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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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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.

JGI / Jamie Grill / Getty Images

Application
Improvement

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.

Sarathy V. Real world problem-solving . Front Hum Neurosci . 2018;12:261. doi:10.3389/fnhum.2018.00261

Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20

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

Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579

Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517

Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7

Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality . Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050

Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition . Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568

National Alliance on Mental Illness. Warning signs and symptoms .

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

35 problem-solving techniques and methods for solving complex problems

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How do you identify problems?

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Tips for more effective problem-solving

Complete problem-solving methods

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

Problem-solving warm-up activities

Closing activities for a problem-solving process.

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

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

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

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

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

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

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

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

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

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

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

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

Tips for more effective problem solving

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

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

Clearly define the problem

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

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

Don’t jump to conclusions

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

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

Try different approaches

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

Don’t take it personally

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

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

Get the right people in the room

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

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

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

Document everything

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

Bring a facilitator

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

Develop your problem-solving skills

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

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

Design a great agenda

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

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

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

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

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

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

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

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

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

2. Lightning Decision Jam

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

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

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

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

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

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

3. Problem Definition Process

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

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

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

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

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

4. The 5 Whys

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

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

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

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

5. World Cafe

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

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

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

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

6. Discovery & Action Dialogue (DAD)

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

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

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

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

7. Design Sprint 2.0

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

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

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

8. Open space technology

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

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

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

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

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

Techniques to identify and analyze problems

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

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

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

Let’s take a look!

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

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

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

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

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

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

10. The Creativity Dice

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

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

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

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

11. Fishbone Analysis

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

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

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

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

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

12. Problem Tree

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

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

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

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

13. SWOT Analysis

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

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

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

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

14. Agreement-Certainty Matrix

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

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

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

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

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

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

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

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

16. Speed Boat

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

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

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

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

17. The Journalistic Six

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

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

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

18. LEGO Challenge

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

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

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

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

19. What, So What, Now What?

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

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

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

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

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

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

20. Journalists

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

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

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

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

Problem-solving techniques for developing solutions

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

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

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

21. Mindspin

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

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

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

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

22. Improved Solutions

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

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

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

23. Four Step Sketch

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

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

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

24. 15% Solutions

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

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

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

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

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

25. How-Now-Wow Matrix

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

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

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

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

26. Impact and Effort Matrix

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

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

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

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

27. Dotmocracy

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

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

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

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

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

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

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

28. Check-in / Check-out

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

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

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

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

29. Doodling Together

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

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

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

30. Show and Tell

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

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

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

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

31. Constellations

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

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

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

32. Draw a Tree

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

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

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

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

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

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

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

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

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

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

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

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

33. One Breath Feedback

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

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

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

34. Who What When Matrix

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

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

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

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

35. Response cards

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

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

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

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

Save time and effort discovering the right solutions

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

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

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

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

Over to you

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

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

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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

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Synonyms of problem

as in challenge
as in question
as in troublesome
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Thesaurus Definition of problem

(Entry 1 of 2)

Synonyms & Similar Words

predicament
Gordian knot
sticky wicket
brainteaser

Antonyms & Near Antonyms

silver bullet
magic bullet
interrogative

Thesaurus Definition of problem (Entry 2 of 2)

troublesome
complicated

problematic

inconvenient
problematical
importunate
discommoding
straightforward
uncomplicated
unproblematic
undemanding

Synonym Chooser

How does the noun problem differ from other similar words?

Some common synonyms of problem are enigma , mystery , puzzle , and riddle . While all these words mean "something which baffles or perplexes," problem applies to a question or difficulty calling for a solution or causing concern.

In what contexts can enigma take the place of problem ?

While the synonyms enigma and problem are close in meaning, enigma applies to utterance or behavior that is very difficult to interpret.

When could mystery be used to replace problem ?

Although the words mystery and problem have much in common, mystery applies to what cannot be fully understood by reason or less strictly to whatever resists or defies explanation.

Where would puzzle be a reasonable alternative to problem ?

The words puzzle and problem are synonyms, but do differ in nuance. Specifically, puzzle applies to an enigma or problem that challenges ingenuity for its solution.

When might riddle be a better fit than problem ?

In some situations, the words riddle and problem are roughly equivalent. However, riddle suggests an enigma or problem involving paradox or apparent contradiction.

Articles Related to problem

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Thesaurus Entries Near problem

Cite this entry.

“Problem.” Merriam-Webster.com Thesaurus , Merriam-Webster, https://www.merriam-webster.com/thesaurus/problem. Accessed 8 Jun. 2024.

Can you solve 4 words at once?

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noun as in difficulty; bad situation

Strongest matches

complication

Strong matches

botheration
disagreement
predicament

Weak matches

can of worms
disputed point
point at issue

noun as in puzzle, question

illustration
brainteaser
cliff-hanger
mind-boggler
sixty-four thousand dollar question

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Example sentences.

We can now create video-game quality simulations to evaluate complex skills like creativity or problem-solving.

The competition will be an ersatz astronaut training program of sorts, including physical challenges, as well as puzzles and problem-solving tasks, as well as emotionally challenging scenarios, according to Deadline.

Lindsey Graham has changed after 25 years in Washington into someone who puts his political fortunes ahead of problem-solving.

When you have armed soldiers on the streets, I think, as a public affairs officer, that’s a perception problem in and of itself.

The problem in Venezuela is not the oil, it’s the political system.

Several times, either because they forgot or they had a technical problem, they connected directly, and we could see them.

Every once in a while, they act swiftly and acknowledge the problem.

