definition for problem solving skills

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What Are Problem-Solving Skills? (Definition, Examples, And How To List On A Resume)

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Summary. Problem-solving skills include analysis, creativity, prioritization, organization, and troubleshooting. To solve a problem, you need to use a variety of skills based on the needs of the situation.

Most jobs essentially boil down to identifying and solving problems consistently and effectively. That’s why employers value problem-solving skills in job candidates for just about every role.

We’ll cover problem-solving methods, ways to improve your problem-solving skills, and examples of showcasing your problem-solving skills during your job search .

Key Takeaways:

If you can show off your problem-solving skills on your resume , in your cover letter , and during a job interview, you’ll be one step closer to landing a job.

Companies rely on employees who can handle unexpected challenges, identify persistent issues, and offer workable solutions in a positive way.

It is important to improve problem solving skill because this is a skill that can be cultivated and nurtured so you can become better at dealing with problems over time.

Types of Problem-Solving Skills

How to improve your problem-solving skills, example answers to problem-solving interview questions, how to show off problem-solving skills on a resume, example resume and cover letter with problem-solving skills, more about problem-solving skills, problem solving skills faqs.

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Problem-solving skills are skills that help you identify and solve problems effectively and efficiently . Your ability to solve problems is one of the main ways that hiring managers and recruiters assess candidates, as those with excellent problem-solving skills are more likely to autonomously carry out their responsibilities.

A true problem solver can look at a situation, find the cause of the problem (or causes, because there are often many issues at play), and then come up with a reasonable solution that effectively fixes the problem or at least remedies most of it.

The ability to solve problems is considered a soft skill , meaning that it’s more of a personality trait than a skill you’ve learned at school, on the job, or through technical training.

That being said, your proficiency with various hard skills will have a direct bearing on your ability to solve problems. For example, it doesn’t matter if you’re a great problem-solver; if you have no experience with astrophysics, you probably won’t be hired as a space station technician .

Problem-solving is considered a skill on its own, but it’s supported by many other skills that can help you be a better problem solver. These skills fall into a few different categories of problem-solving skills.

Problem recognition and analysis. The first step is to recognize that there is a problem and discover what it is or what the root cause of it is.

You can’t begin to solve a problem unless you’re aware of it. Sometimes you’ll see the problem yourself and other times you’ll be told about the problem. Both methods of discovery are very important, but they can require some different skills. The following can be an important part of the process:

Active listening

Data analysis

Historical analysis

Communication

Create possible solutions. You know what the problem is, and you might even know the why of it, but then what? Your next step is the come up with some solutions.

Most of the time, the first solution you come up with won’t be the right one. Don’t fall victim to knee-jerk reactions; try some of the following methods to give you solution options.

Brainstorming

Forecasting

Decision-making

Topic knowledge/understanding

Process flow

Evaluation of solution options. Now that you have a lot of solution options, it’s time to weed through them and start casting some aside. There might be some ridiculous ones, bad ones, and ones you know could never be implemented. Throw them away and focus on the potentially winning ideas.

This step is probably the one where a true, natural problem solver will shine. They intuitively can put together mental scenarios and try out solutions to see their plusses and minuses. If you’re still working on your skill set — try listing the pros and cons on a sheet of paper.

Prioritizing

Evaluating and weighing

Solution implementation. This is your “take action” step. Once you’ve decided which way to go, it’s time to head down that path and see if you were right. This step takes a lot of people and management skills to make it work for you.

Dependability

Teambuilding

Troubleshooting

Follow-Through

Believability

Trustworthiness

Project management

Evaluation of the solution. Was it a good solution? Did your plan work or did it fail miserably? Sometimes the evaluation step takes a lot of work and review to accurately determine effectiveness. The following skills might be essential for a thorough evaluation.

Customer service

Feedback responses

Flexibility

You now have a ton of skills in front of you. Some of them you have naturally and some — not so much. If you want to solve a problem, and you want to be known for doing that well and consistently, then it’s time to sharpen those skills.

Develop industry knowledge. Whether it’s broad-based industry knowledge, on-the-job training , or very specific knowledge about a small sector — knowing all that you can and feeling very confident in your knowledge goes a long way to learning how to solve problems.

Be a part of a solution. Step up and become involved in the problem-solving process. Don’t lead — but follow. Watch an expert solve the problem and, if you pay attention, you’ll learn how to solve a problem, too. Pay attention to the steps and the skills that a person uses.

Practice solving problems. Do some role-playing with a mentor , a professor , co-workers, other students — just start throwing problems out there and coming up with solutions and then detail how those solutions may play out.

Go a step further, find some real-world problems and create your solutions, then find out what they did to solve the problem in actuality.

Identify your weaknesses. If you could easily point out a few of your weaknesses in the list of skills above, then those are the areas you need to focus on improving. How you do it is incredibly varied, so find a method that works for you.

Solve some problems — for real. If the opportunity arises, step in and use your problem-solving skills. You’ll never really know how good (or bad) you are at it until you fail.

That’s right, failing will teach you so much more than succeeding will. You’ll learn how to go back and readdress the problem, find out where you went wrong, learn more from listening even better. Failure will be your best teacher ; it might not make you feel good, but it’ll make you a better problem-solver in the long run.

