

How does it help?

Real-world problem-solving promotes:

• The relevance of STEM education and its connection with the ‘real world’ after school e.g. careers and education opportunities. This can increase student interest and engagement in STEM.
• Active critical-thinking and problem-solving.
• Access to STEM experts and real work environments. This enhances student learning experiences and sparks student interest and engagement.
• STEM education that resembles authentic STEM practice in industry. This can help students understand the realities of the world of the work.

How do you do it?

• Partner with experts or professionals through school-industry partnerships to provide examples/challenges/contexts.
• Gather real examples from local community e.g. local council.

Want to know more?

Research reports.

• Partnering with scientists boosts school students’ and teachers’ confidence in science - The Conversation
• The Australian Industry Group Strengthening School - Industry STEM Skills partnerships - Final Project Report (Page 40)

Case study: Banksia Park International High School and BTG Australasia

Banksia Park International High School in South Australia partnered with BTG Australasia for an extended real world STEM project for Year 8 students. This involved a student visit to BTG’s laboratories, a four-week group project on contamination avoidance in BTG labs and presentations to a panel of BTG employees and other external panellists. The project exposed students to how STEM skills can be applied to a real-world industry problem. It challenged students to think both critically and creatively. It also linked to curriculum learning areas in mathematics, science and technologies. Both the school and BTG were impressed with the enthusiasm and growth of students and were eager to further the partnership.

• STEM By Design / Teacher Preparation

Real-World STEM Problems

by Anne Jolly · Published 12/16/2012 · Updated 10/27/2021

A MiddleWeb Blog

Links checked and updated January 2019. See Anne’s recent posts for more real-world STEM.

STEM teachers pose problems and combine problem solving with project-based learning across disciplines. They work together with students on activities to develop students’ critical thinking, communication, assessment, and inquiry skills.

That’s an impressive job description; however, one source describes the teacher preparation system for STEM teachers as “chaotic, incoherent, and uncoordinated, filled with ‘excellent programs, terrible programs, and many in between.’” That’s not surprising, since the STEM acronym has only been around for a few years. But it certainly needs to improve.

What Good STEM Lessons Do

While things seem a bit muddled on the STEM teacher preparation front, we do know some things about STEM curriculum. We know, for example, that a good STEM lesson accomplishes these things:

• Helps students apply math and science through authentic, hands-on learning
• Includes the use of (or creation of) technology
• Involves students in using an engineering design process
• Engages students in working in collaborative teams
• Appeals equally to girls and boys
• Reinforces relevant math and science standards
• Addresses a real-world problem

Providing students with real-world problems and asking them to brainstorm solutions will bring their higher order thinking skills into play. But for me, identifying real-world problems that students can solve is one of the hardest parts of creating STEM lessons.

They have to be problems that students can reasonably grapple with. And those all-important problems may need to synchronize with a specific set of math and/or science standards from the school system’s pacing guide. Hopefully you don’t have that constraint, but realistically you probably do.

Sites for Real-World Problems

I’ve located some sites that help me come up with real-world problems, and I’m always on the look-out for more. I’m going to share several sites I’ve identified, and I hope that you’ll share some as well. I invite you to click on these sites and mull over the possibilities.

In the Greening STEM section on this site you’ll find ideas for relevant problems. Most environmental topics can fit under standards for either life or physical science, so these may provide you with some real “kid-catchers,” or ideas that snag students’ interest.

Topics include areas such as:

•    Oil spills •    Water pollution •    Air quality •    Endangered species •    Environmental Health

Another favorite site of mine is the Design Squad Nation . They have some real-world problems there that I find intriguing. For example student teams might invent these:

•    Band Instrument •    Electric Gamebox •    Confetti Launcher •    Solar Water Heater •    Speedy Shelter

How cool are those ideas? As a middle school science teacher, I found STEM to be a natural fit for most of the topics I taught. Math, however, seems to be a different matter.

The Problem with Math

One issue I hear repeatedly is that math teachers find it difficult to identify real-world problems and implement STEM projects in math classes. (Note that these math teachers are not able to work collaboratively with science teachers to develop/implement lessons, and must therefore “go-it-alone.”) However, the math teachers who mentioned this are looking determinedly for ways to implement STEM lessons.

The Common Core Standards state: “Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.” This adds urgency to the search for real-world problems that bring in appropriate math standards.

Math standards addressed by the lessons on this site include these and more:

•    Fractions, decimals, percents •    Ratios and proportions •    Estimating and predicting •    Rates and unit rate •    Modeling problems with graphs, tables, and equations •    Comparing, graphing, and interpreting data •    Scale factors •    Geometry and measurement •    Probability •    Proportional reasoning

Another site that links math to real problems is Middle School Math and Science . Students solve problems involving train races, global sun temperature, amount of water usage, and so on. Most of these are Internet-based, so you may want to design some of them as hands-on projects for students. (UPDATE: This Ohio State University site is now an archive, but you’ll still find plenty of useful resources.)

Teach Engineering

No list of real-world problem ideas would be complete without mentioning the Teach Engineering lessons. As you peruse these, read the summary of the lessons rather than relying on the titles. Look for projects that include hands-on ideas, such as those involving microbes, rocket-powered boats, solid fuel reactants, the fisheries bycatch problem , and so on. Notice that many of the lessons have hands-on “Associated Activities.” These generally hands-on investigations bring the “E” in STEM to your students.

I hope these sites will be of value to you, and will assist you in brainstorming ideas for real-world problems. Feel free to share comments or sites of your own. We’re inventing a new specialty and need all the help we can get and share!

For even more STEM lesson ideas, read Anne’s 2018 posts:

How to Make or Find Good STEM Lessons and Design Squad Global’s Super STEM Resources

and her 2020 post:

Need a Real World STEM Project? Try Plastics Pollution

You’ll also find teaching ideas at Anne’s STEM by Design website

Click & use code MWEB1 for 20% off!

Share this:

Tags: STEM curriculum STEM real-world problems STEM teacher preparation teaching STEM

Anne Jolly began her career as a lab scientist, caught the science teaching bug and was recognized as an Alabama Teacher of the Year during her long career as a middle grades science teacher. From 2007-2014 Anne was part of an NSF-funded team that developed middle grades STEM curriculum modules and teacher PD. In 2020-2021 Anne teamed with Flight Works Alabama to develop a workforce-friendly middle school curriculum and is now working on an elementary version. Her book STEM By Design: Strategies & Activities for Grades 4-8 is published by Routledge/EOE in partnership with MiddleWeb.

65 Responses

• Comments 63
• Pingbacks 2

Hello Anne. As a new STEM coordinator, I have to give a STEM presentation to principals for my charter schools. Can you suggest and lessons, books. power points,etc. that would be advantageous? Fondly, Linda Schwerer Pinellas Academy of Math & Science

Hi, Linda – I have a couple of ideas . . . If you contact Susan Pruet – Director if Engaging Youth through Engineering (you can google it) she will send you a copy of a free STEM launcher. It’s a lesson intended to demonstrate the STEM process. You could lead your principals through it if you think they really need a better understanding of the difference in STEM and science experimentation. You could also distribute it to your schools for teachers to use as a launcher into the STEM way of thinking. It has PowerPoint slides with it.

An online document that you might like to look at is “STEM Teachers in Professional Learning Communities: From Good Teachers to Great Teaching.” You can google this document online as well as a National Academies Press document titled “Successful K-12 STEM Education: Identifying Effective Approaches in Science, Technology, Engineering, and Mathematics.”

I’m not sure if you’re trying to introduce these principals to the idea of STEM and convince them that they need to do this, or if you’re trying to show your principals how to do this. Those are two separate presentations – at least.

Good luck with your preparation! You have a lot of research to back up the need for STEM!

Thank you so much Anne! I will get to work! Your advice is very helpful!

I realize this comment is 3 years old, but I came across it just now. I would like to know if Susan Pruet is still available to get that free STEM launcher you mentioned – a lesson intended to demo the STEM process. I would love this.

Harry – thanks for asking. This is still a popular post at MiddleWeb! Anne Jolly’s January 2017 blog post shares the Launcher activity: Launch the New Year with STEM Mini-Lessons!

Thank you! Much appreciated from a fellow Alabaman. (correct use of that word? :) )

I love the STEM idea. But, as a 7th grade math teacher, I don’t see a place in STEM programs to ensure that students understand the basic math skills required by educational standards. For many kids, it takes a long time to understand and be able to apply math concepts. With STEM programming focusing on the project-based approach, where does mastering basic skills fit in?

Mastering math skills and applying them through STEM isn’t actually an either-or situation. If kids see reasons for what they are learning, they tend to learn more deeply and quickly because they are actually engaged in the content. I’ve worked with STEM courses that made use of math that the kids had already learned. I’ve also worked with STEM projects that taught the math kids needed in order to solve the problem. Both were effective. The real purpose of STEM is to ensure that math and science students learn their content more deeply. If that isn’t working, then we’ll need to keep adjusting until we get there. Thanks for asking!

Hi Ann, I am a third grade teacher and currently co-chair a curriculum committee to develop a summer program for Kindergarten through 3rd grade. I am having trouble finding age appropriate STEM lessons for kindergarten through 3rd grade. Do you have ideas or suggestiosn as to where I can start? Thank you.

Hi, Mary! So glad you’re working on developing a summer program. I know someone who’s been there, done that, and I’m going to put you in touch with her. Her name is Susan Pruet and her email is [email protected] . Please shoot her an email and she’ll be happy to tell you about what materials, etc. she uses.

I’d also take a look at the Engineering is Elementary (EiE) curriculum from the Boston Museum of Science. Those are quite thorough and good.

Hi Ann I am a seventh grade science teacher and we are in the early stages of implementing STEMS at our school site.Can this program incorporate all content areas, history, language arts, math and science all in the science classroom? This is not my understanding of how it should be taught. I understand the math and science but to include what the history and language art teacher is teaching doesnt seem to work. I am hoping you can clarify this for me.

Hi, Darren. Wow. You’re gonna be sorry you asked me this . . . my answer won’t be short!

For me personally, STEM includes an indepth, integrated focus on science and math, and on using the engineering design process to solve real-world problems. Technology may be used to help with the solution, or teams of kids may create technology as part of the solution. (Anything made by humans to meet a want or need is designated as technology). This in-depth focus on science and math through STEM has come about as the result of a 21st Century workforce with an increasing need in STEM fields and a lack of STEM-prepared workers. The math and science deficits are sending our industries abroad to find workers qualified for our 21st century workforce.

Now to your question. I see a place for art in the STEM product design – it could be used to make the product teams produce more appealing and desirable – although that may be for the art teacher to work with if it’s going to involve knowing art design principles.

Likewise, you have to use some form of language arts in the communication process (communication is part of the engineering design process); however, it’s used naturally as teams work together to solve the engineering (STEM) challenge and to publicize their solutions. It’s not used try to accomplish specific language arts objectives.

History might be incorporated if you need to set some sort of context for the engineering challenge. But I can’t visualize incorporating specific history objectives during a STEM challenge unless they happen to be a natural fit. And unless you need a historical context for the challenge.

Doing a “force fit” with other subjects doesn’t make much sense to me. Not to mention – class time is already at a premium. STEM work, with its inquiry-based approach, already requires more time than a traditional science (or math) class.

The fact that all subjects are not taught directly in an engineering challenge doesn’t lessen the value of those other subjects. Again – it goes back to the need we’re attempting to meet by going deeper in math and science content through an engineering process.

So for me, in a STEM project students focus on using science and math to solve real world challenges, and they use the engineering design process to bring structure and process to doing that. Language arts and history are always appropriate to the extent that (and if) they add value to the STEM challenge. They shouldn’t be add-ons just for the sake of adding them on.

Remember, however, that there is an intense focus on the science and mathematics objectives in a solid STEM program. And this works best when these two subjects are integrated and the math and science teachers work together on teaching STEM projects.

Now, aren’t you sorry you asked? Seriously – remember this is MY opinion and STEM has other looks as well. I’d advise you to listen openly to the need for including other subjects as explained by your principal or other decision-maker. Then – rather than pushing back – in a positive manner explain how these subjects could fit naturally during the course of the STEM projects. Also explain what you expect to accomplish for your students through STEM and note the limited time you already have. Let me know how it goes. :-)

I am looking for STEM lessons that I can incorporate in my middle school Math Enrichment program which is for advanced math students in grades 6-8 and meets for approximately 10 weeks during the school year. I have been given the charge of creating a Math/STEM enrichment program/curriculum and am looking for resources to help. Currently, our school is implementing STEM curriculum/projects in the Science classrooms, but I need to find more of a mathematical slant. Thanks for your help…..I am so glad I found this website!

Hi, Sharon,

Math is one of the under-resourced areas in terms of lessons that apply real, grade-level math. I’ve seen so many lessons that ask students to “find the average” (my math teachers say it should be “find the median”), and then the writer feels that math has been sufficiently covered. NOT! Some areas of math that I’ve seen successfully developed into STEM lessons include applying what middle school students have learned about flow rate, unit rate, scaling and proportion, and statistics, to name a few.

Susan Pruet – a real math guru – will be writing a post for this blog in August. She’s going to address how math teachers can be STEM teachers, and will give some examples.

Some of the better math lessons I’ve found and adapted are from the Design Squad. This one – making cardboard furniture ( http://pbskids.org/designsquad/build/paper-table/ )- uses geometry. Try browsing around there for ideas. The Design Squad site also has links to other sites as well.