Part of the problem is the mandate of the war and the means with which the U.S. is fighting it do not match up.

The third problem is the evidence of corroborating witnesses.

But this physical involvement, or lack of it, is only part of the problem.

And now let me come to the second problem we opened up in connection with college education—the problem of its extension.

No man can believe it who tests it by his reason in the same way in which he would test any modern problem.

But the essential problem of to-day is to know how far we are to depart from its principles.

We notice that more attention is given to the problem of placing a feature than to that of making a likeness of it.

But the West is not in its essence a time problem; there, they can wait—next week—next month.

Related Words

Words related to problem are not direct synonyms, but are associated with the word problem . Browse related words to learn more about word associations.

noun as in trouble

deep trouble
dire straits
disappointment
inconvenience

noun as in difference of opinion

altercation
apple of discord
controversy
grounds for war
matter at hand
point in question
tender spot

noun as in trouble, inconvenience

aggravation
exasperation
molestation
pain in the neck

noun as in annoyance

disturbance

Viewing 5 / 73 related words

On this page you'll find 128 synonyms, antonyms, and words related to problem, such as: complication, dilemma, dispute, headache, issue, and obstacle.

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Strategies for Solving Word Problems – Math

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

Circle any numbers you’ll use.
Lightly cross out any information you don’t need.
Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

3rd Grade Math Task Cards Mega Bundle | 3rd Grade Math Centers Bundle

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

th Grade 960 Math Task Cards Mega Bundle | 4th Grade Math Centers

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

5th Grade Math Task Cards Mega Bundle - 5th Grade Math Centers

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

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10 Best Strategies for Solving Math Word Problems

$Solving word problem chart$

1. Understand the Problem by Paraphrasing

2. identify key information and variables, 3. translate words into mathematical symbols, 4. break down the problem into manageable parts, 5. draw diagrams or visual representations, 6. use estimation to predict answers, 7. apply logical reasoning for unknown variables, 8. leverage similar problems as templates, 9. check answers in the context of the problem, 10. reflect and learn from mistakes.

Have you ever observed the look of confusion on a student’s face when they encounter a math word problem ? It’s a common sight in classrooms worldwide, underscoring the need for effective strategies for solving math word problems . The main hurdle in solving math word problems is not just the math itself but understanding how to translate the words into mathematical equations that can be solved.

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Generic advice like “read the problem carefully” or “practice more” often falls short in addressing students’ specific difficulties with word problems. Students need targeted math word problem strategies that address the root of their struggles head-on.

A Guide on Steps to Solving Word Problems: 10 Strategies

One of the first steps in tackling a math word problem is to make sure your students understand what the problem is asking. Encourage them to paraphrase the problem in their own words. This means they rewrite the problem using simpler language or break it down into more digestible parts. Paraphrasing helps students grasp the concept and focus on the problem’s core elements without getting lost in the complex wording.

Original Problem: “If a farmer has 15 apples and gives away 8, how many does he have left?”

Paraphrased: “A farmer had some apples. He gave some away. Now, how many apples does he have?”

This paraphrasing helps students identify the main action (giving away apples) and what they need to find out (how many apples are left).

Play these subtraction word problem games in the classroom for free:

Students often get overwhelmed by the details in word problems. Teach them to identify key information and variables essential for solving the problem. This includes numbers , operations ( addition , subtraction , multiplication , division ), and what the question is asking them to find. Highlighting or underlining can be very effective here. This visual differentiation can help students focus on what’s important, ignoring irrelevant details.

Encourage students to underline numbers and circle keywords that indicate operations (like ‘total’ for addition and ‘left’ for subtraction).
Teach them to write down what they’re solving for, such as “Find: Total apples left.”

Problem: “A classroom has 24 students. If 6 more students joined the class, how many students are there in total?”

Key Information:

Original number of students (24)
Students joined (6)
Looking for the total number of students

Here are some fun addition word problems that your students can play for free:

The transition from the language of word problems to the language of mathematics is a critical skill. Teach your students to convert words into mathematical symbols and equations. This step is about recognizing keywords and phrases corresponding to mathematical operations and expressions .

Common Translations:

“Total,” “sum,” “combined” → Addition (+)
“Difference,” “less than,” “remain” → Subtraction (−)
“Times,” “product of” → Multiplication (×)
“Divided by,” “quotient of” → Division (÷)
“Equals” → Equals sign (=)

Problem: “If one book costs $5, how much would 4 books cost?”

Translation: The word “costs” indicates a multiplication operation because we find the total cost of multiple items. Therefore, the equation is 4 × 5 = $20

Complex math word problems can often overwhelm students. Incorporating math strategies for problem solving, such as teaching them to break down the problem into smaller, more manageable parts, is a powerful approach to overcome this challenge. This means looking at the problem step by step rather than simultaneously trying to solve it. Breaking it down helps students focus on one aspect of the problem at a time, making finding the solution more straightforward.

Problem: “John has twice as many apples as Sarah. If Sarah has 5 apples, how many apples do they have together?”

Steps to Break Down the Problem:

Find out how many apples John has: Since John has twice as many apples as Sarah, and Sarah has 5, John has 5 × 2 = 10

Calculate the total number of apples: Add Sarah’s apples to John’s to find the total, 5 + 10 = 15

By splitting the problem into two parts, students can solve it without getting confused by all the details at once.