Once you’ve impressed a hiring manager with top-notch problem-solving skills on your resume and cover letter , you’ll need to continue selling yourself as a problem-solver in the job interview.

There are three main ways that employers can assess your problem-solving skills during an interview:

By asking questions that relate to your past experiences solving problems

Posing hypothetical problems for you to solve

By administering problem-solving tests and exercises

The third method varies wildly depending on what job you’re applying for, so we won’t attempt to cover all the possible problem-solving tests and exercises that may be a part of your application process.

Luckily, interview questions focused on problem-solving are pretty well-known, and most can be answered using the STAR method . STAR stands for situation, task, action, result, and it’s a great way to organize your answers to behavioral interview questions .

Let’s take a look at how to answer some common interview questions built to assess your problem-solving capabilities:

At my current job as an operations analyst at XYZ Inc., my boss set a quarterly goal to cut contractor spending by 25% while maintaining the same level of production and moving more processes in-house. It turned out that achieving this goal required hiring an additional 6 full-time employees, which got stalled due to the pandemic. I suggested that we widen our net and hire remote employees after our initial applicant pool had no solid candidates. I ran the analysis on overhead costs and found that if even 4 of the 6 employees were remote, we’d save 16% annually compared to the contractors’ rates. In the end, all 6 employees we hired were fully remote, and we cut costs by 26% while production rose by a modest amount.

I try to step back and gather research as my first step. For instance, I had a client who needed a graphic designer to work with Crello, which I had never seen before, let alone used. After getting the project details straight, I began meticulously studying the program the YouTube tutorials, and the quick course Crello provides. I also reached out to coworkers who had worked on projects for this same client in the past. Once I felt comfortable with the software, I started work immediately. It was a slower process because I had to be more methodical in my approach, but by putting in some extra hours, I turned in the project ahead of schedule. The client was thrilled with my work and was shocked to hear me joke afterward that it was my first time using Crello.

As a digital marketer , website traffic and conversion rates are my ultimate metrics. However, I also track less visible metrics that can illuminate the story behind the results. For instance, using Google Analytics, I found that 78% of our referral traffic was coming from one affiliate, but that these referrals were only accounting for 5% of our conversions. Another affiliate, who only accounted for about 10% of our referral traffic, was responsible for upwards of 30% of our conversions. I investigated further and found that the second, more effective affiliate was essentially qualifying our leads for us before sending them our way, which made it easier for us to close. I figured out exactly how they were sending us better customers, and reached out to the first, more prolific but less effective affiliate with my understanding of the results. They were able to change their pages that were referring us traffic, and our conversions from that source tripled in just a month. It showed me the importance of digging below the “big picture” metrics to see the mechanics of how revenue was really being generated through digital marketing.

You can bring up your problem-solving skills in your resume summary statement , in your work experience , and under your education section , if you’re a recent graduate. The key is to include items on your resume that speak direclty to your ability to solve problems and generate results.

If you can, quantify your problem-solving accomplishments on your your resume . Hiring managers and recruiters are always more impressed with results that include numbers because they provide much-needed context.

This sample resume for a Customer Service Representative will give you an idea of how you can work problem solving into your resume.

Michelle Beattle 111 Millennial Parkway Chicago, IL 60007 (555) 987-6543 [email protected] Professional Summary Qualified Customer Services Representative with 3 years in a high-pressure customer service environment. Professional, personable, and a true problem solver. Work History ABC Store — Customer Service Representative 01/2015 — 12/2017 Managed in-person and phone relations with customers coming in to pick up purchases, return purchased products, helped find and order items not on store shelves, and explained details and care of merchandise. Became a key player in the customer service department and was promoted to team lead. XYZ Store — Customer Service Representative/Night Manager 01/2018 — 03/2020, released due to Covid-19 layoffs Worked as the night manager of the customer service department and filled in daytime hours when needed. Streamlined a process of moving customers to the right department through an app to ease the burden on the phone lines and reduce customer wait time by 50%. Was working on additional wait time problems when the Covid-19 pandemic caused our stores to close permanently. Education Chicago Tech 2014-2016 Earned an Associate’s Degree in Principles of Customer Care Skills Strong customer service skills Excellent customer complaint resolution Stock record management Order fulfillment New product information Cash register skills and proficiency Leader in problem solving initiatives

You can see how the resume gives you a chance to point out your problem-solving skills and to show where you used them a few times. Your cover letter is your chance to introduce yourself and list a few things that make you stand out from the crowd.