I’m SO glad that you, a math teacher, are taking on this task. Applying math will eliminate forever kids asking “Why should I learn this?”

Keep us posted, and stay in touch.

Thanks for your reply. I will be looking for the post in August and I will look at the Design Squad site as well. I too feel that Math takes a back seat to Science when STEM programs are created and implemented. I hope to change that! I will keep in touch and again, I appreciate your reply and support!!

You are providing amazing resources – thank you! I am starting a STEM program for all 6th, 7th and 8th grade students in our middle school. They will have STEM on three consecutive days (3 – 45 minute blocks) for 12 weeks. This will be a very exciting introductory year for us! My challenge is to design the curriculum this summer, though. I am searching for any type of “canned” curriculum to purchase as a start and then to develop from there. Can you provide any suggestions? Thanks so much!

I, too, have been given the charge of STEM curriculum writing for grades 6-8 in mathematics during the summer. If I find anything useful, I could let you know. It is a daunting task!!

Hi Sharon, Yes that would be excellent, and I will do the same! Nancy

I found a great resource for STEM projects on TeachersPayTeachers.com It is: 21st Century Math Projects. The emphasis is on Math, but STEM oriented. Check it out!

I checked it out, too, Sharon . . . I can’t see to what extent it mirrors STEM lessons, but it certainly seems to do so from what I read. And I love the fact that it’s written from a math perspective. Thanks for pointing out this resource!

Wow. What a feat to accomplish over the summer, Nancy!

Several “For purchase” STEM packages are out there, but I can’t recommend any in particular because I don’t know enough about them. You want your STEM program to integrate math, science, and technology, and to follow an engineering design process. (It’s the engineering piece that many would-be STEM curricula leave out.)

I’ll put out the feelers and see if any show up on the horizon. Check my Twitter feed at @ajollygal – I may get some responses there.

Thanks so much, Anne! I am a bit overwhelmed at the moment, but simultaneously excited about bringing STEM to our school! I appreciate any help or guidance – I will check twitter as well.

I am a parent of a 3rd grader who has been given the task of doing a stem project, and I have no idea how to help her, or what I am looking to do. I do not understand what this curriculum is. Can you please explain to me what I’m supposed to be doing with her

STEM curriculum helps kids apply the science and math they learn in a real world situations. Parents can help a lot with the STEM skills kids need. Here are some posts that contain information I wrote mostly for parents. See if these can give you the information you’re looking for. http://www.middleweb.com/3569/10-stem-tips-for-parents/ http://www.middleweb.com/15579/ideas-activities-stem-summer-slide/ http://www.middleweb.com/22787/reinvent-summer-learning-make-it-up/

Thanks for your question, and for looking for ways to help your daughter in STEM!

please suggest me some hands on activity on maths for 10-15 yrs of age

I am a technology teacher for grades 3-5. I am looking for STEM problems my students can do on the computer. Any ideas?

Thanks for the information on applying STEM. I am actually a spatial ecologist that is teaching gr7-9 mathematics at a small school in South Africa. I feel that we came up with a brilliant idea of how to combine Math and STEM (for those Math teachers that were uncertain). I combined our focus on insects (biology) for the term with all the data chapters (collect, organise, summarise, interpret and report). The learners were tasked with creating a question that we wanted to answer regarding insects and using the data cycle/scientific method (above) to develop a plan how to answer this question. The learners decided to do a survey of insects at the school. They set up a plan of how to collect the insects, did so and then analysed the data and reported their findings. They had to include a section on possible errors/bias in their data. I admit that this is one of the easier sections in math to incorporate into a STEM-type approach but I provide it as an example. The kids loved it!

Thank you so much, Marie! Integrating math and science fits naturally in your example. I appreciate your sharing your idea here, and I wonder if you’d allow me to share it on my website – http://www.stem-by-design.com/ .

You are more than welcome to share it. I think often we are unaware of how what we are doing can be related to STEM/is STEM! (Pls leave my e-mail address anonymous). Thank you Marie

Hello, I work in the scholastic department of a wastewater treatment plant. We provide hands on STEM outreach to schools and community. We are preparing for our second year STEM camp for high school students. Last year we partnered with a local university and focused on microbiology and chemistry. This year we are looking for some additional engaging ideas to incorporate into our 5 day camp. Are there any recommendations that you can provide? Thank you

Hi Ron, I am going to be teaching a Medical Microbiology class this fall. I would love to know how you focused on microbiology and what lessons you may have used. The University of Texas has potential to help us. What university department did you work with? Thanks for any help you can give me.

Hi Ann I am a STEM instructor, using lego materials as hands on instruction materials,how do I make my class more interesting and innovative. I need ideas on how to make my class a real world problem solving session,please your kind recommendations. Thank you

Try this idea . . . your kids should have a real reason for building whatever it is they make with the Legos (or any other materials). Suppose they are studying the human body in science. They could use the Legos to construct a prototype of something to solve a problem – perhaps a model of a miniature artificial arm or leg that would help a disabled person, If the kids have a reason for making something and the freedom to come up with their own designs, this often stimulates interest and innovation.

I am looking or some STEAM projects for 4-5th graders to work on in relation to Earth Day. Does anyone have any suggestions? We are just starting to implement these into our classes at school which ranges from Prek-8 so suggestions for any grade level are welcome and I will pass them on.

Thank you for all of your valuable STEM resources! I’ve enjoyed reading/researching through your site!

I am new to teaching a middle school 9-week STEM class for 6th graders. As of right now, my curriculum/materials consist of a canned STEM program that has zero depth.

I’ve been tasked with overhauling the class – developing a true STEM curriculum. Do you know of any middle school models I could research?

I’d appreciate any help.

Hi, Sarah, Take a look at this STEM launcher on my website at http://www.stem-by-design.com/use-mini-lessons-to-launch-stem-projects/ . It will help your kids get engaged with the “E” in STEM. It’s written for use in math+science classes, but it would be simple to modify and use with your kids. I have two more launchers I can send you if you like this one.

Another idea – look around the website while you’re there. There are plenty free resources and tools (click on the tabs at the top) and you are welcome to use (and modify) any of them.

If you want to check out my book – it has suggestions for developing STEM lessons. If you have a chance to develop STEM projects that carry over from one time the kids meet until the next, that’s the best look. If you only see them once a week or so, then that’s a bit more of an issue. If you want to email me we can probably “chat” more over email than here. [email protected]

Thanks for being a STEM person!

Thank you, Anne! I appreciate your suggestions and resources. When you get a chance, I’d love to take a look at the other launchers.

Hello! I am a 11 year old kid going to Somerset Academy. I am doing a STEM project like all of else as well. I am working with two other friends on this project. In our project there is some different things we must do. Most of all we need to make a product that solves an everyday problem. Our group created and idea with ice cream. Our product name is Drip Catch. It is basically a plastic cup for our ice cream cones whenever it melts. The Ice cram will just fall into the cup looking thing. But….. it does not really work. So I am asking for an idea that is a product that solves everyday problems.

I also forgot to mention I am in 5th grade. Please help me. You only need to give me an easy/ OK difficulty stem project. But.. it must be a product we created and it HAS to solve a problem.

What a neat assignment! I like the Drip Catch idea – I wish it had worked. Can you redesign it so that it will work? I think its a great start.

Let me tell you where you can find some good ideas for STEM projects. Go to the Design Squad at http://pbskids.org/designsquad/projects/ . At the top of the page, click on “Design” or click on “Build.” There are some pretty good ideas there.

I read of a group of kids who designed Popsicles with vitamins in them. Here are some other problems kids tackled. http://read.bi/2DoiBSY Just scroll down to see them.

Have you ever noticed that kids on crutches have a problem carrying things around? Is there some sort of carrier that can be added to crutches so that kids can carry things?

Keep your eyes open. Look for a problem you can help in your community or at your school.

Good luck to you and your friends. I hope you’ll come back and post what you finally decided to do. I bet it will be neat!

Thank you very much! I looked at the links you provided and got some new ideas. But.. my friends and I decided to keep doing the Drip Catch idea! But thx for your help! Bye have a great day/

Thanks, Jaden! Let me know how the Drip Catch works. I thought it sounded like a useful and original idea.

Tom is the STEM fair and we finished! It looks amazing. We made the drip catch with a plastic container and cut it into a circle and a hole inside. SO ready for tom!! Thank you so much.

Good luck!!

HI Anne I am in the process of starting a STEM Summer Academy for 6-8 graders, looking for projects in STEM that will motivate the students

Take a look at “Engineering Is Elementary” (EIE) Curriculum Units. You can find them at( http://www.eie.org/eie-curriculum/curriculum-units .) While they are designed for up to 5th grade, they are easily adaptable for older students. Also check out “Engineering Adventures” at https://www.eie.org/engineering-adventures/curriculum-units .

“Engineering Everywhere” (www.eie.org/engineering-everywhere) is a free Middle School curriculum you may like. It’s designed for youth in afterschool and camp programs.

Another place I go for just fun activity ideas is the Design Squad (pbskids.org/designsquad/projects/)

I hope those give you some good ideas!

Thank you I will keep you posted on how it turns out ; any ideas for projects

What a great resource! I am currently teaching in a small school of 22 P-6 students and have been asked to complete a 1-1.5 hour Maths Problem Solving Session with a STEM focus each week with all of the children. Can you please put me in touch with some resources/activities that are hands on and suitable for multi age/abilities?

Hi, Karlene. One resource that seems popular is the Student Teaming Guide, and it’s a free download on my book website (www.stem-by-design.com). To get it, click the tab at the top of the webpage titled Student Teaming Tips. Scroll to the bottom, and download it and share it.

You may enjoy looking around the website as well. You’ll find plenty of free tools, tips, and teaching ideas there. You’ll also find a free STEM Launcher (a mini-lesson called Stop, Drop, Don’t Pop) to introduce engineering to your students. ( http://bit.ly/2Cvb2cw ) Scroll toward the bottom of the page and you will see 3 pdfs you can download, use, and share.

In my MiddleWeb blog I write about all sorts of topics from lesson design to including girls in STEM. You may wish to look at some of those resources as well. In fact, I’ve just posted another launcher there – the ‘Bama Bears – to help kick off STEM (the engineering component) for 2018.

I also came across another good muliti-grade level resource that I think you’ll like. Take a look at this site: http://bit.ly/2IaNeda

I hope some of these help! Thanks for your work with STEM.

I forgot to include the link to my MW blog – it’s https://www.middleweb.com/category/stem-by-design/

I’m involved in our school’s pilot STEAM classes and found the resources in your post helpful. I’ve used TeachEngineering quite often to help me get ideas.

About the problem with maths, we’ve had the same concern but what we’re aiming to do in our next project is getting the students to collect data themselves than using made-up ones. We think that the authenticity of these activities will increase students’ level of motivation.

Great idea, Ms B! Authenticity is, indeed, the key.

Also consider checking out some of the big math grade-level concepts and targeting one or more of those specific concepts for a STEM challenge. We did that with flow rate. We did an environmental STEM project that dealt with water erosion (that was an authentic problem for our school.) The kids used flow rate to measure and calculate the effectiveness of their barriers. Then they redesigned them and got much better results. And . . . they finally saw a practical use for learning how to calculate flow rate!

I am the middle school science teacher at a Christian school and is desirous of coordinating and developing a STEM curriculum. I have heard a lot about STEM but want to have a clear focus on how to start this first in the middle school then to the rest of the student body.

Hi, Edmund, What an exciting adventure – starting to implement STEM in the elementary school. That’s certainly the right way to do it. Start with this article on building a foundation with elementary STEM: https://www.middleweb.com/26244/building-a-foundation-with-elementary-stem/ . If you haven’t checked out my latest book, STEM by Design , it’s published by Routledge/MiddleWeb. Among other things, this book shares practical tips, principles, and strategies for implementing STEM in Grades 4-8. Those principles can be applied at earlier grades as well. You may enjoy looking around the book website as well at https://www.STEM-by-Design.com . You’ll find plenty of free tools, tips, and teaching ideas there. You’ll also find a free STEM Launcher (mini-lesson called Stop, Drop, Don’t Pop) to introduce engineering to your students. I’ve posted another launcher – the ‘Bama Bears – on my MiddleWeb blog site. You can modify both of these to help kick off STEM (the engineering component) for this fall.

hii, i’am education student , and i want to work on stem activity based on problem solving for grade 4 to 6 math student , but i don’t have any idea what should i doo :(

One place to start is looking at issues in your community. Also checking news geared towards kids (news depth, TFK, and National Geographic. Then get creative around the engineering design process.

You might also check out Design Squad Global, Dana. There are a lot of super STEM activities for all grade levels on that site. Good luck with your STEM activities.

Hi Anne, I don’t teach but I was wondering if you could give me ideas for STEM ideas for some of my peers. It is a school project so I’ve got to knock it out of the ballpark. Appreciate it. Thanks. Please get back to me before 2/20/19. Thanks again.

Hi, Yen-Dow,

A couple of suggestions that will help you find ideas: Go to Design Squad Global Lesson Plans. ( https://to.pbs.org/2XcjPXBd/ ). They have some amazing ideas there.

You might try this MiddleWeb blog post I wrote. ( http://bit.ly/2BK3qmS )

And look at Science Buddies. They have a lot of good resources there. (Note: The Science Buddies site requires a free account to access all the details. Just takes a minute.)

I hope those suggestions will be of some help!