Explore these fun multiplication word problem games:

Diagrams and visual representations can be incredibly helpful for students, especially when dealing with spatial or quantity relationships in word problems. Encourage students to draw simple sketches or diagrams to represent the problem visually. This can include drawing bars for comparison, shapes for geometry problems, or even a simple distribution to better understand division or multiplication problems .

Problem: “A garden is 3 times as long as it is wide. If the width is 4 meters, how long is the garden?”

Visual Representation: Draw a rectangle and label the width as 4 meters. Then, sketch the length to represent it as three times the width visually, helping students see that the length is 4 × 3 = 12

Estimation is a valuable skill in solving math word problems, as it allows students to predict the answer’s ballpark figure before solving it precisely. Teaching students to use estimation can help them check their answers for reasonableness and avoid common mistakes.

Problem: “If a book costs $4.95 and you buy 3 books, approximately how much will you spend?”

Estimation Strategy: Round $4.95 to the nearest dollar ($5) and multiply by the number of books (3), so 5 × 3 = 15. Hence, the estimated total cost is about $15.

Estimation helps students understand whether their final answer is plausible, providing a quick way to check their work against a rough calculation.

Check out these fun estimation and prediction word problem worksheets that can be of great help:

$Card Image$

When students encounter problems with unknown variables, it’s crucial to introduce them to logical reasoning. This strategy involves using the information in the problem to deduce the value of unknown variables logically. One of the most effective strategies for solving math word problems is working backward from the desired outcome. This means starting with the result and thinking about the steps leading to that result, which can be particularly useful in algebraic problems.

Problem: “A number added to three times itself equals 32. What is the number?”

Working Backward:

Let the unknown number be x.

The equation based on the problem is x + 3x = 32

Solve for x by simplifying the equation to 4x=32, then dividing by 4 to find x=8.

By working backward, students can more easily connect the dots between the unknown variable and the information provided.

Practicing problems of similar structure can help students recognize patterns and apply known strategies to new situations. Encourage them to leverage similar problems as templates, analyzing how a solved problem’s strategy can apply to a new one. Creating a personal “problem bank”—a collection of solved problems—can be a valuable reference tool, helping students see the commonalities between different problems and reinforcing the strategies that work.

Suppose students have solved a problem about dividing a set of items among a group of people. In that case, they can use that strategy when encountering a similar problem, even if it’s about dividing money or sharing work equally.

It’s essential for students to learn the habit of checking their answers within the context of the problem to ensure their solutions make sense. This step involves going back to the original problem statement after solving it to verify that the answer fits logically with the given information. Providing a checklist for this process can help students systematically review their answers.

Checklist for Reviewing Answers:

Re-read the problem: Ensure the question was understood correctly.
Compare with the original problem: Does the answer make sense given the scenario?
Use estimation: Does the precise answer align with an earlier estimation?
Substitute back: If applicable, plug the answer into the problem to see if it works.

Problem: “If you divide 24 apples among 4 children, how many apples does each child get?”

After solving, students should check that they understood the problem (dividing apples equally).

Their answer (6 apples per child) fits logically with the number of apples and children.

Their estimation aligns with the actual calculation.

Substituting back 4×6=24 confirms the answer is correct.

Teaching students to apply logical reasoning, leverage solved problems as templates, and check their answers in context equips them with a robust toolkit for tackling math word problems efficiently and effectively.

One of the most effective ways for students to improve their problem-solving skills is by reflecting on their errors, especially with math word problems. Using word problem worksheets is one of the most effective strategies for solving word problems, and practicing word problems as it fosters a more thoughtful and reflective approach to problem-solving

These worksheets can provide a variety of problems that challenge students in different ways, allowing them to encounter and work through common pitfalls in a controlled setting. After completing a worksheet, students can review their answers, identify any mistakes, and then reflect on them in their mistake journal. This practice reinforces mathematical concepts and improves their math problem solving strategies over time.

3 Additional Tips for Enhancing Word Problem-Solving Skills

Before we dive into the importance of reflecting on mistakes, here are a few impactful tips to enhance students’ word problem-solving skills further:

1. Utilize Online Word Problem Games

Incorporate online games that focus on math word problems into your teaching. These interactive platforms make learning fun and engaging, allowing students to practice in a dynamic environment. Games can offer instant feedback and adaptive challenges, catering to individual learning speeds and styles.

Here are some word problem games that you can use for free:

2. Practice Regularly with Diverse Problems

Consistent practice with a wide range of word problems helps students become familiar with different questions and mathematical concepts. This exposure is crucial for building confidence and proficiency.

Start Practicing Word Problems with these Printable Word Problem Worksheets:

$Card Image$

3. Encourage Group Work

Solving word problems in groups allows students to share strategies and learn from each other. A collaborative approach is one of the best strategies for solving math word problems that can unveil multiple methods for tackling the same problem, enriching students’ problem-solving toolkit.

Conclusion

Mastering math word problems is a journey of small steps. Encourage your students to practice regularly, stay curious, and learn from their mistakes. These strategies for solving math word problems are stepping stones to turning challenges into achievements. Keep it simple, and watch your students grow their confidence and skills, one problem at a time.

Frequently Asked Questions (FAQs)

How can i help my students stay motivated when solving math word problems.

Encourage small victories and use engaging tools like online games to make practice fun and rewarding.

What's the best way to teach beginners word problems?

Begin with simple problems that integrate everyday scenarios to make the connection between math and real-life clear and relatable.

How often should students practice math word problems?

Regular, daily practice with various problems helps build confidence and problem-solving skills over time.

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Appendix A: Applications

Apply a problem-solving strategy to basic word problems, learning outcomes.