Michelle Beattle 111 Millennial Parkway Chicago, IL 60007 (555) 987-6543 [email protected] Dear Mary McDonald, I am writing in response to your ad on Zippia for a Customer Service Representative . Thank you for taking the time to consider me for this position. Many people believe that a job in customer service is simply listening to people complain all day. I see the job as much more than that. It’s an opportunity to help people solve problems, make their experience with your company more enjoyable, and turn them into life-long advocates of your brand. Through my years of experience and my educational background at Chicago Tech, where I earned an Associate’s Degree in the Principles of Customer Care, I have learned that the customers are the lifeline of the business and without good customer service representatives, a business will falter. I see it as my mission to make each and every customer I come in contact with a fan. I have more than five years of experience in the Customer Services industry and had advanced my role at my last job to Night Manager. I am eager to again prove myself as a hard worker, a dedicated people person, and a problem solver that can be relied upon. I have built a professional reputation as an employee that respects all other employees and customers, as a manager who gets the job done and finds solutions when necessary, and a worker who dives in to learn all she can about the business. Most of my customers have been very satisfied with my resolution ideas and have returned to do business with us again. I believe my expertise would make me a great match for LMNO Store. I have enclosed my resume for your review, and I would appreciate having the opportunity to meet with you to further discuss my qualifications. Thank you again for your time and consideration. Sincerely, Michelle Beattle

You’ve no doubt noticed that many of the skills listed in the problem-solving process are repeated. This is because having these abilities or talents is so important to the entire course of getting a problem solved.

In fact, they’re worthy of a little more attention. Many of them are similar, so we’ll pull them together and discuss how they’re important and how they work together.

Communication, active listening, and customer service skills. No matter where you are in the process of problem-solving, you need to be able to show that you’re listening and engaged and really hearing what the problem is or what a solution may be.

Obviously, the other part of this is being able to communicate effectively so people understand what you’re saying without confusion. Rolled into this are customer service skills , which really are all about listening and responding appropriately — it’s the ultimate in interpersonal communications.

Analysis (data and historical), research, and topic knowledge/understanding. This is how you intellectually grasp the issue and approach it. This can come from studying the topic and the process or it can come from knowledge you’ve gained after years in the business. But the best solutions come from people who thoroughly understand the problem.

Creativity, brainstorming, troubleshooting, and flexibility. All of you creative thinkers will like this area because it’s when your brain is at its best.

Coming up with ideas, collaborating with others, leaping over hurdles, and then being able to change courses immediately, if need be, are all essential. If you’re not creative by nature, then having a team of diverse thinkers can help you in this area.

Dependability, believability, trustworthiness, and follow-through. Think about it, these are all traits a person needs to have to make change happen and to make you comfortable taking that next step with them. Someone who is shifty and shady and never follows through, well, you’re simply not going to do what they ask, are you?

Leadership, teambuilding, decision-making, and project management. These are the skills that someone who is in charge is brimming with. These are the leaders you enjoy working for because you know they’re doing what they can to keep everything in working order. These skills can be learned but they’re often innate.

Prioritizing, prediction, forecasting, evaluating and weighing, and process flow. If you love flow charts, data analysis, prediction modeling, and all of that part of the equation, then you might have some great problem-solving abilities.

These are all great skills because they can help you weed out bad ideas, see flaws, and save massive amounts of time in trial and error.

What is a good example of problem-solving skills?

Good examples of porblem-solving skills include research, analysis, creativity, communciation, and decision-making. Each of these skills build off one another to contribute to the problem solving process. Research and analysis allow you to identify a problem.

Creativity and analysis help you consider different solutions. Meanwhile, communication and decision-making are key to working with others to solve a problem on a large scale.

What are 3 key attributes of a good problem solver?

3 key attributes of a good problem solver are persistence, intellegince, and empathy. Persistence is crucial to remain motivated to work through challenges. Inellegince is needed to make smart, informed choices. Empathy is crucial to maintain positive relationships with others as well as yourself.

What can I say instead of problem-solving skills?

Instead of saying problem-solving skills, you can say the following:

Critical thinker

Solutions-oriented

Engineering

Using different words is helpful, especially when writing your resume and cover letter.

What is problem-solving in the workplace?

Problem-solving in the workplace is the ability to work through any sort of challenge, conflict, or unexpected situation and still achieve business goals. Though it varies by profession, roblem-solving in the workplace is very important for almost any job, because probelms are inevitable. You need to have the appropriate level of problem-solving skills if you want to succeed in your career, whatever it may be.

Department of Labor – Problem Solving and Critical Thinking

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Kristin Kizer is an award-winning writer, television and documentary producer, and content specialist who has worked on a wide variety of written, broadcast, and electronic publications. A former writer/producer for The Discovery Channel, she is now a freelance writer and delighted to be sharing her talents and time with the wonderful Zippia audience.

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What Are Problem-Solving Skills?

Definition & Examples of Problem-Solving Skills

• Problem-solving skills help you determine why an issue is happening and how to resolve that issue.

Learn more about problem-solving skills and how they work.

Problem-solving skills help you solve issues quickly and effectively. It's one of the  key skills that employers  seek in job applicants, as employees with these skills tend to be self-reliant. Problem-solving skills require quickly identifying the underlying issue and implementing a solution.

Problem-solving is considered a  soft skill  (a personal strength) rather than a hard skill that's learned through education or training. You can improve your problem-solving skills by familiarizing yourself with common issues in your industry and learning from more experienced employees.

How Problem-Solving Skills Work

Problem-solving starts with identifying the issue. For example, a teacher might need to figure out how to improve student performance on a writing proficiency test. To do that, the teacher will review the writing tests looking for areas of improvement. They might see that students can construct simple sentences, but they're struggling with writing paragraphs and organizing those paragraphs into an essay.