Selam, Türkiye’de ilkokul öğretmeniyim. Bio ekonomi ile ilgili STEM projesi geliştirmek istiyorum.Fikirlerinizi almak benim için muhteşem olacaktır.Teşekkür ederim.

Selam, Candan. Thanks for teaching STEM to elementary students.To find ideas for bio economy projects, please go to this link: https://www.middleweb.com/39326/how-elementary-stem-can-meet-the-future/ . At the end of this article you will find links to six sites that have good lessons you may be able to use. I hope this helps, and please continue your good work.

Hello Anne, Such a wonderful site! So I am interested in researching teacher’s beliefs about integrated STEM education and if it can improve science and math skills for my dissertation. I am planning to explore authentic tasks in both science and math. What do you think about this idea? How can I explore this topic in greater depth? Can you recommend me some readings? Should I use the same authentic activities for both math and science or can I use scientific inquiry in science and models in math? Hoping to hear your thoughts.

Also, I forgot to mention that I would be focusing on primary schools so if you can suggest me some readings.

[…] By Anne JollySummary by MiddleWeb Smartbrief"Providing STEM students with real-world challenges fuels their curiosity & investigative interests, writes science educator Anne Jolly. But where do teachers find problems worthy of investigation? In a new post at MiddleWeb's STEM Imagineering blog, Jolly makes the case for real-world problem solving and points to Internet resources that can help teachers find suitable challenges in science, math and engineering."  […]

[…] head over heels in a STEM project—before the familiar acronym had even burst onto the scene. See Real World STEM Problems for some suggestions for projects students might focus […]

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October 1, 2018

To Solve Real-World Problems, We Need Interdisciplinary Science

Solving today’s complex, global problems will take interdisciplinary science

By Graham A. J. Worthy & Cherie L. Yestrebsky

T he Indian River Lagoon, a shallow estuary that stretches for 156 miles along Florida's eastern coast, is suffering from the activities of human society. Poor water quality and toxic algal blooms have resulted in fish kills, manatee and dolphin die-offs, and takeovers by invasive species. But the humans who live here have needs, too: the eastern side of the lagoon is buffered by a stretch of barrier islands that are critical to Florida's economy, tourism and agriculture, as well as for launching NASA missions into space.

As in Florida, many of the world's coastlines are in serious trouble as a result of population growth and the pollution it produces. Moreover, the effects of climate change are accelerating both environmental and economic decline. Given what is at risk, scientists like us—a biologist and a chemist at the University of Central Florida—feel an urgent need to do research that can inform policy that will increase the resiliency and sustainability of coastal communities. How can our research best help balance environmental and social needs within the confines of our political and economic systems? This is the level of complexity that scientists must enter into instead of shying away from.

Although new technologies will surely play a role in tackling issues such as climate change, rising seas and coastal flooding, we cannot rely on innovation alone. Technology generally does not take into consideration the complex interactions between people and the environment. That is why coming up with solutions will require scientists to engage in an interdisciplinary team approach—something that is common in the business world but is relatively rare in universities.

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Universities are a tremendous source of intellectual power, of course. But students and faculty are typically organized within departments, or academic silos. Scientists are trained in the tools and language of their respective disciplines and learn to communicate their findings to one another using specific jargon.

When the goal of research is a fundamental understanding of a physical or biological system within a niche community, this setup makes a lot of sense. But when the problem the research is trying to solve extends beyond a closed system and includes its effects on society, silos create a variety of barriers. They can limit creativity, flexibility and nimbleness and actually discourage scientists from working across disciplines. As professors, we tend to train our students in our own image, inadvertently producing specialists who have difficulty communicating with the scientist in the next building—let alone with the broader public. This makes research silos ineffective at responding to developing issues in policy and planning, such as how coastal communities and ecosystems worldwide will adapt to rising seas.

Science for the Bigger Picture

As scientists who live and work in Florida, we realized that we needed to play a bigger role in helping our state—and country—make evidence-based choices when it comes to vulnerable coastlines. We wanted to make a more comprehensive assessment of both natural and human-related impacts to the health, restoration and sustainability of our coastal systems and to conduct long-term, integrated research.

At first, we focused on expanding research capacity in our biology, chemistry and engineering programs because each already had a strong coastal research presence. Then, our university announced a Faculty Cluster Initiative, with a goal of developing interdisciplinary academic teams focused on solving tomorrow's most challenging societal problems. While putting together our proposal, we discovered that there were already 35 faculty members on the Orlando campus who studied coastal issues. They belonged to 12 departments in seven colleges, and many of them had never even met. It became clear that simply working on the same campus was insufficient for collaboration.

So we set out to build a team of people from a wide mix of backgrounds who would work in close proximity to one another on a daily basis. These core members would also serve as a link to the disciplinary strengths of their tenure home departments. Initially, finding experts who truly wanted to embrace the team aspect was more difficult than we thought. Although the notion of interdisciplinary research is not new, it has not always been encouraged in academia. Some faculty who go in that direction still worry about whether it will threaten their recognition when applying for grants, seeking promotions or submitting papers to high-impact journals. We are not suggesting that traditional academic departments should be disbanded. On the contrary, they give the required depth to the research, whereas the interdisciplinary team gives breadth to the overall effort.

Our cluster proposal was a success, and in 2019 the National Center for Integrated Coastal Research (UCF Coastal) was born. Our goal is to guide more effective economic development, environmental stewardship, hazard-mitigation planning and public policy for coastal communities. To better integrate science with societal needs, we have brought together biologists, chemists, engineers and biomedical researchers with anthropologists, sociologists, political scientists, planners, emergency managers and economists. It seems that the most creative perspectives on old problems have arisen when people with different training and life experiences are talking through issues over cups of coffee. After all, "interdisciplinary" must mean more than just different flavors of STEM. In academia, tackling the effects of climate change demands more rigorous inclusion of the social sciences—an area that has been frequently overlooked.

The National Science Foundation, as well as other groups, requires that all research proposals incorporate a social sciences component, as an attempt to assess the broader implications of projects. Unfortunately, in many cases, a social scientist is simply added to a proposal only to check a box rather than to make a true commitment to allowing that discipline to inform the project. Instead social, economic and policy needs must be considered at the outset of research design, not as an afterthought. Otherwise our work might fail at the implementation stage, which means we will not be as effective as we could be in solving real-world problems. As a result, the public might become skeptical about how much scientists can contribute toward solutions.

Connecting with the Public

The reality is that communicating research findings to the public is an increasingly critical responsibility of scientists. Doing so has a measurable effect on how politicians prioritize policy, funding and regulations. UCF Coastal was brought into a world where science is not always respected—sometimes it is even portrayed as the enemy. There has been a significant erosion of trust in science over recent years, and we must work more deliberately to regain it. The public, we have found, wants to see quality academic research that is grounded in the societal challenges we are facing. That is why we are melding pure academic research with applied research to focus on issues that are immediate—helping a town or business recovering from a hurricane, for example—as well as long term, such as directly advising a community on how to build resiliency as flooding becomes more frequent.

As scientists, we cannot expect to explain the implications of our research to the wider public if we cannot first understand one another. A benefit of regularly working side by side is that we are crafting a common language, reconciling the radically different meanings that the same words can have to a variety of specialists. Finally, we are learning to speak to one another with more clarity and understand more explicitly how our niches fit into the bigger picture. We are also more aware of culture and industry as driving forces in shaping consensus and policy. Rather than handing city planners a stack of research papers and walking away, UCF Coastal sees itself as a collaborator that listens instead of just lecturing.

This style of academic mission is not only relevant to issues around climate change. It relates to every aspect of modern society, including genetic engineering, automation, artificial intelligence, and so on. The launch of UCF Coastal garnered positive attention from industry, government agencies, local communities and academics. We think that is because people do want to come together to solve problems, but they need a better mechanism for doing so. We hope to be that conduit while inspiring other academic institutions to do the same.

After all, we have been told for years to "think globally, act locally" and that "all politics is local." Florida's Indian River Lagoon will be restored only if there is engagement among residents, local industries, academics, government agencies and nonprofit organizations. As scientists, it is our responsibility to help everyone involved understand that problems that took decades to create will take decades to fix. We need to present the most helpful solutions while explaining the intricacies of the trade-offs for each one. Doing so is possible only if we see ourselves as part of an interdisciplinary, whole-community approach. By listening and responding to fears and concerns, we can make a stronger case for why scientifically driven decisions will be more effective in the long run.

Graham A. J. Worthy is founder and director of the National Center for Integrated Coastal Research at the University of Central Florida (UCF Coastal) and chairs the university's department of biology. His research focuses on how marine ecosystems respond to natural and anthropogenic perturbations.

Cherie L. Yestrebsky is a professor in the University of Central Florida's department of chemistry. Her research expertise is in environmental chemistry and remediation of pollutants in the environment.

How to Use Real-World Problems to Teach Elementary School Math: 6 Tips

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When you think back on elementary school math, do you have fond memories of the countless worksheets you completed on adding fractions or solving division problems? Probably not.

Researchers and educators have been pushing for years for schools to move away from teaching math through a set of equations with no context around them, and towards an approach that pushes kids to use numerical reasoning to solve real problems, mirroring the way that they’ll encounter the use of math as adults.

The strategy is largely about setting kids up for success in the professional world, and educators can lay the groundwork decades earlier, even in kindergarten .

Here are some tips for using a real world problem-solving approach to teaching math to elementary school students.

1. There’s more than one right answer and more than one right method

A “real world task” can be as simple as asking students to think of equations that will get them to a particular “target” number, say, 14. Students could say 7 plus 7 is 14 or they could say 25 minus 11 is 14. Neither answer is better than the other, and that lesson teaches kids that there are multiple ways to use math to solve problems.

2. Give kids a chance to explain their thinking

The process you use to solve a real world math problem can be just as important as arriving at the correct answer, said Robbi Berry, who teaches 5th grade in Las Cruces, N.M. Her students have learned not to ask her if a particular answer is correct, she said, because she’ll turn the question back on them, asking them to explain how they know that it is right. She also gives her students a chance to explain to one another how they arrived at a particular solution, “We always share our strategies so that the kids can see the different ways” to arrive at an answer, she said. Students get excited, she said, when one of their classmates comes up with an approach they never would have thought of. “Math is creative,” Berry said. “It’s not just learning and memorizing.”

3. Be willing to deal with some off-the-wall answers

Problem solving does not necessarily mean going to the word problems in your textbook, said Latrenda Knighten, a mathematics instructional coach in Baton Rouge, La. For little kids, it can be as simple as showing a group of geometric shapes and asking what they have in common. Students may go off track a bit by talking about things like color, she said, but teachers can steer them towards thinking about things like how a rectangle differs from a triangle.

4. Let your students push themselves

Tackling these richer, real-world problems can be tougher than solving equations on a worksheet. And that is a good thing, said Jo Boaler, a professor at Stanford University and an expert on math education. “It’s really good for your brain to struggle,” she said. “We don’t want kids getting right answers all the time because that’s not giving their brains a really good workout.” These types of problems require collaboration, a skill that many don’t associate with math, but that is key to how math reasoning works beyond the classroom. The complexity and difficulty of the tasks means that students “have to talk to each other and really figure out what to do, what’s a good method?”

5. Celebrate ‘favorite mistakes’ to encourage intellectual risk taking

Wrong answers should be viewed as learning opportunities, Berry said. When one of her students makes an error, she asks if she can share it with the class as a “favorite mistake.” Most of the time, students are comfortable with that, and the class will work together to figure how the misstep happened.

6. Remember there’s no such thing as a being born with a ‘math brain’

Some teachers believe that certain students are just naturally good at math, and others are not, Boaler said. But that’s not true. “Brains are constantly shaping, changing, developing, connecting, and there is no fixed anything,” said Boaler, who often works alongside neuroscientists. What’s more, many elementary school teachers lack confidence in their own math abilities, she said. “They think they can’t do [math],” Boaler said. “And they often pass those ideas on” to their students.

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Research does solve real-world problems: experts must work together to make it happen

Deputy Vice Chancellor Research & Innovation, University of South Australia

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Tanya Monro receives funding from the Australian Research Council. She is Deputy Vice Chancellor of the University of South Australia, a member of the Commonwealth Science Council, the CSIRO board, the SA Economic Development Board and Defence SA.

University of South Australia provides funding as a member of The Conversation AU.

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Generating knowledge is one of the most exciting aspects of being human. The inventiveness required to apply this knowledge to solve practical problems is perhaps our most distinctive attribute.

But right now we have before us some hairy challenges – whether that be figuring our how to save our coral reefs from warmer water , landing a human on Mars , eliminating the gap in life expectancy between the “haves” and “have-nots” or delivering reliable carbon-free energy .

It’s commonly said that an interdisciplinary approach is vital if we are to tackle such real world challenges. But what does this really mean?

Read more: It takes a community to raise a startup

Listen and read with care and you’ll start to notice that the words crossdisciplinary, multidisciplinary, interdisciplinary and transdisciplinary are used interchangeably. These words describe distinctly different ways of harnessing the power of disciplinary expertise to chart a course into the unknown.

In navigation, the tools and methods matter – choose differently and you’ll end up in a different spot. How we go about creating knowledge and solving problems really matters – it changes not only what questions can be asked and answered but fundamentally shapes what’s possible.

What is a discipline?

For centuries we have organised research within disciplines, and this has delivered extraordinary depths of knowledge.

But what is a discipline? It’s a shared language, an environment in which there’s no need to explain the motivation for one’s work, and in which people have a shared sense of what’s valuable.