Practice mindfulness with your attitude about word problems
Apply a general problem-solving strategy to solve word problems

Approach Word Problems with a Positive Attitude

The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?

Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in the cartoon below?

A cartoon image of a girl with a sad expression writing on a piece of paper is shown. There are 5 thought bubbles. They read,

Negative thoughts about word problems can be barriers to success.

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts like the student in the cartoon below. Read the positive thoughts and say them out loud.

A cartoon image of a girl with a confident expression holding some books is shown. There are 4 thought bubbles. They read,

When it comes to word problems, a positive attitude is a big step toward success.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn’t do three years ago. Whether it’s driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

Use a Problem-Solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then you’ve increased your math vocabulary as you learned about more algebraic procedures, and you’ve had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we’ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We’ll demonstrate the strategy as we solve the following problem.

Pete bought a shirt on sale for $[latex]18[/latex], which is one-half the original price. What was the original price of the shirt?

Solution: Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

Let [latex]p=[/latex] the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

Step 6. Check the answer in the problem and make sure it makes sense.

We found that [latex]p=36[/latex], which means the original price was [latex]\text{\$36}[/latex]. Does [latex]\text{\$36}[/latex] make sense in the problem? Yes, because [latex]18[/latex] is one-half of [latex]36[/latex], and the shirt was on sale at half the original price.

Step 7. Answer the question with a complete sentence.

The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was [latex]\text{\$36}[/latex].”

If this were a homework exercise, our work might look like this:

We list the steps we took to solve the previous example.

Problem-Solving Strategy

Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the internet.
Identify what you are looking for.
Name what you are looking for. Choose a variable to represent that quantity.
Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
Solve the equation using good algebra techniques.
Check the answer in the problem. Make sure it makes sense.
Answer the question with a complete sentence.

For a review of how to translate algebraic statements into words, watch the following video.

Let’s use this approach with another example.

Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[/latex] apples to the picnic. How many bananas did he bring?

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

Nga’s car insurance premium increased by [latex]\text{\$60}[/latex], which was [latex]\text{8%}[/latex] of the original cost. What was the original cost of the premium?

Write Algebraic Expressions from Statements: Form ax+b and a(x+b). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Hub7ku7UHT4 . License : CC BY: Attribution
Question ID 142694, 142722, 142735, 142761. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License, CC-BY + GPL
Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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Word problem situations and the best way to build student confidence

by Jennifer Van Blair | Oct 12, 2022 | Math

A few years ago, my students tanked a word problem situations assessment. When talking with my principal at the time, he said, “If we improve students’ reading abilities, then their word problem understanding will improve also.”

Intrigued by this thought, I looked at the scores on this assessment focusing on at level readers. The assumption is that if students struggle to read, then they will struggle with word problems as well. Before I tell you what the data showed, let’s take a little quiz:

Guess what the data actually showed? Of the students that were at level readers, only 3 of them passed the assessment. 70% of my at level readers had failed the test. So the claim that if we focus on improving reading in order to increase math scores was false from my own personal experience.

What was the problem then? If students could solve the same types of problems when presented to them from a procedural standpoint, but failed when the same type of operation was required in a word problem situation, the issue was related to the way I was teaching word problems in the first place, not reading comprehension.

How do we teach word problem situations?

My first year teaching, I remember sitting in another teacher’s classroom during a professional development.

Hanging on the wall was a set of steps for solving word problems. At the time, I thought this was a novel idea, so I snapped a picture so that I could make my own version of it in my classroom. I made it and used it for a few years. Let me tell you right now, word problem situation success DID NOT improve.

Being in the classroom for over 10 years, and being an avid user of Pinterest and Instagram, I found that this model, known as CUBES, was not novel.

The idea is that we want to make word problems as simple as possible for your students. So, we use a set of repeatable steps and simplify the process. We think our students will be more successful because we have simplified word problem situations. However, circling numbers, boxing keywords, and underlining the question does little for our students.

Boxing keywords and placing a bulletin board doesn’t improve student success. Neither does a keyword bulletin board. It does lead to a lack of understanding when it comes to solving word problem situations. It was shown that students who rely on keyword identification strategies, rather than comprehending word problems as the stories that they are, are MORE often incorrect.

Word problems are stories. When we teach reading, we teach our students to identify story elements like characters, setting, and plot. This allows them to check their understanding. We encourage them to visualize the story. The same strategies work with story problems also. Word problem situation instruction needs to be more than just a reduced formula of circle, box, and underline.

Genres of Word Problem Situations:

Just as stories come in a variety of genres, word problems come in a variety of types. At the elementary level, there are eight different types of word problem situations commonly encountered:

$word problem situations$

Brain science, specifically cognitive load theory , states that by building familiarity with lower level concepts, more brain power can be devoted to higher level thinking skills.

Deciding what operations should be used to solve a problem is a higher level thinking skill. A similar study focused on how experts approach new types of physics problems.

The shorthand version of this research showed that experts relied on previous problems they encountered, the associated equations and operations they used to solve those problems, and decided if those same solutions were useful with this new type of problem.

They were MORE accurate than novices at approaching these same problems.. The freshman physics students who lacked the experience with these problem types and the associated equations to solve were MORE often wrong as they relied on keywords to help decide what to do.

As math teachers this means that we need to give our students opportunities to work with word problem situations. They need experiences in solving them. This will broaden their depth of knowledge for future problem solving situations.

Word Problem Situation Sorts:

How do we do this? Word Problem Sorts are a fantastic way to help students develop their understanding of word problem situations. The best part is, you probably have a number of examples of word problems that you can use already at your fingertips.