To solve the problem, the teacher would work with students on how and when to write compound sentences, how to write paragraphs, and ways to organize an essay.

Theresa Chiechi / The Balance

There are five steps typically used in problem-solving.

1. Analyze Contributing Factors

To solve a problem, you must find out what caused it. This requires you to gather and evaluate data, isolate possible contributing circumstances, and pinpoint what needs to be addressed for a resolution.

To do this, you'll use skills like :

• Data gathering
• Data analysis
• Fact-finding
• Historical analysis

2. Generate Interventions

Once you’ve determined the cause, brainstorm possible solutions. Sometimes this involves teamwork since two (or more) minds are often better than one. A single strategy is rarely the obvious route to solving a complex problem; devising a set of alternatives helps you cover your bases and reduces your risk of exposure should the first strategy you implement fail.

This involves skills like :

• Brainstorming
• Creative thinking
• Forecasting
• Project design
• Project planning

3. Evaluate Solutions

Depending on the nature of the problem and your chain of command, evaluating best solutions may be performed by assigned teams, team leads, or forwarded to corporate decision-makers. Whoever makes the decision must evaluate potential costs, required resources, and possible barriers to successful solution implementation.

This requires several skills, including:

• Corroboration
• Test development
• Prioritizing

4. Implement a Plan

Once a course of action has been decided, it must be implemented along with benchmarks that can quickly and accurately determine whether it’s working. Plan implementation also involves letting personnel know about changes in standard operating procedures.

This requires skills like:

• Project management
• Project implementation
• Collaboration
• Time management
• Benchmark development

5. Assess the Solution's Effectiveness

Once a solution is implemented, the best problem-solvers have systems in place to evaluate if and how quickly it's working. This way, they know as soon as possible whether the issue has been resolved or whether they’ll have to change their response to the problem mid-stream.

This requires:

• Communication
• Customer feedback
• Follow-through
• Troubleshooting

Here's an example of showing your problem-solving skills in a cover letter.

When I was first hired as a paralegal, I inherited a backlog of 25 sets of medical records that needed to be summarized, each of which was hundreds of pages long. At the same time, I had to help prepare for three major cases, and there weren’t enough hours in the day. After I explained the problem to my supervisor, she agreed to pay me to come in on Saturday mornings to focus on the backlog. I was able to eliminate the backlog in a month.

Here's another example of how to show your problem-solving skills in a cover letter:

When I joined the team at Great Graphics as Artistic Director, the designers had become uninspired because of a former director who attempted to micro-manage every step in the design process. I used weekly round-table discussions to solicit creative input and ensured that each designer was given full autonomy to do their best work. I also introduced monthly team-based competitions that helped build morale, spark new ideas, and improve collaboration.

Highlighting Problem-Solving Skills

• Since this is a skill that's important to most employers, put them front and center on your resume, cover letter, and in interviews.

If you're not sure what to include, look to previous roles—whether in academic, work, or volunteer settings—for examples of challenges you met and problems you solved. Highlight relevant examples in your  cover letter and use bullet points in your resume to show how you solved a problem.

During interviews, be ready to describe situations you've encountered in previous roles, the processes you followed to address problems, the skills you applied, and the results of your actions. Potential employers are eager to hear a  coherent narrative of the ways you've used problem-solving skills .

Interviewers may pose hypothetical problems for you to solve. Base your answers on the five steps and refer to similar problems you've resolved, if possible. Here are tips for answering problem-solving interview questions , with examples of the best answers.

Key Takeaways

• It's one of the key skills that employers seek in job applicants.
• Problem-solving starts with identifying the issue, coming up with solutions, implementing those solutions, and evaluating their effectiveness. 

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Article • 7 min read

What Is Problem Solving?

Find a solution to any problem you face.

By the Mind Tools Content Team

We all spend a lot of our time solving problems, both at work and in our personal lives.

Some problems are small, and we can quickly sort them out ourselves. But others are complex challenges that take collaboration, creativity, and a considerable amount of effort to solve.

At work, the types of problems we face depend largely on the organizations we're in and the jobs we do. A manager in a cleaning company, for example, might spend their day untangling staffing issues, resolving client complaints, and sorting out problems with equipment and supplies. An aircraft designer, on the other hand, might be grappling with a problem about aerodynamics, or trying to work out why a new safety feature isn't working. Meanwhile, a politician might be exploring solutions to racial injustice or climate change.

But whatever issues we face, there are some common ways to tackle them effectively. And we can all boost our confidence and ability to succeed by building a strong set of problem-solving skills.

Mind Tools offers a large collection of resources to help you do just that!

How Well Do You Solve Problems?

Start by taking an honest look at your existing skills. What's your current approach to solving problems, and how well is it working? Our quiz, How Good Is Your Problem Solving? lets you analyze your abilities, and signposts ways to address any areas of weakness.

Define Every Problem

The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem – not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work. However, if you look a bit deeper, the real issue might be a general lack of training, or an unreasonable workload across the team.

Tools like 5 Whys , Appreciation and Root Cause Analysis get you asking the right questions, and help you to work through the layers of a problem to uncover what's really going on.