For example, my background discipline is optical physics. I know what it’s like to be able to skip down the corridor and say,

“I’ve figured out how we can get broadband flat dispersion - we just need to tailor the radial profile!”

…and have people instantly not just know what I mean, but be able to add their own ideas and drive the work forward.

In long-established disciplines it’s often necessary to focus in a narrow area to be able to extend the limits of knowledge within the time-frame of a PhD. And while it’s rarely obvious at the time what benefits will flow from digging a little deeper, our way of life has been transformed over and over as result.

Disciplines focus talent and so can be amazingly efficient ways of generating knowledge. But they can also be extraordinarily difficult to penetrate from the outside without understanding that discipline’s particular language and shared values.

The current emphasis on real-world impact has sharpened awareness on the need to translate knowledge into outcomes. It has also brought attention to the critical role partnerships with industry and other end-users of research play in this process.

Creating impact across disciplines

Try to solve a problem with the tools of a single discipline alone, and it’s as if you have a hammer - everything starts to look like a nail. It’s usually obvious when expertise from more than one discipline is needed.

Consider a panel of experts drawn from different fields to each apply the tools of their field to a problem that’s been externally framed. This has traditionally been how expertise from the social sciences is brought to bear on challenges in public health or the environment.

This is a crossdisciplinary approach , which can produce powerful outcomes provided that those who posed the question are positioned to make decisions based on the knowledge generated. But the research fields themselves are rarely influenced by this glancing encounter with different approaches to knowledge generation.

Multidisciplinary research involves the application of tools from one discipline to questions from other fields. An example is the application of crystallography, discovered by the Braggs, to unravel the structure of proteins . This requires concepts to transfer across domains, sometimes in real time but usually with a lag of years or decades.

Read more: If we really want an ideas boom, we need more women at the top tiers of science

Interdisciplinary research happens when researchers from different fields come together to pose a challenge that wouldn’t be possible in isolation. One example is the highly transparent optical fibres that underpin intercontinental telecommunication networks.

The knowledge creation that made this possible involved glass chemists, optical physicists and communication engineers coming together to articulate the possible, and develop the shared language required to make it a reality. When fields go on this journey together over decades, new fields are born.

In this example the question itself was clear – how can we harness the transparency of silica glass to create optical transmission systems that can transport large volumes of data over long distances?

But what about the questions we don’t know how to pose because without knowledge of another field we don’t know what’s possible? This line of reasoning leads us into the domain of transdisciplinary research .

Transdisciplinary research requires a willingness to craft new questions – whether because they were considered intractable or because without the inspiration from left field they simply didn’t arise. An example of this is applying photonics to IVF incubators - the idea that it could be possible to “listen” to how embryos experience their environment is unlikely to have arisen without bringing these fields together.

Read more: National Science Statement a positive gesture but lacks policy solutions: experts

In my own field, physics, I discovered that when talking to people from other areas the simple question “what would you like to measure?” quickly led to uncharted territory.

Before long we were usually, together, posing fundamentally new questions and establishing teams to tackle them. This can be scary territory but it’s tremendously rewarding and creates space for creativity and the emergence of disruptive technologies.

Excellence, communication, co-location, funding

One of the best ways of getting out of a disciplinary silo is to take every opportunity to talk to others outside your field. Disciplinary excellence is the starting point to get to the table.

And while disciplinary collaborations can flourish over large distances because they share a language and values, it’s usually true that once you mix disciplines co-location becomes a real asset. Then of course there are the questions of how we fund and organise research concentrations to allow inter- and transdisciplinary research to flourish.

With the increased emphasis on impact, these questions are becoming ever more pressing. Organisations that get this right will thrive.

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26 Snappy Answers to the Question “When Are We Ever Going to Use This Math in Real Life?”

Next time they ask, you’ll be ready.

As a math teacher, how many times have you heard frustrated students ask, “When are we ever going to use this math in real life!?” We know, it’s maddening! Especially for those of us who love math so much we’ve devoted our lives to sharing it with others.

It may very well be true that students won’t use some of the more abstract mathematical concepts they learn in school unless they choose to work in specific fields. But the underlying skills they develop in math class—like taking risks, thinking logically and solving problems—will last a lifetime and help them solve work-related and real-world problems.

Here are 26 images and accompanying comebacks to share with your students to get them thinking about all the different and unexpected ways they might use math in their futures!

1. If you go bungee jumping, you might want to know a thing or two about trajectories.

https://giphy.com/gifs/funny-fail-5OuUiP0we57b2

Source: GIPHY

2. When you invest your money, you’ll do better if you understand concepts such as interest rates, risk vs. reward, and probability.

3. once you’re a driver, you’ll need to be able to calculate things like reaction time and stopping distance., 4. in case of a zombie apocalypse, you’re going to want to explore geometric progressions, interpret data and make predictions in order to stay human..

Trigger an outbreak of learning and infectious fun in your classroom with this Zombie Apocalypse activity from TI’s STEM Behind Hollywood series.

5. Before you tackle that home wallpaper project, you’ll need to calculate just how much wall paper glue you need per square foot.

6. when you buy your first house and apply for a 30-year mortgage, you may be shocked by the reality of what interest compounded over 30 years looks like., 7. to be a responsible pet owner, you’ll need to calculate how much hamster food to have on hand., 8. even if you’re just an armchair athlete, you can’t believe the math involved in kicking field goals.

Check out this Field Goal for the Win activity that encourages students to model, explore and explain the dynamics of kicking a football through the uprights.

9. When you double a recipe, you’re going to need to understand ratios so your dinner guests don’t look like this.

10. before you take that family road trip , you’re going to want to calculate time and distance., 11. before you go candy shopping, you’re going to have to figure out x trick or treaters times x pieces of candy equals…, 12. if  you grow up to be an ice cream scientist, you’re going to have to understand the effect of temperature and pressure at the molecular level..

https://giphy.com/gifs/ice-lick-cream-3Z1kRYmLRQm5y

Explore states of matter and the processes that change cow milk into a cone of delicious decadence with this Ice Cream, Cool Science activity .

13. Once you have little ones, you’ll need to know how many diapers to buy for the month.

14. because what if it’s your turn to organize the annual ping pong tournament, and there are 7 players at a club with 4 tables, where each player plays against each other player, 15. when dressing for the day, you might want to consider the percent likelihood of rain., 16. if you go into medical research, you’re going to have to know how to solve equations..

Learn more about inspiring careers that improve lives with STEM Behind Health , a series of free activities from TI.

17. Understanding percentages will help you get the best deal at the mall. For example, how much will something cost with 40% off? What about once the 8% tax is added? What if it’s advertised as half-off?

https://giphy.com/gifs/blue-kawaii-pink-5aplc3D2G0IrC

18. Budgeting for vacation will require figuring out how many hours at your pay rate you’ll have to work to afford the trip you want.

19. when you volunteer to host the company holiday party, you’ll need to figure out how much food to get., 20. if you grow up to be a super villain, you’re going to need to use math to determine the most effective way to slow down the superhero and keep him from saving the day..

Put your students in the role of an arch-villain’s minions with Science Friction, a STEM Behind Hollywood activity .

21. You’ll definitely want to understand how to budget your money so you don’t look like this at the grocery checkout.

22. if you don’t work the numbers out in advance, you might at some point regret choosing that expensive out-of-state college., 23. before taking on a building project, remember the old saying—measure twice, cut once., 24. if have aspirations of being a fashion designer, you’ll have to understand geometry in order to make the perfect twirling skirt.

https://giphy.com/gifs/loop-bunny-ballet-yarFJggnH24da

Geometry and fashion design intersect in this STEM Behind Cool Careers activity .

25. Everyone loves a good bargain! Figuring out the best deal is not only fun, it’s smart!

26. if you can’t manage calculations, running the numbers at the car dealership might leave you feeling like this:, you might also like.

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Real World Examples of Quadratic Equations

A Quadratic Equation looks like this:

Quadratic equations pop up in many real world situations!

Here we have collected some examples for you, and solve each using different methods:

• Factoring Quadratics
• Completing the Square
• Graphing Quadratic Equations
• The Quadratic Formula
• Online Quadratic Equation Solver

Each example follows three general stages:

• Take the real world description and make some equations
• Use your common sense to interpret the results

Balls, Arrows, Missiles and Stones

When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster ...

... and a Quadratic Equation tells you its position at all times!

Example: Throwing a Ball

A ball is thrown straight up, from 3 m above the ground, with a velocity of 14 m/s. when does it hit the ground.

Ignoring air resistance, we can work out its height by adding up these three things: (Note: t is time in seconds)

Add them up and the height h at any time t is:

h = 3 + 14t − 5t 2

And the ball will hit the ground when the height is zero:

3 + 14t − 5t 2 = 0

Which is a Quadratic Equation !

In "Standard Form" it looks like:

−5t 2 + 14t + 3 = 0

It looks even better when we multiply all terms by −1 :

5t 2 − 14t − 3 = 0

Let us solve it ...

There are many ways to solve it, here we will factor it using the "Find two numbers that multiply to give ac , and add to give b " method in Factoring Quadratics :

ac = −15 , and b = −14 .

The factors of −15 are: −15, −5, −3, −1, 1, 3, 5, 15

By trying a few combinations we find that −15 and 1 work (−15×1 = −15, and −15+1 = −14)

The "t = −0.2" is a negative time, impossible in our case.

The "t = 3" is the answer we want:

The ball hits the ground after 3 seconds!

Here is the graph of the Parabola h = −5t 2 + 14t + 3

It shows you the height of the ball vs time

Some interesting points:

(0,3) When t=0 (at the start) the ball is at 3 m

(−0.2,0) says that −0.2 seconds BEFORE we threw the ball it was at ground level. This never happened! So our common sense says to ignore it.

(3,0) says that at 3 seconds the ball is at ground level.

Also notice that the ball goes nearly 13 meters high.

Note: You can find exactly where the top point is!

The method is explained in Graphing Quadratic Equations , and has two steps:

Find where (along the horizontal axis) the top occurs using −b/2a :

• t = −b/2a = −(−14)/(2 × 5) = 14/10 = 1.4 seconds

Then find the height using that value (1.4)

• h = −5t 2 + 14t + 3 = −5(1.4) 2 + 14 × 1.4 + 3 = 12.8 meters

So the ball reaches the highest point of 12.8 meters after 1.4 seconds.

Example: New Sports Bike

You have designed a new style of sports bicycle!

Now you want to make lots of them and sell them for profit.

Your costs are going to be:

• $700,000 for manufacturing set-up costs, advertising, etc
• $110 to make each bike

Based on similar bikes, you can expect sales to follow this "Demand Curve":

Where "P" is the price.

For example, if you set the price:

• at $0, you just give away 70,000 bikes
• at $350, you won't sell any bikes at all
• at $300 you might sell 70,000 − 200×300 = 10,000 bikes

So ... what is the best price? And how many should you make?

Let us make some equations!

How many you sell depends on price, so use "P" for Price as the variable

Profit = −200P 2 + 92,000P − 8,400,000

Yes, a Quadratic Equation. Let us solve this one by Completing the Square .

Solve: −200P 2 + 92,000P − 8,400,000 = 0

Step 1 Divide all terms by -200

Step 2 Move the number term to the right side of the equation:

Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation:

(b/2) 2 = (−460/2) 2 = (−230) 2 = 52900

Step 4 Take the square root on both sides of the equation:

Step 5 Subtract (-230) from both sides (in other words, add 230):

What does that tell us? It says that the profit is ZERO when the Price is $126 or $334

But we want to know the maximum profit, don't we?

It is exactly half way in-between! At $230

And here is the graph:

The best sale price is $230 , and you can expect:

• Unit Sales = 70,000 − 200 x 230 = 24,000
• Sales in Dollars = $230 x 24,000 = $5,520,000
• Costs = 700,000 + $110 x 24,000 = $3,340,000
• Profit = $5,520,000 − $3,340,000 = $2,180,000

A very profitable venture.

Example: Small Steel Frame

Your company is going to make frames as part of a new product they are launching.

The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm 2

The inside of the frame has to be 11 cm by 6 cm

What should the width x of the metal be?

Area of steel before cutting:

Area of steel after cutting out the 11 × 6 middle:

Let us solve this one graphically !

Here is the graph of 4x 2 + 34x :

The desired area of 28 is shown as a horizontal line.

The area equals 28 cm 2 when:

x is about −9.3 or 0.8

The negative value of x make no sense, so the answer is:

x = 0.8 cm (approx.)

Example: River Cruise

A 3 hour river cruise goes 15 km upstream and then back again. the river has a current of 2 km an hour. what is the boat's speed and how long was the upstream journey.

There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land:

• Let x = the boat's speed in the water (km/h)
• Let v = the speed relative to the land (km/h)

Because the river flows downstream at 2 km/h:

• when going upstream, v = x−2 (its speed is reduced by 2 km/h)
• when going downstream, v = x+2 (its speed is increased by 2 km/h)

We can turn those speeds into times using:

time = distance / speed

(to travel 8 km at 4 km/h takes 8/4 = 2 hours, right?)

And we know the total time is 3 hours:

total time = time upstream + time downstream = 3 hours

Put all that together:

total time = 15/(x−2) + 15/(x+2) = 3 hours

Now we use our algebra skills to solve for "x".

First, get rid of the fractions by multiplying through by (x-2) (x+2) :

3(x-2)(x+2) = 15(x+2) + 15(x-2)

Expand everything:

3(x 2 −4) = 15x+30 + 15x−30

Bring everything to the left and simplify:

3x 2 − 30x − 12 = 0

It is a Quadratic Equation!