You have access to your:

School adopted curriculum
Task cards for different word problem situations

My favorite type of word problem sorts are those that involve numberless word problems.

When we remove the numbers from word problems, we are focusing student attention NOT on actually solving the problem, but the context of the situation. Instead of having students solve the problems, asking students to think about what kind of problems these are and classify them accordingly is more meaningful in developing their understanding of word problem situations.

How do you do a word problem situations sort:

Keep it simple:.

Decide if you are going to focus on ALL eight types of word problems, or one or two types.
Deciding to use ALL eight types is a great beginning and end of the year activity. Why? This is a wonderful time to get to know your students, their thoughts, feelings and experiences with word problems. Furthermore, it gives you a baseline of understanding to track student progress over the year.
Even if you choose one word problem type, within it there are three different types of situations that arise. Take for example ADD TO PROBLEMS . You have the starting amount, the difference, and the RESULT. This means, depending on what information you do or do not have, you can have problems that have the TOTAL (result), the STARTING amount, or that have the DIFFERENCE. In this one problem type, your students will have to discuss if they would need to ADD to find the solution, or subtract.
Choosing two or three different problem types may be beneficial on a unit about MULTIPLICATION. Situations that call for multiplication include AREA PROBLEMS, ARRAY PROBLEMS, and EQUAL GROUP PROBLEMS. Having students sort problems based on the type of word problem situation is a great way to focus students on context clues when deciding the types of word problems they are working on.

Split students into groups

In order to increase participation and support learning in a large group setting, having students work in pairs, or triads at the most, gives students more opportunities to engage in the learning process. Quiet students feel more comfortable talking in a small group setting. It is important to consider the equity of experiences and opportunities for students to engage with word problems. Small groups increase access to content, and help reluctant students to participate more.

Give student groups either the SAME set of cards with the same problems, or split situations up among the WHOLE class.

Either of these methods will give students opportunities to discuss, listen to other groups, and discuss whether or not they agree with their classmates.

If you are using a small set of cards with each small group getting one card, display the types of word problems or situations that the class has. For example, you could tell the class that some word problems require one of the four operations, and that there are ONLY 2 of each operation in the entire class.

Student groups can then make their case for which operation they believe their situation calls for in order to solve and why. With either approach, your students are going to be talking, discussing, and thinking at a higher level during your math block time.

Keep it a mystery

Instead of justifying student responses as correct or incorrect, leave it till the end. Hold out the reveal, allowing for lively debate and drama in your math class. Imagine if there were only two situation cards that called for MULTIPLICATION, but 3 groups claimed that their word problem called for this operation? You have created drama and left students in a state of dilemma, a time of TRUE mathematical growth according to Joan Boaler in her book Mathematical Mindsets .

To conclude, and to help you get started with a word problem sort, I have a set of 8 word problems for you to try in your classroom.

These problems are NUMBERLESS, so they can be used in any upper elementary classroom. I invite you to try them with your students and focus not on solving these problems, but in sparking lively debate and discussion in your math classroom.

Don’t forget to come back and share in the comments how it went.

Want to learn more? I have created a course on PopPD ALL about word problems. I walk you through my three step approach to building confident word problem solvers. Check it out!

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Bridging the labor mismatch in US construction

The US construction sector seems set for a jobs boom. The US Bipartisan Infrastructure Law projects $550 billion of new infrastructure investment over the next decade, which our modeling suggests could create 3.2 million new jobs across the nonresidential construction value chain. That’s approximately a 30 percent increase in the overall US nonresidential construction workforce, which would mean 300,000 to 600,000 new workers entering the sector—every year.

This is a big ask for an industry that is already struggling to find the people it needs. In October 2021, 402,000 construction positions 1 Included both nonresidential and residential construction openings. Further granularity is not available from the US Bureau of Labor Statistics. remained unfilled at the end of the month, the second-highest level recorded since data collection began in December 2000.

In this environment, wages have already increased significantly since the onset of the COVID-19 pandemic, reflecting intense competition for employees, with employers offering higher pay or other nonwage benefits. Between December 2019 and 2021, construction wages grew by 7.9 percent. 2 Quarterly Census of Employment and Wages, US Bureau of Labor Statistics. Competition from other sectors for the same pool of labor is heating up, too. For example, over the same period, transportation and warehousing wages grew by 12.6 percent. The prospect of higher pay and better working conditions is already tempting experienced workers away from construction and into these and other sectors.

No end in sight

Today’s mismatches are likely to persist because of structural shifts in the labor market. The relationship between job openings and unemployment has departed from historical trends. In January 2022—two years from the start of the pandemic—the US unemployment rate stood at 4.0 percent, close to its prepandemic level of 3.5 percent. Job openings remained exceptionally high, however, with 10.9 million unfilled positions as of the end of December 2021, compared with 5.9 million in December 2019.

This labor supply imbalance has multiple root causes, some shorter term and cyclical while others are more structural in nature. For example, the pandemic brought forward the retirements of many in the baby-boomer generation, with an estimated 3.2 million leaving the workforce in 2020—over a million more than in any year before 2016. According to the American Opportunity Survey , among those who are unemployed, concerns about physical health, mental health, and lack of childcare remain the dominant impediments preventing reentry into the workforce. Research on the “Great Attrition/Great Attraction” also highlights the importance of nonwage components of the employee value proposition. Record job openings and quit rates highlight employees’ growing emphasis on feeling valued by their organization, supportive management, and flexibility and autonomy at work.