However, defining a problem doesn't mean deciding how to solve it straightaway. It's important to look at the issue from a variety of perspectives. If you commit yourself too early, you can end up with a short-sighted solution. The CATWOE checklist provides a powerful reminder to look at many elements that may contribute to the problem, keeping you open to a variety of possible solutions.

Understanding Complexity

As you define your problem, you'll often discover just how complicated it is. There are likely several interrelated issues involved. That's why it's important to have ways to visualize, simplify and make sense of this tangled mess!

Affinity Diagrams are great for organizing many different pieces of information into common themes, and for understanding the relationships between them.

Another popular tool is the Cause-and-Effect Diagram . To generate viable solutions, you need a solid understanding of what's causing the problem.

When your problem occurs within a business process, creating a Flow Chart , Swim Lane Diagram or a Systems Diagram will help you to see how various activities and inputs fit together. This may well highlight a missing element or bottleneck that's causing your problem.

Quite often, what seems to be a single problem turns out to be a whole series of problems. The Drill Down technique prompts you to split your problem into smaller, more manageable parts.

General Problem-Solving Tools

When you understand the problem in front of you, you’re ready to start solving it. With your definition to guide you, you can generate several possible solutions, choose the best one, then put it into action. That's the four-step approach at the heart of good problem solving.

There are various problem-solving styles to use. For example:

• Constructive Controversy is a way of widening perspectives and energizing discussions.
• Inductive Reasoning makes the most of people’s experiences and know-how, and can speed up solution finding.
• Means-End Analysis can bring extra clarity to your thinking, and kick-start the process of implementing solutions.

Specific Problem-Solving Systems

Some particularly complicated or important problems call for a more comprehensive process. Again, Mind Tools has a range of approaches to try, including:

• Simplex , which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your organization.
• Appreciative Inquiry , which is a uniquely positive way of solving problems by examining what's working well in the areas surrounding them.
• Soft Systems Methodology , which takes you through four stages to uncover more details about what's creating your problem, and then define actions that will improve the situation.

Further Problem-Solving Strategies

Good problem solving requires a number of other skills – all of which are covered by Mind Tools.

For example, we have a large section of resources to improve your Creativity , so that you come up with a range of possible solutions.

By strengthening your Decision Making , you'll be better at evaluating the options, selecting the best ones, then choosing how to implement them.

And our Project Management collection has valuable advice for strengthening the whole problem-solving process. The resources there will help you to make effective changes – and then keep them working long term.

Problems are an inescapable part of life, both in and out of work. So we can all benefit from having strong problem-solving skills.

It's important to understand your current approach to problem solving, and to know where and how to improve.

Define every problem you encounter – and understand its complexity, rather than trying to solve it too soon.

There's a range of general problem-solving approaches, helping you to generate possible answers, choose the best ones, and then implement your solution.

Some complicated or serious problems require more specific problem-solving systems, especially when they relate to business processes.

By boosting your creativity, decision-making and project-management skills, you’ll become even better at solving all the problems you face.

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Action learning sets.

Solving Problems by Doing and Discussing

Cause and Effect Analysis

Identifying the Likely Causes of Problems

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Everybody can benefit from having good problem solving skills as we all encounter problems on a daily basis. Some of these problems are obviously more severe or complex than others.

It would be wonderful to have the ability to solve all problems efficiently and in a timely fashion without difficulty, unfortunately though there is no one way in which all problems can be solved.

You will discover, as you read through our pages on problem solving, that the subject is complex.

However well prepared we are for problem solving, there is always an element of the unknown. Although planning and structuring will help make the problem solving process more likely to be successful, good judgement and an element of good luck will ultimately determine whether problem solving was a success.

Interpersonal relationships fail and businesses fail because of poor problem solving.

This is often due to either problems not being recognised or being recognised but not being dealt with appropriately.

Problem solving skills are highly sought after by employers as many companies rely on their employees to identify and solve problems.

A lot of the work in problem solving involves understanding what the underlying issues of the problem really are - not the symptoms. Dealing with a customer complaint may be seen as a problem that needs to be solved, and it's almost certainly a good idea to do so. The employee dealing with the complaint should be asking what has caused the customer to complain in the first place, if the cause of the complaint can be eliminated then the problem is solved.

In order to be effective at problem solving you are likely to need some other key skills, which include:

Creativity. Problems are usually solved either intuitively or systematically. Intuition is used when no new knowledge is needed - you know enough to be able to make a quick decision and solve the problem, or you use common sense or experience to solve the problem. More complex problems or problems that you have not experienced before will likely require a more systematic and logical approach to solve, and for these you will need to use creative thinking. See our page on Creative Thinking for more information.

Researching Skills. Defining and solving problems often requires you to do some research: this may be a simple Google search or a more rigorous research project. See our Research Methods section for ideas on how to conduct effective research.

Team Working. Many problems are best defined and solved with the input of other people. Team working may sound like a 'work thing' but it is just as important at home and school as well as in the workplace. See our Team-Working page for more.

Emotional Intelligence. It is worth considering the impact that a problem and/or its solution has on you and other people. Emotional intelligence, the ability to recognise the emotions of yourself and others, will help guide you to an appropriate solution. See our Emotional Intelligence pages for more.