Let us solve it using the Quadratic Formula :

Where a , b and c are from the Quadratic Equation in "Standard Form": ax 2 + bx + c = 0

Solve 3x 2 - 30x - 12 = 0

Answer: x = −0.39 or 10.39 (to 2 decimal places)

x = −0.39 makes no sense for this real world question, but x = 10.39 is just perfect!

Answer: Boat's Speed = 10.39 km/h (to 2 decimal places)

And so the upstream journey = 15 / (10.39−2) = 1.79 hours = 1 hour 47min

And the downstream journey = 15 / (10.39+2) = 1.21 hours = 1 hour 13min

Example: Resistors In Parallel

Two resistors are in parallel, like in this diagram:

The total resistance has been measured at 2 Ohms, and one of the resistors is known to be 3 ohms more than the other.

What are the values of the two resistors?

The formula to work out total resistance "R T " is:

1 R T   =   1 R 1 + 1 R 2

In this case, we have R T = 2 and R 2 = R 1 + 3

1 2   =   1 R 1 + 1 R 1 +3

To get rid of the fractions we can multiply all terms by 2R 1 (R 1 + 3) and then simplify:

Yes! A Quadratic Equation!

Let us solve it using our Quadratic Equation Solver .

• Enter 1, −1 and −6
• And you should get the answers −2 and 3

R 1 cannot be negative, so R 1 = 3 Ohms is the answer.

The two resistors are 3 ohms and 6 ohms.

Quadratic Equations are useful in many other areas:

For a parabolic mirror, a reflecting telescope or a satellite dish, the shape is defined by a quadratic equation.

Quadratic equations are also needed when studying lenses and curved mirrors.

And many questions involving time, distance and speed need quadratic equations.

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Hypothesis and theory article, real world problem-solving.

• Human-Robot Interaction Laboratory, Department of Computer Science, Tufts University, Medford, MA, United States

Real world problem-solving (RWPS) is what we do every day. It requires flexibility, resilience, resourcefulness, and a certain degree of creativity. A crucial feature of RWPS is that it involves continuous interaction with the environment during the problem-solving process. In this process, the environment can be seen as not only a source of inspiration for new ideas but also as a tool to facilitate creative thinking. The cognitive neuroscience literature in creativity and problem-solving is extensive, but it has largely focused on neural networks that are active when subjects are not focused on the outside world, i.e., not using their environment. In this paper, I attempt to combine the relevant literature on creativity and problem-solving with the scattered and nascent work in perceptually-driven learning from the environment. I present my synthesis as a potential new theory for real world problem-solving and map out its hypothesized neural basis. I outline some testable predictions made by the model and provide some considerations and ideas for experimental paradigms that could be used to evaluate the model more thoroughly.

1. Introduction

In the Apollo 13 space mission, astronauts together with ground control had to overcome several challenges to bring the team safely back to Earth ( Lovell and Kluger, 2006 ). One of these challenges was controlling carbon dioxide levels onboard the space craft: “For 2 days straight [they] had worked on how to jury-rig the Odysseys canisters to the Aquarius's life support system. Now, using materials known to be available onboard the spacecraft—a sock, a plastic bag, the cover of a flight manual, lots of duct tape, and so on—the crew assembled a strange contraption and taped it into place. Carbon dioxide levels immediately began to fall into the safe range” ( Team, 1970 ; Cass, 2005 ).

The success of Apollo 13's recovery from failure is often cited as a glowing example of human resourcefulness and inventiveness alongside more well-known inventions and innovations over the course of human history. However, this sort of inventive capability is not restricted to a few creative geniuses, but an ability present in all of us, and exemplified in the following mundane example. Consider a situation when your only suit is covered in lint and you do not own a lint remover. You see a roll of duct tape, and being resourceful you reason that it might be a good substitute. You then solve the problem of lint removal by peeling a full turn's worth of tape and re-attaching it backwards onto the roll to expose the sticky side all around the roll. By rolling it over your suit, you can now pick up all the lint.

In both these examples (historic as well as everyday), we see evidence for our innate ability to problem-solve in the real world. Solving real world problems in real time given constraints posed by one's environment are crucial for survival. At the core of this skill is our mental capability to get out of “sticky situations” or impasses, i.e., difficulties that appear unexpectedly as impassable roadblocks to solving the problem at hand. But, what are the cognitive processes that enable a problem solver to overcome such impasses and arrive at a solution, or at least a set of promising next steps?

A central aspect of this type of real world problem solving, is the role played by the solver's surrounding environment during the problem-solving process. Is it possible that interaction with one's environment can facilitate creative thinking? The answer to this question seems somewhat obvious when one considers the most famous anecdotal account of creative problem solving, namely that of Archimedes of Syracuse. During a bath, he found a novel way to check if the King's crown contained non-gold impurities. The story has traditionally been associated with the so-called “Eureka moment,” the sudden affective experience when a solution to a particularly thorny problem emerges. In this paper, I want to temporarily turn our attention away from the specific “aha!” experience itself and take particular note that Archimedes made this discovery, not with his eyes closed at a desk, but in a real-world context of a bath 1 . The bath was not only a passive, relaxing environment for Archimedes, but also a specific source of inspiration. Indeed it was his noticing the displacement of water that gave him a specific methodology for measuring the purity of the crown; by comparing how much water a solid gold bar of the same weight would displace as compared with the crown. This sort of continuous environmental interaction was present when the Apollo 13 engineers discovered their life-saving solution, and when you solved the suit-lint-removal problem with duct tape.

The neural mechanisms underlying problem-solving have been extensively studied in the literature, and there is general agreement about the key functional networks and nodes involved in various stages of problem-solving. In addition, there has been a great deal of work in studying the neural basis for creativity and insight problem solving, which is associated with the sudden emergence of solutions. However, in the context of problem-solving, creativity, and insight have been researched as largely an internal process without much interaction with and influence from the external environment ( Wegbreit et al., 2012 ; Abraham, 2013 ; Kounios and Beeman, 2014 ) 2 . Thus, there are open questions of what role the environment plays during real world problem-solving (RWPS) and how the brain enables the assimilation of novel items during these external interactions.

In this paper, I synthesize the literature on problem-solving, creativity and insight, and particularly focus on how the environment can inform RWPS. I explore three environmentally-informed mechanisms that could play a critical role: (1) partial-cue driven context-shifting, (2) heuristic prototyping and learning novel associations, and (3) learning novel physical inferences. I begin first with some intuitions about real world problem solving, that might help ground this discussion and providing some key distinctions from more traditional problem solving research. Then, I turn to a review of the relevant literature on problem-solving, creativity, and insight first, before discussing the three above-mentioned environmentally-driven mechanisms. I conclude with a potential new model and map out its hypothesized neural basis.

2. Problem Solving, Creativity, and Insight

2.1. what is real world problem-solving.

Archimedes was embodied in the real world when he found his solution. In fact, the real world helped him solve the problem. Whether or not these sorts of historic accounts of creative inspiration are accurate 3 , they do correlate with some of our own key intuitions about how problem solving occurs “in the wild.” Real world problem solving (RWPS) is different from those that occur in a classroom or in a laboratory during an experiment. They are often dynamic and discontinuous, accompanied by many starts and stops. Solvers are never working on just one problem. Instead, they are simultaneously juggling several problems of varying difficulties and alternating their attention between them. Real world problems are typically ill-defined, and even when they are well-defined, often have open-ended solutions. Coupled with that is the added aspect of uncertainty associated with the solver's problem solving strategies. As introduced earlier, an important dimension of RWPS is the continuous interaction between the solver and their environment. During these interactions, the solver might be inspired or arrive at an “aha!” moment. However, more often than not, the solver experiences dozens of minor discovery events— “hmmm, interesting…” or “wait, what?…” moments. Like discovery events, there's typically never one singular impasse or distraction event. The solver must iterate through the problem solving process experiencing and managing these sorts of intervening events (including impasses and discoveries). In summary, RWPS is quite messy and involves a tight interplay between problem solving, creativity, and insight. Next, I explore each of these processes in more detail and explicate a possible role of memory, attention, conflict management and perception.

2.2. Analytical Problem-Solving

In psychology and neuroscience, problem-solving broadly refers to the inferential steps taken by an agent 4 that leads from a given state of affairs to a desired goal state ( Barbey and Barsalou, 2009 ). The agent does not immediately know how this goal can be reached and must perform some mental operations (i.e., thinking) to determine a solution ( Duncker, 1945 ).

The problem solving literature divides problems based on clarity (well-defined vs. ill-defined) or on the underlying cognitive processes (analytical, memory retrieval, and insight) ( Sprugnoli et al., 2017 ). While memory retrieval is an important process, I consider it as a sub-process to problem solving more generally. I first focus on analytical problem-solving process, which typically involves problem-representation and encoding, and the process of forming and executing a solution plan ( Robertson, 2016 ).

2.2.1. Problem Definition and Representation

An important initial phase of problem-solving involves defining the problem and forming a representation in the working memory. During this phase, components of the prefrontal cortex (PFC), default mode network (DMN), and the dorsal anterior cingulate cortex (dACC) have been found to be activated. If the problem is familiar and well-structured, top-down executive control mechanisms are engaged and the left prefrontal cortex including the frontopolar, dorso-lateral (dlPFC), and ventro-lateral (vlPFC) are activated ( Barbey and Barsalou, 2009 ). The DMN along with the various structures in the medial temporal lobe (MTL) including the hippocampus (HF), parahippocampal cortex, perirhinal and entorhinal cortices are also believed to have limited involvement, especially in episodic memory retrieval activities during this phase ( Beaty et al., 2016 ). The problem representation requires encoding problem information for which certain visual and parietal areas are also involved, although the extent of their involvement is less clear ( Anderson and Fincham, 2014 ; Anderson et al., 2014 ).

2.2.1.1. Working memory

An important aspect of problem representation is the engagement and use of working memory (WM). The WM allows for the maintenance of relevant problem information and description in the mind ( Gazzaley and Nobre, 2012 ). Research has shown that WM tasks consistently recruit the dlPFC and left inferior frontal cortex (IC) for encoding an manipulating information; dACC for error detection and performance adjustment; and vlPFC and the anterior insula (AI) for retrieving, selecting information and inhibitory control ( Chung and Weyandt, 2014 ; Fang et al., 2016 ).

2.2.1.2. Representation

While we generally have a sense for the brain regions that are functionally influential in problem definition, less is known about how exactly events are represented within these regions. One theory for how events are represented in the PFC is the structured event complex theory (SEC), in which components of the event knowledge are represented by increasingly higher-order convergence zones localized within the PFC, akin to the convergence zones (from posterior to anterior) that integrate sensory information in the brain ( Barbey et al., 2009 ). Under this theory, different zones in the PFC (left vs. right, anterior vs. posterior, lateral vs. medial, and dorsal vs. ventral) represent different aspects of the information contained in the events (e.g., number of events to be integrated together, the complexity of the event, whether planning, and action is needed). Other studies have also suggested the CEN's role in tasks requiring cognitive flexibility, and functions to switch thinking modes, levels of abstraction of thought and consider multiple concepts simultaneously ( Miyake et al., 2000 ).

Thus, when the problem is well-structured, problem representation is largely an executive control activity coordinated by the PFC in which problem information from memory populates WM in a potentially structured representation. Once the problem is defined and encoded, planning and execution of a solution can begin.

2.2.2. Planning

The central executive network (CEN), particularly the PFC, is largely involved in plan formation and in plan execution. Planning is the process of generating a strategy to advance from the current state to a goal state. This in turn involves retrieving a suitable solution strategy from memory and then coordinating its execution.

2.2.2.1. Plan formation

The dlPFC supports sequential planning and plan formation, which includes the generation of hypothesis and construction of plan steps ( Barbey and Barsalou, 2009 ). Interestingly, the vlPFC and the angular gyrus (AG), implicated in a variety of functions including memory retrieval, are also involved in plan formation ( Anderson et al., 2014 ). Indeed, the AG together with the regions in the MTL (including the HF) and several other regions form a what is known as the “core” network. The core network is believed to be activated when recalling past experiences, imagining fictitious, and future events and navigating large-scale spaces ( Summerfield et al., 2010 ), all key functions for generating plan hypotheses. A recent study suggests that the AG is critical to both episodic simulation, representation, and episodic memory ( Thakral et al., 2017 ). One possibility for how plans are formulated could involve a dynamic process of retrieving an optimal strategy from memory. Research has shown significant interaction between striatal and frontal regions ( Scimeca and Badre, 2012 ; Horner et al., 2015 ). The striatum is believed to play a key role in declarative memory retrieval, and specifically helping retrieve optimal (or previously rewarded) memories ( Scimeca and Badre, 2012 ). Relevant to planning and plan formation, Scimeca & Badre have suggested that the striatum plays two important roles: (1) in mapping acquired value/utility to action selection, and thereby helping plan formation, and (2) modulation and re-encoding of actions and other plan parameters. Different types of problems require different sets of specialized knowledge. For example, the knowledge needed to solve mathematical problems might be quite different (albeit overlapping) from the knowledge needed to select appropriate tools in the environment.