Additionally, the pipeline of new construction workers is not flowing as freely as it once did. Training programs have been slow to restart operations after pandemic-driven safety concerns led to their suspension the spring of 2020. The industry is finding it more difficult to attract the international workforce that has been an important source of talent for engineering, design, and contracting activities. Net migration has been falling since 2016, a trend accelerated by COVID-19 travel restrictions. 3 Population estimates, US Census Bureau. Between 2016 and 2021, net migration declined steadily from 1.06 million to 244,000.

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Impact on projects.

The interconnected nature of the construction value chain means that the labor mismatch generates knock-on effects across the project life cycle and supply chain. By late 2021, project owners were reporting that up to 25 percent of material deliveries to sites were either late or incomplete. In project execution, the combination of higher hourly rates, premiums and incentives, and overtime payments was resulting in overall labor costs as much as double prepandemic levels. Meanwhile, difficulty accessing skilled and experienced people was leading some owners to report project delays related to issues around the quality and productivity of on-site work.

In some US cities and their suburbs, wage growth has surpassed the level seen in core Gulf Coast counties at the height of the shale oil boom. Labor shortages in the shale sector drove wages up by 5 to 10 percent and were correlated with steep drops in productivity. The productivity of some tasks fell by 40 percent or more during shale construction peaks (exhibit), and overall productivity declined by about 40 percent per year when labor was in short supply. This forced owners to extend project timelines by 20 to 25 percent. The impact of a long-term, nationwide labor mismatch might be even more severe than the shale industry’s experience, given that oil companies were able to attract new workers from around the country.

Getting back into balance

The labor mismatch in the construction sector is bad today, and set to get worse. To avoid a decade or more of rising costs, falling productivity, and ever-increasing project delays, companies in the industry should consider thoughtful actions now.

Those actions could address three components of the challenge. First, companies could do everything possible to maximize productivity through measures aimed at improving efficiency across the value chain. Second, they could expand the pool of available labor by doubling down on accessing diverse talent and working harder to retain the employees already in their organization. Finally, they could consider making labor a strategic priority, with senior leadership attention within companies.

Improving construction productivity

Companies could access a range of levers to reduce the labor content required per job and drive to improve productivity in project development and delivery. Those levers involve changes to project designs and fresh thinking about when, where, and how work is done.

Improvements in productivity occur long before work starts on the ground. They include rigorous control of project scope, design simplification, and standardization. Increasing the use of off-site and modular construction , for example, could allow projects to capture multiple benefits, including accelerated design cycles; the greater productivity associated with industrialized, factory floor manufacturing techniques; automation; and less time spent on site.

Smarter execution management, enabled by digital technologies and analytics techniques could drive better, faster decision making during project delivery. Real-time data collection, for example, gives project managers earlier, more detailed insights about progress, allowing them to intervene more effectively to maintain productivity and keep projects on track. Intelligent simulation software allows teams to evaluate hundreds of thousands of possible critical paths, identifying approaches that could be more efficient or less risky than the conventional wisdom.

Lean construction is another proven way to drive significant and sustainable productivity improvements. Establishing a centralized, continuous improvement engine could enhance on-site execution through integrated planning, performance management, and waste elimination. Key stakeholders across the project work with a common, agreed set of key performance indicators. That allows them to address issues in real time and facilitates collaboration to reduce waste and variability work. Capability building across the planning and construction teams could help team members understand and adopt lean construction practices.

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Reimagining talent.

To ensure access to the skills they need, construction sector companies can accelerate the onboarding of recruits, boost retention by revisiting what employees want beyond wages, and invest more in developing their pipelines of future workers.

In the near term, employers could prioritize review of job applications and reduce the number of steps in both the interview and onboarding process. In the medium term, both the public and private sectors could look to reduce hiring timelines and shift to a skills-based approach when hiring.

In the medium term, retaining current staff and attracting new talent will both turn on understanding of what employees value beyond wages. Competitive wages are now table stakes, so employees are thinking about a broader set of benefits and workplace characteristics when making decisions about where to work. Research on attrition in the postpandemic workplace has shown that they are placing more emphasis on autonomy, flexibility, support, and upward mobility.

In the longer term, the construction industry can consider a new approach to talent attraction, development, and retention. Talent acquisition could begin early, through partnerships with educational institutions including universities, colleges, and high schools. These partnerships could boost awareness of the possibilities of a career in the sector and ensure future employees have appropriate skills prior to onboarding.

Companies could also look more widely for potential recruits, considering individuals who have taken alternative educational paths, such as technical degrees or hands-on experience. The Rework America Alliance , a Markle-led coalition in which McKinsey is a partner, illustrates the importance of skills-based, rather than credential-based, hiring. A skills-based perspective is key to tapping into the talents of the 106 million workers who have built capabilities through experience but whose talents are often unrecognized because they don’t have a four-year college degree. A skills-based approach could be complemented by reimagining apprenticeships to bring younger students and vocational talent into the industry at an earlier stage in their careers.

Employers could consider working with a range of nontraditional sources of talent, including veteran-transition programs, formerly incarcerated individuals, and others. Homeboy Industries provides an example of the local impact, effectiveness, and potential of working with often overlooked population segments. Moreover, identifying and attracting talent from outside the traditional paths used by the construction industry could also help it to increase the diversity of its workforce. Today, 88 percent of the sector’s workforce is White and 89 percent is male. 4 Labor Force Statistics from the Current Population Survey Database, US Bureau of Labor Statistics, accessed March 10, 2022.