Risk Management. Solving a problem involves a certain amount of risk - this risk needs to be weighed up against not solving the problem. You may find our Risk Management page useful.

Decision Making . Problem solving and decision making are closely related skills, and making a decision is an important part of the problem solving process as you will often be faced with various options and alternatives. See Decision Making for more.

The measure of success is not whether you have a tough problem to deal with, but whether it is the same problem you had last year.

John Foster Dulles, Former US Secretary of State.

What is a Problem?

The Concise Oxford Dictionary (1995) defines a problem as:

“ A doubtful or difficult matter requiring a solution ”

“ Something hard to understand or accomplish or deal with.”

It is worth also considering our own view of what a problem is.

We are constantly exposed to opportunities in life, at work, at school and at home. However many opportunities are missed or not taken full advantage of. Often we are unsure how to take advantage of an opportunity and create barriers - reasons why we can't take advantage. These barriers can turn a potentially positive situation into a negative one, a problem.

Are we missing the 'big problem'? It is human nature to notice and focus on small, easy to solve problems but much harder to work on the big problems that may be causing some of the smaller ones.

It's useful to consider the following questions when faced with a problem.

Is the problem real or perceived?

Is this problem really an opportunity?

Does the problem need solving?

All problems have two features in common: goals and barriers.

Problems involve setting out to achieve some objective or desired state of affairs and can include avoiding a situation or event.

Goals can be anything that you wish to achieve, or where you want to be. If you are hungry then your goal is probably to eat something. If you are the head of an organisation (CEO), then your main goal may be to maximise profits and this main goal may need to be split into numerous sub-goals in order to fulfil the ultimate aim of increasing profits.

If there were no barriers in the way of achieving a goal, then there would be no problem. Problem solving involves overcoming the barriers or obstacles that prevent the immediate achievement of goals.

Following our examples above, if you feel hungry then your goal is to eat. A barrier to this may be that you have no food available - so you take a trip to the supermarket and buy some food, removing the barrier and thus solving the problem. Of course for the CEO wanting to increase profits there may be many more barriers preventing the goal from being reached. The CEO needs to attempt to recognise these barriers and remove them or find other ways to achieve the goals of the organisation.

Our problem solving pages provide a simple and structured approach to problem solving.

The approach referred to is generally designed for problem solving in an organisation or group context, but can also be easily adapted to work at an individual level at home or in education.

Trying to solve a complex problem alone however can be a mistake. The old adage " A problem shared is a problem halved " is sound advice.

Talking to others about problems is not only therapeutic but can help you see things from a different point of view, opening up more potential solutions.

Stages of Problem Solving

Effective problem solving usually involves working through a number of steps or stages, such as those outlined below.

Problem Identification:

This stage involves: detecting and recognising that there is a problem; identifying the nature of the problem; defining the problem.

The first phase of problem solving may sound obvious but often requires more thought and analysis. Identifying a problem can be a difficult task in itself. Is there a problem at all? What is the nature of the problem, are there in fact numerous problems? How can the problem be best defined? By spending some time defining the problem you will not only understand it more clearly yourself but be able to communicate its nature to others, which leads to the second phase.

Structuring the Problem:

This stage involves: a period of observation, careful inspection, fact-finding and developing a clear picture of the problem.

Following on from problem identification, structuring the problem is all about gaining more information about the problem and increasing understanding. This phase is all about fact finding and analysis, building a more comprehensive picture of both the goal(s) and the barrier(s). This stage may not be necessary for very simple problems but is essential for problems of a more complex nature.

Looking for Possible Solutions:

During this stage you will generate a range of possible courses of action, but with little attempt to evaluate them at this stage.

From the information gathered in the first two phases of the problem solving framework it is now time to start thinking about possible solutions to the identified problem. In a group situation this stage is often carried out as a brain-storming session, letting each person in the group express their views on possible solutions (or part solutions). In organisations different people will have different expertise in different areas and it is useful, therefore, to hear the views of each concerned party.

Making a Decision:

This stage involves careful analysis of the different possible courses of action and then selecting the best solution for implementation.

This is perhaps the most complex part of the problem solving process. Following on from the previous step it is now time to look at each potential solution and carefully analyse it. Some solutions may not be possible, due to other problems like time constraints or budgets. It is important at this stage to also consider what might happen if nothing was done to solve the problem - sometimes trying to solve a problem that leads to many more problems requires some very creative thinking and innovative ideas.

Finally, make a decision on which course of action to take - decision making is an important skill in itself and we recommend that you see our pages on decision making .

Implementation:

This stage involves accepting and carrying out the chosen course of action.

Implementation means acting on the chosen solution. During implementation more problems may arise especially if identification or structuring of the original problem was not carried out fully.

Monitoring/Seeking Feedback:

The last stage is about reviewing the outcomes of problem solving over a period of time, including seeking feedback as to the success of the outcomes of the chosen solution.

The final stage of problem solving is concerned with checking that the process was successful. This can be achieved by monitoring and gaining feedback from people affected by any changes that occurred. It is good practice to keep a record of outcomes and any additional problems that occurred.