Thus far, I have discussed planning and problem representation as being domain-independent, which has allowed me to outline key areas of the PFC, MTL, and other regions relevant to all problem-solving. However, some types of problems require domain-specific knowledge for which other regions might need to be recruited. For example, when planning for tool-use, the superior parietal lobe (SPL), supramarginal gyrus (SMG), anterior inferior parietal lobe (AIPL), and certain portions of the temporal and occipital lobe involved in visual and spatial integration have been found to be recruited ( Brandi et al., 2014 ). It is believed that domain-specific information stored in these regions is recovered and used for planning.

2.2.2.2. Plan execution

Once a solution plan has been recruited from memory and suitably tuned for the problem on hand, the left-rostral PFC, caudate nucleus (CN), and bilateral posterior parietal cortices (PPC) are responsible for translating the plan into executable form ( Stocco et al., 2012 ). The PPC stores and maintains “mental template” of the executable form. Hemispherical division of labor is particularly relevant in planning where it was shown that when planning to solve a Tower of Hanoi (block moving) problem, the right PFC is involved in plan construction whereas the left PFC is involved in controlling processes necessary to supervise the execution of the plan ( Newman and Green, 2015 ). On a separate note and not the focus of this paper, plan execution and problem-solving can require the recruitment of affective and motivational processing in order to supply the agent with the resolve to solve problems, and the vmPFC has been found to be involved in coordinating this process ( Barbey and Barsalou, 2009 ).

2.3. Creativity

During the gestalt movement in the 1930s, Maier noted that “most instances of “real” problem solving involves creative thinking” ( Maier, 1930 ). Maier performed several experiments to study mental fixation and insight problem solving. This close tie between insight and creativity continues to be a recurring theme, one that will be central to the current discussion. If creativity and insight are linked to RWPS as noted by Maier, then it is reasonable to turn to the creativity and insight literature for understanding the role played by the environment. A large portion of the creativity literature has focused on viewing creativity as an internal process, one in which the solvers attention is directed inwards, and toward internal stimuli, to facilitate the generation of novel ideas and associations in memory ( Beaty et al., 2016 ). Focusing on imagination, a number of researchers have looked at blinking, eye fixation, closing eyes, and looking nowhere behavior and suggested that there is a shift of attention from external to internal stimuli during creative problem solving ( Salvi and Bowden, 2016 ). The idea is that shutting down external stimuli reduces cognitive load and focuses attention internally. Other experiments studying sleep behavior have also noted the beneficial role of internal stimuli in problem solving. The notion of ideas popping into ones consciousness, suddenly, during a shower is highly intuitive for many and researchers have attempted to study this phenomena through the lens of incubation, and unconscious thought that is internally-driven. There have been several theories and counter-theories proposed to account specifically for the cognitive processes underlying incubation ( Ritter and Dijksterhuis, 2014 ; Gilhooly, 2016 ), but none of these theories specifically address the role of the external environment.

The neuroscience of creativity has also been extensively studied and I do not focus on an exhaustive literature review in this paper (a nice review can be found in Sawyer, 2011 ). From a problem-solving perspective, it has been found that unlike well-structured problems, ill-structured problems activate the right dlPFC. Most of the past work on creativity and creative problem-solving has focused on exploring memory structures and performing internally-directed searches. Creative idea generation has primarily been viewed as internally directed attention ( Jauk et al., 2012 ; Benedek et al., 2016 ) and a primary mechanism involved is divergent thinking , which is the ability to produce a variety of responses in a given situation ( Guilford, 1962 ). Divergent thinking is generally thought to involve interactions between the DMN, CEN, and the salience network ( Yoruk and Runco, 2014 ; Heinonen et al., 2016 ). One psychological model of creative cognition is the Geneplore model that considers two major phases of generation (memory retrieval and mental synthesis) and exploration (conceptual interpretation and functional inference) ( Finke et al., 1992 ; Boccia et al., 2015 ). It has been suggested that the associative mode of processing to generate new creative association is supported by the DMN, which includes the medial PFC, posterior cingulate cortex (PCC), tempororparietal juntion (TPJ), MTL, and IPC ( Beaty et al., 2014 , 2016 ).

That said, the creativity literature is not completely devoid of acknowledging the role of the environment. In fact, it is quite the opposite. Researchers have looked closely at the role played by externally provided hints from the time of the early gestalt psychologists and through to present day studies ( Öllinger et al., 2017 ). In addition to studying how hints can help problem solving, researchers have also looked at how directed action can influence subsequent problem solving—e.g., swinging arms prior to solving the two-string puzzle, which requires swinging the string ( Thomas and Lleras, 2009 ). There have also been numerous studies looking at how certain external perceptual cues are correlated with creativity measures. Vohs et al. suggested that untidiness in the environment and the increased number of potential distractions helps with creativity ( Vohs et al., 2013 ). Certain colors such as blue have been shown to help with creativity and attention to detail ( Mehta and Zhu, 2009 ). Even environmental illumination, or lack thereof, have been shown to promote creativity ( Steidle and Werth, 2013 ). However, it is important to note that while these and the substantial body of similar literature show the relationship of the environment to creative problem solving, they do not specifically account for the cognitive processes underlying the RWPS when external stimuli are received.

2.4. Insight Problem Solving

Analytical problem solving is believed to involve deliberate and conscious processing that advances step by step, allowing solvers to be able to explain exactly how they solved it. Inability to solve these problems is often associated with lack of required prior knowledge, which if provided, immediately makes the solution tractable. Insight, on the other hand, is believed to involve a sudden and unexpected emergence of an obvious solution or strategy sometimes accompanied by an affective aha! experience. Solvers find it difficult to consciously explain how they generated a solution in a sequential manner. That said, research has shown that having an aha! moment is neither necessary nor sufficient to insight and vice versa ( Danek et al., 2016 ). Generally, it is believed that insight solvers acquire a full and deep understanding of the problem when they have solved it ( Chu and Macgregor, 2011 ). There has been an active debate in the problem solving community about whether insight is something special. Some have argued that it is not, and that there are no special or spontaneous processes, but simply a good old-fashioned search of a large problem space ( Kaplan and Simon, 1990 ; MacGregor et al., 2001 ; Ash and Wiley, 2006 ; Fleck, 2008 ). Others have argued that insight is special and suggested that it is likely a different process ( Duncker, 1945 ; Metcalfe, 1986 ; Kounios and Beeman, 2014 ). This debate lead to two theories for insight problem solving. MacGregor et al. proposed the Criterion for Satisfactory Progress Theory (CSPT), which is based on Newell and Simons original notion of problem solving as being a heuristic search through the problem space ( MacGregor et al., 2001 ). The key aspect of CSPT is that the solver is continually monitoring their progress with some set of criteria. Impasses arise when there is a criterion failure, at which point the solver tries non-maximal but promising states. The representational change theory (RCT) proposed by Ohlsson et al., on the other hand, suggests that impasses occur when the goal state is not reachable from an initial problem representation (which may have been generated through unconscious spreading activation) ( Ohlsson, 1992 ). In order to overcome an impasse, the solver needs to restructure the problem representation, which they can do by (1) elaboration (noticing new features of a problem), (2) re-encoding fixing mistaken or incomplete representations of the problem, and by (3) changing constraints. Changing constraints is believed to involve two sub-processes of constraint relaxation and chunk-decomposition.

The current position is that these two theories do not compete with each other, but instead complement each other by addressing different stages of problem solving: pre- and post-impasse. Along these lines, Ollinger et al. proposed an extended RCT (eRCT) in which revising the search space and using heuristics was suggested as being a dynamic and iterative and recursive process that involves repeated instances of search, impasse and representational change ( Öllinger et al., 2014 , 2017 ). Under this theory, a solver first forms a problem representation and begins searching for solutions, presumably using analytical problem solving processes as described earlier. When a solution cannot be found, the solver encounters an impasse, at which point the solver must restructure or change the problem representation and once again search for a solution. The model combines both analytical problem solving (through heuristic searches, hill climbing and progress monitoring), and creative mechanisms of constraint relaxation and chunk decomposition to enable restructuring.

Ollingers model appears to comprehensively account for both analytical and insight problem solving and, therefore, could be a strong candidate to model RWPS. However, while compelling, it is nevertheless an insufficient model of RWPS for many reasons, of which two are particularly significant for the current paper. First, the model does explicitly address mechanisms by which external stimuli might be assimilated. Second, the model is not sufficiently flexible to account for other events (beyond impasse) occurring during problem solving, such as distraction, mind-wandering and the like.

So, where does this leave us? I have shown the interplay between problem solving, creativity and insight. In particular, using Ollinger's proposal, I have suggested (maybe not quite explicitly up until now) that RWPS involves some degree of analytical problem solving as well as the post-impasse more creative modes of problem restructuring. I have also suggested that this model might need to be extended for RWPS along two dimensions. First, events such as impasses might just be an instance of a larger class of events that intervene during problem solving. Thus, there needs to be an accounting of the cognitive mechanisms that are potentially influenced by impasses and these other intervening events. It is possible that these sorts of events are crucial and trigger a switch in attentional focus, which in turn facilitates switching between different problem solving modes. Second, we need to consider when and how externally-triggered stimuli from the solver's environment can influence the problem solving process. I detail three different mechanisms by which external knowledge might influence problem solving. I address each of these ideas in more detail in the next two sections.

3. Event-Triggered Mode Switching During Problem-Solving

3.1. impasse.

When solving certain types of problems, the agent might encounter an impasse, i.e., some block in its ability to solve the problem ( Sprugnoli et al., 2017 ). The impasse may arise because the problem may have been ill-defined to begin with causing incomplete and unduly constrained representations to have been formed. Alternatively, impasses can occur when suitable solution strategies cannot be retrieved from memory or fail on execution. In certain instances, the solution strategies may not exist and may need to be generated from scratch. Regardless of the reason, an impasse is an interruption in the problem solving process; one that was running conflict-free up until the point when a seemingly unresolvable issue or an error in the predicted solution path was encountered. Seen as a conflict encountered in the problem-solving process it activates the anterior cingulate cortex (ACC). It is believed that the ACC not only helps detect the conflict, but also switch modes from one of “exploitation” (planning) to “exploration” (search) ( Quilodran et al., 2008 ; Tang et al., 2012 ), and monitors progress during resolution ( Chu and Macgregor, 2011 ). Some mode switching duties are also found to be shared with the AI (the ACC's partner in the salience network), however, it is unclear exactly the extent of this function-sharing.

Even though it is debatable if impasses are a necessary component of insight, they are still important as they provide a starting point for the creativity ( Sprugnoli et al., 2017 ). Indeed, it is possible that around the moment of impasse, the AI and ACC together, as part of the salience network play a crucial role in switching thought modes from analytical planning mode to creative search and discovery mode. In the latter mode, various creative mechanisms might be activated allowing for a solution plan to emerge. Sowden et al. and many others have suggested that the salience network is potentially a candidate neurobiological mechanism for shifting between thinking processes, more generally ( Sowden et al., 2015 ). When discussing various dual-process models as they relate to creative cognition, Sowden et al. have even noted that the ACC activation could be useful marker to identify shifting as participants work creative problems.

3.2. Defocused Attention

As noted earlier, in the presence of an impasse there is a shift from an exploitative (analytical) thinking mode to an exploratory (creative) thinking mode. This shift impacts several networks including, for example, the attention network. It is believed attention can switch between a focused mode and a defocused mode. Focused attention facilitates analytic thought by constraining activation such that items are considered in a compact form that is amenable to complex mental operations. In the defocused mode, agents expand their attention allowing new associations to be considered. Sowden et al. (2015) note that the mechanism responsible for adjustments in cognitive control may be linked to the mechanisms responsible for attentional focus. The generally agreed position is that during generative thinking, unconscious cognitive processes activated through defocused attention are more prevalent, whereas during exploratory thinking, controlled cognition activated by focused attention becomes more prevalent ( Kaufman, 2011 ; Sowden et al., 2015 ).

Defocused attention allows agents to not only process different aspects of a situation, but to also activate additional neural structures in long term memory and find new associations ( Mendelsohn, 1976 ; Yoruk and Runco, 2014 ). It is believed that cognitive material attended to and cued by positive affective state results in defocused attention, allowing for more complex cognitive contexts and therefore a greater range of interpretation and integration of information ( Isen et al., 1987 ). High attentional levels are commonly considered a typical feature of highly creative subjects ( Sprugnoli et al., 2017 ).

4. Role of the Environment

In much of the past work the focus has been on treating creativity as largely an internal process engaging the DMN to assist in making novel connections in memory. The suggestion has been that “individual needs to suppress external stimuli and concentrate on the inner creative process during idea generation” ( Heinonen et al., 2016 ). These ideas can then function as seeds for testing and problem-solving. While true of many creative acts, this characterization does not capture how creative ideas arise in many real-world creative problems. In these types of problems, the agent is functioning and interacting with its environment before, during and after problem-solving. It is natural then to expect that stimuli from the environment might play a role in problem-solving. More specifically, it can be expected that through passive and active involvement with the environment, the agent is (1) able to trigger an unrelated, but potentially useful memory relevant for problem-solving, (2) make novel connections between two events in memory with the environmental cue serving as the missing link, and (3) incorporate a completely novel information from events occuring in the environment directly into the problem-solving process. I explore potential neural mechanisms for these three types of environmentally informed creative cognition, which I hypothesize are enabled by defocused attention.