Looking at labor through a strategic lens

Labor and skills shortages have the potential to slow growth and erode profitability across the construction value chain. For C-suites, there’s no other single issue that could protect against significant cost erosion. Companies could consider establishing a systematic talent acquisition and retention program, led by a C-level executive and a core part of the CEO agenda. That program could first be tasked with building a robust fact base on current and emerging labor needs and availability gaps. It could then identify a bold set of initiatives that address labor-related issues across the value chain. This exercise starts in the boardroom, but it doesn’t stop there. Leadership will likely need to be increasingly present in the field and on the job site too, celebrating and recognizing top talent throughout the organization.

The labor challenge extends well beyond corporate boundaries. Since the successful delivery of a project could be jeopardized by labor shortages in a single value-chain participant, project owners and contractors may want to adapt the structure of project relationships and contracts. Moving away from traditional contracting methods to collaborative contracts , for example, allows participants to share market risks and opportunities as a project evolves, rather than baking in worst-case estimates at the outset of negotiations.

The US construction sector is poised to revitalize, replace, and expand the country’s infrastructure. Done right, that will power inclusive growth and set up the economy for success in the 21st century. To do so, the sector will need to address its labor challenges. That calls for the application of a diverse set of tools and approaches to create better jobs, get the most out of its people, and optimize agility and collaboration across the value chain.

Garo Hovnanian is a partner in McKinsey’s Philadelphia office, Ryan Luby is a senior knowledge expert in the New York office, and Shannon Peloquin is a partner in the Bay Area office.

The authors wish to thank Tim Bacon, Luis Campos, Roberto Charron, Justin Dahl, Rebecca de Sa, Bonnie Dowling, Bryan Hancock, Rawad Hasrouni, Adi Kumar, Jonathan Law, Michael Neary, Nikhil Patel, Gaby Pierre, Jose Maria Quiros, Kurt Schoeffler, Shubham Singhal, Stephanie Stefanski, Jennifer Volz, and Jonathan Ward for their contributions to this article.

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Why Is the North Korea Problem So Hard to Solve?

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The North Korea problem is set to get worse before it gets better. North Korea continues to perfect the reentry technology, targeting capability, and solid-fuel missiles that will dramatically increase the potency and reach of its nuclear weapons, overwhelm missile defenses on the Korean Peninsula, and threaten America’s homeland and allies in Asia. There are even renewed expectations of a seventh nuclear test or some other provocation timed to make a splash before the U.S. presidential election.

In January, North Korean leader Kim Jong Un publicly designated South Korea as his country’s “primary enemy” and renounced peaceful unification, essentially rolling back a decades-long unification policy supported by his forefathers. These moves take on extra significance when viewed against the backdrop of Pyongyang’s geopolitical shift toward embracing autocracies and the Kim regime’s consistent calls for “war preparations” since early 2023. Meanwhile, Pyongyang is bear-hugging Moscow, sending it artillery and missiles in return for much-needed supplies like food and oil and possibly even military technology .

The result is an approaching crisis that calls for a recalibrated approach. As in years past, the North Korea policy debate has hardened into competing camps. One side wants to double down on deterrence and complete denuclearization, and the other wants engagement and arms control. If nothing else, the two camps agree that the status quo is unsustainable. And neither side is advocating for a modern incarnation of the “strategic patience” policy practiced during the Obama administration. And yet, without another plan, Washington will be stuck with a policy of not-so-strategic patience.

Today’s challenges stem from North Korea’s complex history, U.S.-North Korean system incompatibility, path dependency, decades of mistrust, and North Korea’s evolving strategic priorities. To overcome these challenges, we recommend forgoing a grand bargain in favor of a more incremental approach. This should combine deterrence, assurance, and engagement to build incentives for progress that can succeed whether or not Kim Jong Un comes to the table.

Histor of Complexity

The origins of the North Korea problem stem from Japanese colonialism, America’s broken promise to come to Korea’s aid in 1882, and a post–World War II trusteeship that set the stage for the peninsula’s ongoing ideological rivalry. The North Korean invasion that followed, green-lit by the Soviet Union and rescued from the jaws of defeat by Communist China, triggered a civil war that evolved into a regional war and a satellite war. The conflict threatened to escalate into a nuclear superpower showdown. While that thankfully never happened, the Korean War nonetheless initiated the pattern of Cold War proxy confrontation that continues to this day. At the end of the war, two years of difficult talks culminated in an uneasy armistice that remains in force, so the belligerents are stuck in a technical state of war until a political solution is reached.

North Korea’s decision making has always been affected by the wider geopolitical context. Kim Il Sung boldly ignored Soviet leader Nikita Khrushchev’s direct guidance to dial down his cult of personality and embrace pluralistic governance. Over the years, Moscow and Beijing have both struggled to control their junior partner. As former Chinese Communist Party Chairman Mao Zedong told a Soviet diplomat in 1956, North Korea ignores China’s advice “100 percent” of the time, while it “listens to you” 70 percent of the time. During the Sino-Soviet split, the animosity between Beijing and Moscow was the crucial factor Kim needed to secure defense pacts from both countries, working each against the other.

The mistrust cuts both ways. Although the Soviets helped North Korea establish a nuclear reactor at Yongbyon in the 1950s, Pyongyang’s leaders didn’t fully commit to developing nuclear weapons until the 1970s, as they grew concerned about the credibility of their patrons and warily witnessed South Korea’s economic ascendance. The lesson for North Korea? Perhaps that when it courts multiple patrons, it can minimize their influence while maximizing benefits. We may be seeing echoes of this approach today as Kim courts Russian President Vladimir Putin while keeping China at arm’s length .