Continue to: Identifying and Structuring Problems Social Problem Solving

See also: Project Management Risk Management Effective Decision Making

What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

• Identify the issue : Recognize the problem that needs to be solved.
• Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
• Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
• Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
• Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
• Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
• Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

• Brainstorming with others
• Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
• Analyzing cause and effect
• Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

• Creating a list of potential ideas to solve the problem
• Grouping and categorizing similar solutions
• Prioritizing potential solutions based on feasibility, cost, and resources required
• Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

• SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
• Decision-making matrices
• Pros and cons lists
• Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

• Communicating the solution to relevant parties
• Setting timelines and milestones
• Assigning tasks and responsibilities
• Monitoring the solution and making adjustments as necessary
• Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

• Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
• Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
• SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
• Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

• Generate a diverse range of solutions
• Encourage all team members to participate
• Foster creative thinking

When brainstorming, remember to:

• Reserve judgment until the session is over
• Encourage wild ideas
• Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

• 5 Whys : Ask “why” five times to get to the underlying cause.
• Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
• Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

• List your problem’s strengths, such as relevant resources or strong partnerships.
• Identify its weaknesses, such as knowledge gaps or limited resources.
• Explore opportunities, like trends or new technologies, that could help solve the problem.
• Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

• Write the problem in the center of a blank page.
• Draw branches from the central problem to related sub-problems or contributing factors.
• Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

• Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
• Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
• Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

• Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
• Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
• Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

• Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
• Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
• Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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Problem-Solving Strategies and Obstacles

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

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

• Discovery of the problem
• Deciding to tackle the issue
• Seeking to understand the problem more fully
• Researching available options or solutions
• Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

• Perceptually recognizing the problem
• Representing the problem in memory
• Considering relevant information that applies to the problem
• Identifying different aspects of the problem
• Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

• Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
• Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
• Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
• Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

• Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
• Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
• Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
• Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

• Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
• Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
• Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
• Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
• Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
• Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9

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Why Problem-Solving Skills Are Essential for Leaders in Any Industry

• 17 Jan 2023

Any organization offering a product or service is in the business of solving problems.

Whether providing medical care to address health issues or quick convenience to those hungry for dinner, a business’s purpose is to satisfy customer needs .

In addition to solving customers’ problems, you’ll undoubtedly encounter challenges within your organization as it evolves to meet customer needs. You’re likely to experience growing pains in the form of missed targets, unattained goals, and team disagreements.

Yet, the ubiquity of problems doesn’t have to be discouraging; with the right frameworks and tools, you can build the skills to solve consumers' and your organization’s most challenging issues.

Here’s a primer on problem-solving in business, why it’s important, the skills you need, and how to build them.

Access your free e-book today.

What Is Problem-Solving in Business?

Problem-solving is the process of systematically removing barriers that prevent you or others from reaching goals.

Your business removes obstacles in customers’ lives through its products or services, just as you can remove obstacles that keep your team from achieving business goals.

Design Thinking

Design thinking , as described by Harvard Business School Dean Srikant Datar in the online course Design Thinking and Innovation , is a human-centered , solutions-based approach to problem-solving and innovation. Originally created for product design, design thinking’s use case has evolved . It’s now used to solve internal business problems, too.

The design thinking process has four stages :

• Clarify: Clarify a problem through research and feedback from those impacted.
• Ideate: Armed with new insights, generate as many solutions as possible.
• Develop: Combine and cull your ideas into a short list of viable, feasible, and desirable options before building prototypes (if making physical products) and creating a plan of action (if solving an intangible problem).
• Implement: Execute the strongest idea, ensuring clear communication with all stakeholders about its potential value and deliberate reasoning.

Using this framework, you can generate innovative ideas that wouldn’t have surfaced otherwise.

Creative Problem-Solving

Another, less structured approach to challenges is creative problem-solving , which employs a series of exercises to explore open-ended solutions and develop new perspectives. This is especially useful when a problem’s root cause has yet to be defined.

You can use creative problem-solving tools in design thinking’s “ideate” stage, which include:

• Brainstorming: Instruct everyone to develop as many ideas as possible in an allotted time frame without passing judgment.
• Divergent thinking exercises: Rather than arriving at the same conclusion (convergent thinking), instruct everyone to come up with a unique idea for a given prompt (divergent thinking). This type of exercise helps avoid the tendency to agree with others’ ideas without considering alternatives.
• Alternate worlds: Ask your team to consider how various personas would manage the problem. For instance, how would a pilot approach it? What about a young child? What about a seasoned engineer?

It can be tempting to fall back on how problems have been solved before, especially if they worked well. However, if you’re striving for innovation, relying on existing systems can stunt your company’s growth.

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

Why Is Problem-Solving Important for Leaders?

While obstacles’ specifics vary between industries, strong problem-solving skills are crucial for leaders in any field.

Whether building a new product or dealing with internal issues, you’re bound to come up against challenges. Having frameworks and tools at your disposal when they arise can turn issues into opportunities.

As a leader, it’s rarely your responsibility to solve a problem single-handedly, so it’s crucial to know how to empower employees to work together to find the best solution.

Your job is to guide them through each step of the framework and set the parameters and prompts within which they can be creative. Then, you can develop a list of ideas together, test the best ones, and implement the chosen solution.

Related: 5 Design Thinking Skills for Business Professionals

4 Problem-Solving Skills All Leaders Need

1. problem framing.