4.1. Partial Cues Trigger Relevant Memories Through Context-Shifting

I have previously discussed the interaction between the MTL and PFC in helping select task-relevant and critical memories for problem-solving. It is well-known that pattern completion is an important function of the MTL and one that enables memory retrieval. Complementary Learning Theory (CLS) and its recently updated version suggest that the MTL and related structures support initial storage as well as retrieval of item and context-specific information ( Kumaran et al., 2016 ). According to CLS theory, the dentate gyrus (DG) and the CA3 regions of the HF are critical to selecting neural activity patterns that correspond to particular experiences ( Kumaran et al., 2016 ). These patterns might be distinct even if experiences are similar and are stabilized through increases in connection strengths between the DG and CA3. Crucially, because of the connection strengths, reactivation of part of the pattern can activate the rest of it (i.e., pattern completion). Kumaran et al. have further noted that if consistent with existing knowledge, these new experiences can be quickly replayed and interleaved into structured representations that form part of the semantic memory.

Cues in the environment provided by these experiences hold partial information about past stimuli or events and this partial information converges in the MTL. CLS accounts for how these cues might serve to reactivate partial patterns, thereby triggering pattern completion. When attention is defocused I hypothesize that (1) previously unnoticed partial cues are considered, and (2) previously noticed partial cues are decomposed to produce previously unnoticed sub-cues, which in turn are considered. Zabelina et al. (2016) have shown that real-world creativity and creative achievement is associated with “leaky attention,” i.e., attention that allows for irrelevant information to be noticed. In two experiments they systematically explored the relationship between two notions of creativity— divergent thinking and real-world creative achievement—and the use of attention. They found that attentional use is associated in different ways for each of the two notions of creativity. While divergent thinking was associated with flexible attention, it does not appear to be leaky. Instead, selective focus and inhibition components of attention were likely facilitating successful performance on divergent thinking tasks. On the other hand, real-world creative achievement was linked to leaky attention. RWPS involves elements of both divergent thinking and of real-world creative achievement, thus I would expect some amount of attentional leaks to be part of the problem solving process.

Thus, it might be the case that a new set of cues or sub-cues “leak” in and activate memories that may not have been previously considered. These cues serve to reactivate a diverse set of patterns that then enable accessing a wide range of memories. Some of these memories are extra-contextual, in that they consider the newly noticed cues in several contexts. For example, when unable to find a screwdriver, we might consider using a coin. It is possible that defocused attention allows us to consider the coin's edge as being a potentially relevant cue that triggers uses for the thin edge outside of its current context in a coin. The new cues (or contexts) may allow new associations to emerge with cues stored in memory, which can occur during incubation. Objects and contexts are integrated into memory automatically into a blended representation and changing contexts disrupts this recognition ( Hayes et al., 2007 ; Gabora, 2016 ). Cue-triggered context shifting allows an agent to break-apart a memory representation, which can then facilitate problem-solving in new ways.

4.2. Heuristic Prototyping Facilitates Novel Associations

It has long been the case that many scientific innovations have been inspired by events in nature and the surrounding environment. As noted earlier, Archimedes realized the relationship between the volume of an irregularly shaped object and the volume of water it displaced. This is an example of heuristic prototyping where the problem-solver notices an event in the environment, which then triggers the automatic activation of a heuristic prototype and the formation of novel associations (between the function of the prototype and the problem) which they can then use to solve the problem ( Luo et al., 2013 ). Although still in its relative infancy, there has been some recent research into the neural basis for heuristic prototyping. Heuristic prototype has generally been defined as an enlightening prototype event with a similar element to the current problem and is often composed of a feature and a function ( Hao et al., 2013 ). For example, in designing a faster and more efficient submarine hull, a heuristic prototype might be a shark's skin, while an unrelated prototype might be a fisheye camera ( Dandan et al., 2013 ).

Research has shown that activating the feature function of the right heuristic prototype and linking it by way of semantic similarity to the required function of the problem was the key mechanism people used to solve several scienitific insight problems ( Yang et al., 2016 ). A key region activated during heuristic prototyping is the dlPFC and it is believed to be generally responsible for encoding the events into memory and may play an important role in selecting and retrieving the matched unsolved technical problem from memory ( Dandan et al., 2013 ). It is also believed that the precuneus plays a role in automatic retrieval of heuristic information allowing the heuristic prototype and the problem to combine ( Luo et al., 2013 ). In addition to semantic processing, certain aspects of visual imagery have also been implicated in heuristic prototyping leading to the suggestion of the involvement of Broadman's area BA 19 in the occipital cortex.

There is some degree of overlap between the notions of heuristic prototyping and analogical transfer (the mapping of relations from one domain to another). Analogical transfer is believed to activate regions in the left medial fronto-parietal system (dlPFC and the PPC) ( Barbey and Barsalou, 2009 ). I suggest here that analogical reasoning is largely an internally-guided process that is aided by heuristic prototyping which is an externally-guided process. One possible way this could work is if heuristic prototyping mechanisms help locate the relevant memory with which to then subsequently analogize.

4.3. Making Physical Inferences to Acquire Novel Information

The agent might also be able to learn novel facts about their environment through passive observation as well as active experimentation. There has been some research into the neural basis for causal reasoning ( Barbey and Barsalou, 2009 ; Operskalski and Barbey, 2016 ), but beyond its generally distributed nature, we do not know too much more. Beyond abstract causal reasoning, some studies looked into the cortical regions that are activated when people watch and predict physical events unfolding in real-time and in the real-world ( Fischer et al., 2016 ). It was found that certain regions were associated with representing types of physical concepts, with the left intraparietal sulcus (IPS) and left middle frontal gyrus (MFG) shown to play a role in attributing causality when viewing colliding objects ( Mason and Just, 2013 ). The parahippocampus (PHC) was associated with linking causal theory to observed data and the TPJ was involved in visualizing movement of objects and actions in space ( Mason and Just, 2013 ).

5. Proposed Theory

I noted earlier that Ollinger's model for insight problem solving, while serving as a good candidate for RWPS, requires extension. In this section, I propose a candidate model that includes some necessary extensions to Ollinger's framework. I begin by laying out some preliminary notions that underlie the proposed model.

5.1. Dual Attentional Modes

I propose that the attention-switching mechanism described earlier is at the heart of RWPS and enables two modes of operation: focused and defocused mode. In the focused mode, the problem representation is more or less fixed, and problem solving proceeds in a focused and goal directed manner through search, planning, and execution mechanisms. In the defocused mode, problem solving is not necessarily goal directed, but attempts to generate ideas, driven by both internal and external items.

At first glance, these modes might seem similar to convergent and divergent thinking modes postulated by numerous others to account for creative problem solving. Divergent thinking allows for the generation of new ideas and convergent thinking allows for verification and selection of generated ideas. So, it might seem that focused mode and convergent thinking are similar and likewise divergent and defocused mode. They are, however, quite different. The modes relate less to idea generation and verification, and more to the specific mechanisms that are operating with regard to a particular problem at a particular moment in time. Convergent and divergent processes may be occurring during both defocused and focused modes. Some degree of divergent processes may be used to search and identify specific solution strategies in focused mode. Also, there might be some degree of convergent idea verification occuring in defocused mode as candidate items are evaluated for their fit with the problem and goal. Thus, convergent and divergent thinking are one amongst many mechanisms that are utilized in focused and defocused mode. Each of these two modes has to do with degree of attention placed on a particular problem.

There have been numerous dual-process and dual-systems models of cognition proposed over the years. To address criticisms raised against these models and to unify some of the terminology, Evans & Stanovich proposed a dual-process model comprising Type 1 and Type 2 thought ( Evans and Stanovich, 2013 ; Sowden et al., 2015 ). Type 1 processes are those that are believed to be autonomous and do not require working memory. Type 2 processes, on the other hand, are believed to require working memory and are cognitively decoupled to prevent real-world representations from becoming confused with mental simulations ( Sowden et al., 2015 ). While acknowledging various other attributes that are often used to describe dual process models (e.g., fast/slow, associative/rule-based, automatic/controlled), Evans & Stanovich note that these attributes are merely frequent correlates and not defining characteristics of Type 1 or Type 2 processes. The proposed dual attentional modes share some similarities with the Evans & Stanovich Type 1 and 2 models. Specifically, Type 2 processes might occur in focused attentional mode in the proposed model as they typically involve the working memory and certain amount of analytical thought and planning. Similarly, Type 1 processes are likely engaged in defocused attentional mode as there are notions of associative and generative thinking that might be facilitated when attention has been defocused. The crucial difference between the proposed model and other dual-process models is that the dividing line between focused and defocused attentional modes is the degree of openness to internal and external stimuli (by various networks and functional units in the brain) when problem solving. Many dual process models were designed to classify the “type” of thinking process or a form of cognitive processing. In some sense, the “processes” in dual process theories are characterized by the type of mechanism of operation or the type of output they produced. Here, I instead characterize and differentiate the modes of thinking by the receptivity of different functional units in the brain to input during problem solving.

This, however, raises a different question of the relationship between these attentional modes and conscious vs. unconscious thinking. It is clear that both the conscious and unconscious are involved in problem solving, as well as in RWPS. Here, I claim that a problem being handled is, at any given point in time, in either a focused mode or in a defocused mode. When in the focused mode, problem solving primarily proceeds in a manner that is available for conscious deliberation. More specifically, problem space elements and representations are tightly managed and plans and strategies are available in the working memory and consciously accessible. There are, however, secondary unconscious operations in the focused modes that includes targeted memory retrieval and heuristic-based searches. In the defocused mode, the problem is primarily managed in an unconscious way. The problem space elements are broken apart and loosely managed by various mechanisms that do not allow for conscious deliberation. That said, it is possible that some problem parameters remain accessible. For example, it is possible that certain goal information is still maintained consciously. It is also possible that indexes to all the problems being considered by the solver are maintained and available to conscious awareness.

5.2. RWPS Model

Returning to Ollinger's model for insight problem solving, it now becomes readily apparent how this model can be modified to incorporate environmental effects as well as generalizing the notion of intervening events beyond that of impasses. I propose a theory for RWPS that begins with standard analytical problem-solving process (See Figures 1 , 2 ).

Figure 1 . Summary of neural activations during focused problem-solving (Left) and defocused problem-solving (Right) . During defocused problem-solving, the salience network (insula and ACC) coordinates the switching of several networks into a defocused attention mode that permits the reception of a more varied set of stimuli and interpretations via both the internally-guided networks (default mode network DMN) and externally guided networks (Attention). PFC, prefrontal cortex; ACC, anterior cingulate cortex; PCC, posterior cingulate cortex; IPC, inferior parietal cortex; PPC, posterior parietal cortex; IPS, intra-parietal sulcus; TPJ, temporoparietal junction; MTL, medial temporal lobe; FEF, frontal eye field.

Figure 2 . Proposed Model for Real World Problem Solving (RWPS). The corresponding neural correlates are shown in italics. During problem-solving, an initial problem representation is formed based on prior knowledge and available perceptual information. The problem-solving then proceeds in a focused, goal-directed mode until the goal is achieved or a defocusing event (e.g., impasse or distraction) occurs. During focused mode operation, the solver interacts with the environment in directed manner, executing focused plans, and allowing for predicted items to be activated by the environment. When a defocusing event occurs, the problem-solving then switches into a defocused mode until a focusing event (e.g., discovery) occurs. In defocused mode, the solver performs actions unrelated to the problem (or is inactive) and is receptive to a set of environmental triggers that activate novel aspects using the three mechanisms discussed in this paper. When a focusing event occurs, the diffused problem elements cohere into a restructured representation and problem-solving returns into a focused mode.

5.2.1. Focused Problem Solving Mode

Initially, both prior knowledge and perceptual entities help guide the creation of problem representations in working memory. Prior optimal or rewarding solution strategies are obtained from LTM and encoded in the working memory as well. This process is largely analytical and the solver interacts with their environment through focused plan or idea execution, targeted observation of prescribed entities, and estimating prediction error of these known entities. More specifically, when a problem is presented, the problem representations are activated and populated into working memory in the PFC, possibly in structured representations along convergence zones. The PFC along with the Striatum and the MTL together attempt at retrieving an optimal or previously rewarded solution strategy from long term memory. If successfully retrieved, the solution strategy is encoded into the PPC as a mental template, which then guides relevant motor control regions to execute the plan.

5.2.2. Defocusing Event-Triggered Mode Switching

The search and solve strategy then proceeds analytically until a “defocusing event” is encountered. The salience network (AI and ACC) monitor for conflicts and attempt to detect any such events in the problem-solving process. As long as no conflicts are detected, the salience network focuses on recruiting networks to achieve goals and suppresses the DMN ( Beaty et al., 2016 ). If the plan execution or retrieval of the solution strategy fails, then a defocusing event is detected and the salience network performs mode switching. The salience network dynamically switches from the focused problem-solving mode to a defocused problem-solving mode ( Menon, 2015 ). Ollinger's current model does not account for other defocusing events beyond an impasse, but it is not inconceivable that there could be other such events triggered by external stimuli (e.g., distraction or an affective event) or by internal stimuli (e.g., mind wandering).