One key skill for any leader is framing problems in a way that makes sense for their organization. Problem framing is defined in Design Thinking and Innovation as determining the scope, context, and perspective of the problem you’re trying to solve.

“Before you begin to generate solutions for your problem, you must always think hard about how you’re going to frame that problem,” Datar says in the course.

For instance, imagine you work for a company that sells children’s sneakers, and sales have plummeted. When framing the problem, consider:

• What is the children’s sneaker market like right now?
• Should we improve the quality of our sneakers?
• Should we assess all children’s footwear?
• Is this a marketing issue for children’s sneakers specifically?
• Is this a bigger issue that impacts how we should market or produce all footwear?

While there’s no one right way to frame a problem, how you do can impact the solutions you generate. It’s imperative to accurately frame problems to align with organizational priorities and ensure your team generates useful ideas for your firm.

To solve a problem, you need to empathize with those impacted by it. Empathy is the ability to understand others’ emotions and experiences. While many believe empathy is a fixed trait, it’s a skill you can strengthen through practice.

When confronted with a problem, consider whom it impacts. Returning to the children’s sneaker example, think of who’s affected:

• Your organization’s employees, because sales are down
• The customers who typically buy your sneakers
• The children who typically wear your sneakers

Empathy is required to get to the problem’s root and consider each group’s perspective. Assuming someone’s perspective often isn’t accurate, so the best way to get that information is by collecting user feedback.

For instance, if you asked customers who typically buy your children’s sneakers why they’ve stopped, they could say, “A new brand of children’s sneakers came onto the market that have soles with more traction. I want my child to be as safe as possible, so I bought those instead.”

When someone shares their feelings and experiences, you have an opportunity to empathize with them. This can yield solutions to their problem that directly address its root and shows you care. In this case, you may design a new line of children’s sneakers with extremely grippy soles for added safety, knowing that’s what your customers care most about.

Related: 3 Effective Methods for Assessing Customer Needs

3. Breaking Cognitive Fixedness

Cognitive fixedness is a state of mind in which you examine situations through the lens of past experiences. This locks you into one mindset rather than allowing you to consider alternative possibilities.

For instance, your cognitive fixedness may make you think rubber is the only material for sneaker treads. What else could you use? Is there a grippier alternative you haven’t considered?

Problem-solving is all about overcoming cognitive fixedness. You not only need to foster this skill in yourself but among your team.

4. Creating a Psychologically Safe Environment

As a leader, it’s your job to create an environment conducive to problem-solving. In a psychologically safe environment, all team members feel comfortable bringing ideas to the table, which are likely influenced by their personal opinions and experiences.

If employees are penalized for “bad” ideas or chastised for questioning long-held procedures and systems, innovation has no place to take root.

By employing the design thinking framework and creative problem-solving exercises, you can foster a setting in which your team feels comfortable sharing ideas and new, innovative solutions can grow.

How to Build Problem-Solving Skills

The most obvious answer to how to build your problem-solving skills is perhaps the most intimidating: You must practice.

Again and again, you’ll encounter challenges, use creative problem-solving tools and design thinking frameworks, and assess results to learn what to do differently next time.

While most of your practice will occur within your organization, you can learn in a lower-stakes setting by taking an online course, such as Design Thinking and Innovation . Datar guides you through each tool and framework, presenting real-world business examples to help you envision how you would approach the same types of problems in your organization.

Are you interested in uncovering innovative solutions for your organization’s business problems? Explore Design Thinking and Innovation —one of our online entrepreneurship and innovation courses —to learn how to leverage proven frameworks and tools to solve challenges. Not sure which course is right for you? Download our free flowchart .

About the Author

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48 Problem Solving

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

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

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

Definition of Problem Solving

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

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

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

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

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

Definition of Problem

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

Types of Problems

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

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

Cognitive Processes in Problem Solving

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

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

Knowledge for Problem Solving

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

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

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

Historical Approaches to Problem Solving

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

Early Conceptions

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

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

Associationism

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

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

Gestalt Psychology

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

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

Information Processing

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

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

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

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

Classic Issues in Problem Solving

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

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

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

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

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

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

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

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

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

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

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

Current and Future Issues in Problem Solving

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

Decision Making

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

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

Intelligence and Creativity

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

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

Teaching of Thinking Skills

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

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

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

Expert Problem Solving

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

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

Analogical Reasoning

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

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

Mathematical and Scientific Problem Solving

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

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

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

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

Everyday Thinking

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

Cognitive Neuroscience of Problem Solving

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

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

Future Directions

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

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Further Reading

Baron, J. ( 2008 ). Thinking and deciding (4th ed). New York: Cambridge University Press.

Duncker, K. ( 1945 ). On problem solving. Psychological Monographs , 58(3) (Whole No. 270).

Holyoak, K. J. , & Morrison, R. G. ( 2005 ). The Cambridge handbook of thinking and reasoning . New York: Cambridge University Press.

Mayer, R. E. , & Wittrock, M. C. ( 2006 ). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 287–304). Mahwah, NJ: Erlbaum.

Sternberg, R. J. , & Ben-Zeev, T. ( 2001 ). Complex cognition: The psychology of human thought . New York: Oxford University Press.

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

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The importance of problem-solving skills

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