5.2.3. Defocused Problem Solving Mode

In defocused mode, the problem is operated on by mechanisms that allow for the generation and testing of novel ideas. Several large-scale brain networks are recruited to explore and generate new ideas. The search for novel ideas is facilitated by generally defocused attention, which in turn allows for creative idea generation from both internal as well as external sources. The salience network switches operations from defocused event detection to focused event or discovery detection, whereby for example, environmental events or ideas that are deemed interesting can be detected. During this idea exploration phase, internally, the DMN is no longer suppressed and attempts to generate new ideas for problem-solving. It is known that the IPC is involved in the generation of new ideas ( Benedek et al., 2014 ) and together with the PPC in coupling different information together ( Simone Sandkühler, 2008 ; Stocco et al., 2012 ). Beaty et al. (2016) have proposed that even this internal idea-generation process can be goal directed, thereby allowing for a closer working relationship between the CEN and the DMN. They point to neuroimaging evidence that support the possibility that the executive control network (comprising the lateral prefrontal and inferior parietal regions) can constrain and direct the DMN in its process of generating ideas to meet task-specific goals via top down monitoring and executive control ( Beaty et al., 2016 ). The control network is believed to maintain an “internal train of thought” by keeping the task goal activated, thereby allowing for strategic and goal-congruent searches for ideas. Moreover, they suggest that the extent of CEN involvement in the DMN idea-generation may depend on the extent to which the creative task is constrained. In the RWPS setting, I would suspect that the internal search for creative solutions is not entirely unconstrained, even in the defocused mode. Instead, the solver is working on a specified problem and thus, must maintain the problem-thread while searching for solutions. Moreover, self-generated ideas must be evaluated against the problem parameters and thereby might need some top-down processing. This would suggest that in such circumstances, we would expect to see an increased involvement of the CEN in constraining the DMN.

On the external front, several mechanisms are operating in this defocused mode. Of particular note are the dorsal attention network, composed of the visual cortex (V), IPS and the frontal eye field (FEF) along with the precuneus and the caudate nucleus allow for partial cues to be considered. The MTL receives synthesized cue and contextual information and populates the WM in the PFC with a potentially expanded set of information that might be relevant for problem-solving. The precuneus, dlPFC and PPC together trigger the activation and use of a heuristic prototype based on an event in the environment. The caudate nucleus facilitates information routing between the PFC and PPC and is involved in learning and skill acquisition.

5.2.4. Focusing Event-Triggered Mode Switching

The problem's life in this defocused mode continues until a focusing event occurs, which could be triggered by either external (e.g., notification of impending deadline, discovery of a novel property in the environment) or internal items (e.g., goal completion, discovery of novel association or updated relevancy of a previously irrelevant item). As noted earlier, an internal train of thought may be maintained that facilitates top-down evaluation of ideas and tracking of these triggers ( Beaty et al., 2016 ). The salience network switches various networks back to the focused problem-solving mode, but not without the potential for problem restructuring. As noted earlier, problem space elements are maintained somewhat loosely in the defocused mode. Thus, upon a focusing event, a set or subset of these elements cohere into a tight (restructured) representation suitable for focused mode problem solving. The process then repeats itself until the goal has been achieved.

5.3. Model Predictions

5.3.1. single-mode operation.

The proposed RWPS model provides several interesting hypotheses, which I discuss next. First, the model assumes that any given problem being worked on is in one mode or another, but not both. Thus, the model predicts that there cannot be focused plan execution on a problem that is in defocused mode. The corollary prediction is that novel perceptual cues (as those discussed in section 4) cannot help the solver when in focused mode. The corollary prediction, presumably has some support from the inattentional blindness literature. Inattentional blindness is when perceptual cues are not noticed during a task (e.g., counting the number of basketball passes between several people, but not noticing a gorilla in the scene) ( Simons and Chabris, 1999 ). It is possible that during focused problem solving, that external and internally generated novel ideas are simply not considered for problem solving. I am not claiming that these perceptual cues are always ignored, but that they are not considered within the problem. Sometimes external cues (like distracting occurrences) can serve as defocusing events, but the model predicts that the actual content of these cues are not themselves useful for solving the specific problem at hand.

When comparing dual-process models Sowden et al. (2015) discuss shifting from one type of thinking to another and explore how this shift relates to creativity. In this regard, they weigh the pros and cons of serial vs. parallel shifts. In dual-process models that suggest serial shifts, it is necessary to disengage one type of thought prior to engaging the other or to shift along a continuum. Whereas, in models that suggest parallel shifts, each of the thinking types can operate in parallel. Per this construction, the proposed RWPS model is serial, however, not quite in the same sense. As noted earlier, the RWPS model is not a dual-process model in the same sense as other dual process model. Instead, here, the thrust is on when the brain is receptive or not receptive to certain kinds of internal and external stimuli that can influence problem solving. Thus, while the modes may be serial with respect to a certain problem, it does not preclude the possibility of serial and parallel thinking processes that might be involved within these modes.

5.3.2. Event-Driven Transitions

The model requires an event (defocusing or focusing) to transition from one mode to another. After all why else would a problem that is successfully being resolved in the focused mode (toward completion) need to necessarily be transferred to defocused mode? These events are interpreted as conflicts in the brain and therefore the mode-switching is enabled by the saliency network and the ACC. Thus, the model predicts that there can be no transition from one mode to another without an event. This is a bit circular, as an event is really what triggers the transition in the first place. But, here I am suggesting that an external or internal cue triggered event is what drives the transition, and that transitions cannot happen organically without such an event. In some sense, the argument is that the transition is discontinuous, rather than a smooth one. Mind-wandering is good example of when we might drift into defocused mode, which I suggest is an example of an internally driven event caused by an alternative thought that takes attention away from the problem.

A model assumption underlying RWPS is that events such as impasses have a similar effect to other events such as distraction or mind wandering. Thus, it is crucial to be able to establish that there exists of class of such events and they have a shared effect on RWPS, which is to switch attentional modes.

5.3.3. Focused Mode Completion

The model also predicts that problems cannot be solved (i.e., completed) within the defocused mode. A problem can be considered solved when a goal is reached. However, if a goal is reached and a problem is completed in the defocused mode, then there must have not been any converging event or coherence of problem elements. While it is possible that the solver arbitrarily arrived at the goal in a diffused problem space and without conscious awareness of completing the task or even any converging event or problem recompiling, it appears somewhat unlikely. It is true that there are many tasks that we complete without actively thinking about it. We do not think about what foot to place in front of another while walking, but this is not an instance of problem solving. Instead, this is an instance of unconscious task completion.

5.3.4. Restructuring Required

The model predicts that a problem cannot return to a focused mode without some amount of restructuring. That is, once defocused, the problem is essentially never the same again. The problem elements begin interacting with other internally and externally-generated items, which in turn become absorbed into the problem representation. This prediction can potentially be tested by establishing some preliminary knowledge, and then showing one group of subjects the same knowledge as before, while showing the another group of subjects different stimuli. If the model's predictions hold, the problem representation will be restructured in some way for both groups.

There are numerous other such predictions, which are beyond the scope of this paper. One of the biggest challenges then becomes evaluating the model to set up suitable experiments aimed at testing the predictions and falsifying the theory, which I address next.

6. Experimental Challenges and Paradigms

One of challenges in evaluating the RWPS is that real world factors cannot realistically be accounted for and sufficiently controlled within a laboratory environment. So, how can one controllably test the various predictions and model assumptions of “real world” problem solving, especially given that by definition RWPS involves the external environment and unconscious processing? At the expense of ecological validity, much of insight problem solving research has employed an experimental paradigm that involves providing participants single instances of suitably difficult problems as stimuli and observing various physiological, neurological and behavioral measures. In addition, through verbal protocols, experimenters have been able to capture subjective accounts and problem solving processes that are available to the participants' conscious. These experiments have been made more sophisticated through the use of timed-hints and/or distractions. One challenge with this paradigm has been the selection of a suitable set of appropriately difficult problems. The classic insight problems (e.g., Nine-dot, eight-coin) can be quite difficult, requiring complicated problem solving processes, and also might not generalize to other problems or real world problems. Some in the insight research community have moved in the direction of verbal tasks (e.g., riddles, anagrams, matchstick rebus, remote associates tasks, and compound remote associates tasks). Unfortunately, these puzzles, while providing a great degree of controllability and repeatability, are even less realistic. These problems are not entirely congruent with the kinds of problems that humans are solving every day.

The other challenge with insight experiments is the selection of appropriate performance and process tracking measures. Most commonly, insight researchers use measures such as time to solution, probability of finding solution, and the like for performance measures. For process tracking, verbal protocols, coded solution attempts, and eye tracking are increasingly common. In neuroscientific studies of insight various neurological measures using functional magnetic resonance imaging (fMRI), electroencephalography (EEGs), transcranial direct current stimulation (tDCS), and transcranial magnetic stimulation (tMS) are popular and allow for spatially and temporally localizing an insight event.

Thus, the challenge for RWPS is two-fold: (1) selection of stimuli (real world problems) that are generalizable, and (2) selection of measures (or a set of measures) that can capture key aspects of the problem solving process. Unfortunately, these two challenges are somewhat at odds with each other. While fMRI and various neuroscientific measures can capture the problem solving process in real time, it is practically difficult to provide participants a realistic scenario while they are laying flat on their back in an fMRI machine and allowed to move nothing more than a finger. To begin addressing this conundrum, I suggest returning to object manipulation problems (not all that different from those originally introduced by Maier and Duncker nearly a century ago), but using modern computing and user-interface technologies.

One pseudo-realistic approach is to generate challenging object manipulation problems in Virtual Reality (VR). VR has been used to describe 3-D environment displays that allows participants to interact with artificially projected, but experientially realistic scenarios. It has been suggested that virtual environments (VE) invoke the same cognitive modules as real equivalent environmental experience ( Foreman, 2010 ). Crucially, since VE's can be scaled and designed as desired, they provide a unique opportunity to study pseudo-RWPS. However, a VR-based research approach has its limitations, one of which is that it is nearly impossible to track participant progress through a virtual problem using popular neuroscientific measures such as fMRI because of the limited mobility of connected participants.

Most of the studies cited in this paper utilized an fMRI-based approach in conjunction with a verbal or visual task involving problem-solving or creative thinking. Very few, if any, studies involved the use physical manipulation, and those physical manipulations were restricted to limited finger movements. Thus, another pseudo-realistic approach is allowing subjects to teleoperate robotic arms and legs from inside the fMRI machine. This paradigm has seen limited usage in psychology and robotics, in studies focused on Human-Robot interaction ( Loth et al., 2015 ). It could be an invaluable tool in studying real-time dynamic problem-solving through the control of a robotic arm. In this paradigm a problem solving task involving physical manipulation is presented to the subject via the cameras of a robot. The subject (in an fMRI) can push buttons to operate the robot and interact with its environment. While the subjects are not themselves moving, they can still manipulate objects in the real world. What makes this paradigm all the more interesting is that the subject's manipulation-capabilities can be systematically controlled. Thus, for a particular problem, different robotic perceptual and manipulation capabilities can be exposed, allowing researchers to study solver-problem dynamics in a new way. For example, even simple manipulation problems (e.g., re-arranging and stacking blocks on a table) can be turned into challenging problems when the robotic movements are restricted. Here, the problem space restrictions are imposed not necessarily on the underlying problem, but on the solver's own capabilities. Problems of this nature, given their simple structure, may enable studying everyday practical creativity without the burden of devising complex creative puzzles. Crucial to note, both these pseudo-realistic paradigms proposed demonstrate a tight interplay between the solver's own capabilities and their environment.

7. Conclusion

While the neural basis for problem-solving, creativity and insight have been studied extensively in the past, there is still a lack of understanding of the role of the environment in informing the problem-solving process. Current research has primarily focused on internally-guided mental processes for idea generation and evaluation. However, the type of real world problem-solving (RWPS) that is often considered a hallmark of human intelligence has involved both a dynamic interaction with the environment and the ability to handle intervening and interrupting events. In this paper, I have attempted to synthesize the literature into a unified theory of RWPS, with a specific focus on ways in which the environment can help problem-solve and the key neural networks involved in processing and utilizing relevant and useful environmental information. Understanding the neural basis for RWPS will allow us to be better situated to solve difficult problems. Moreover, for researchers in computer science and artificial intelligence, clues into the neural underpinnings of the computations taking place during creative RWPS, can inform the design the next generation of helper and exploration robots which need these capabilities in order to be resourceful and resilient in the open-world.

Author Contributions

The author confirms being the sole contributor of this work and approved it for publication.

The research for this Hypothesis/Theory Article was funded by the authors private means. Publication costs will be covered by my institution: Tufts University, Medford, MA, USA.

Conflict of Interest Statement

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

Acknowledgments

I am indebted to Professor Matthias Scheutz, Professor Elizabeth Race, Professor Ayanna Thomas, and Professor. Shaun Patel for providing guidance with the research and the manuscript. I am also grateful for the facilities provided by Tufts University, Medford, MA, USA.

1. ^ My intention is not to ignore the benefits of a concentrated internal thought process which likely occurred as well, but merely to acknowledge the possibility that the environment might have also helped.

2. ^ The research in insight does extensively use “hints” which are, arguably, a form of external influence. But these hints are highly targeted and might not be available in this explicit form when solving problems in the real world.

3. ^ The accuracy of these accounts has been placed in doubt. They often are recounted years later, with inaccuracies, and embellished for dramatic effect.

4. ^ I use the term “agent” to refer to the problem-solver. The term agent is more general than “creature” or “person” or “you" and is intentionally selected to broadly reference humans, animals as well as artificial agents. I also selectively use the term “solver.”

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Keywords: creativity, problem-solving, insight, attention network, salience network, default mode network

Citation: Sarathy V (2018) Real World Problem-Solving. Front. Hum. Neurosci . 12:261. doi: 10.3389/fnhum.2018.00261

Received: 03 August 2017; Accepted: 06 June 2018; Published: 26 June 2018.

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Copyright © 2018 Sarathy. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Vasanth Sarathy, [email protected]