The same context has informed North Korea’s guns-versus-butter thinking. From the early postwar years, the Kim regime engaged in an economic policy debate over accumulation (investment) versus consumption, sometimes leading to dueling narratives on national defense and the civilian economy. This debate began as early as the mid-1950s and continues to this day.

After the armistice, different factions within the North Korean leadership waged a tug-of-war over whether to give priority to heavy industry (accumulation) or light industry and agriculture (consumption). Though Kim was pressured by the Soviets to find a balanced approach — giving priority to heavy industry while developing light industry and agriculture at the same time — his preference was always to improve the economy by prioritizing heavy industry. The turning point came in 1961 and 1962, when the Soviet Union instilled a “fear of abandonment” in North Korea. Moscow parted ways with the Chinese and Albanian communist parties, and during the Cuban missile crisis, it reached a deal with the United States, which Kim Il Sung viewed as a betrayal of its Cuban ally. These events prompted North Korea to adopt a policy of simultaneous economic and defense development (the country’s original byungjin policy) in December 1962, in effect giving priority to national defense.

Contemporary North Korea is the consequence of those unsolved legacy problems compounded over time. The Kim family regime continually chooses guns over butter, so while the domestic economy languishes , the military has made major strides in developing advanced weapons systems. Today, North Korea presents a conventional, nuclear, chemical, and biological threat, which is also a global proliferation problem and a dangerous precedent eroding the sustainability of the Treaty on the Non-Proliferation of Nuclear Weapons. North Korea’s example is now a veritable roadmap for rogue states seeking nuclear weapons: Just grit your teeth and suffer sanctions for a while, and you too can own your own nukes and threaten your neighbors .

Policy Shift Meets Policy Inertia

There is a political cost in both Washington and Pyongyang for the compromises needed to move the ball forward. Both the United States and North Korea have thus become loss-averse, prioritizing the avoidance of setbacks over the prospect of making gains. Stubbornness has further become part and parcel of the strategic approach.

For the United States, it’s about path dependency, the process whereby policymaking becomes hardened and resistant to change, even as it no longer serves America’s interests. Although most U.S. analysts will concede that complete denuclearization is not feasible (or never was), no U.S. president wants to go down in history as having given up on that goal. Washington is unwilling to abandon denuclearization and also unwilling to confront the possibility that America may not be able to convince North Korea to denuclearize no matter what incentives are offered. That’s because North Korea’s nuclear weapons are not simply for defensive purposes: They are also intended to achieve a coercive effect, mobilize regime support, and hedge against overreliance on China and Russia.

North Korea also has its own calculus and unique and difficult to interpret ways of communicating its bargaining position. Some analysts forget that, amid the pageantry and fanfare of a sit-down summit, Kim Jong Un lost face when the prospects for a deal disintegrated during his second summit with Donald Trump in Hanoi. Although Kim is the undisputed leader of a unitary autocratic system, he nonetheless has a constituency of elites to answer to . Pyongyang complains of America’s “hostile policy” and has previously made denuclearization contingent on its removal. But when pushed by American diplomats to define what this means, the North Korean interlocutors won’t (or can’t). Although North Korea does not have a formal definition of “hostile policy,” a review of the country’s official statements and media commentary shows that it covers a broad range of issues that Pyongyang views as tarnishing its image or posing a threat to its regime security — from discussions of North Korea’s human rights conditions to sanctions and U.S.-South Korean combined military drills . A maximum and ambiguous definition is useful for creating negotiating space, and the trumped-up existential security threat is a handy pretext for the regime’s totalitarian control.

Further complicating the North Korea conundrum for U.S. policymakers are the apparent strategic policy shifts that Pyongyang has undertaken in recent years. The root of these shifts can be traced back to the collapse of the Hanoi summit and the lack of a diplomatic breakthrough between the two countries by the end of 2019. Kim Jong Un’s warning at the end of 2019 of a “long confrontation” with the United States accurately predicted where the North would be headed. Over the next five years, it would take a number of provocative steps. First, Pyongyang announced a five-year defense development plan centered on advancing nuclear capabilities. It also resume d intercontinental ballistic missile testing that it had suspended in April 2018 and declare d that “there will be no longer any bargaining over” the North’s nuclear weapons. This essentially scrapped a three-decade policy of normalizing relations with the United States through denuclearization, started by Kim Il Sung and upheld by Kim Jong Il. Finally, Kim Jong Un designated South Korea as the “primary enemy” and shut the door to peaceful unification, which again was a reversal of his predecessors’ national unification policy. As North Korea shifted away from the United States and South Korea, it pivoted back to China and Russia, which marked a reversal of another three-decade policy: nonalignment with these two great power neighbors. Kim Jong Un’s understanding of the changing global order, which he described as being “multipolar” and in a “neo–Cold War,” coupled with Russia’s invasion of Ukraine, appears to have spurred Pyongyang’s pivot away from Washington.

Limitations

The historical enmity between the United States and North Korea is multigenerational and baked into the culture. North Koreans are taught that the United States and South Korea started the Korean War (called “the Great Fatherland Liberation War”) and remain an urgent threat to this day. Given the paucity of rival narratives, most of the country’s 25 million people accept this fact. In America as well, most people view North Korea as backward, pesky, irrational, and even evil. The country is a problem to deal with or an obstacle to surmount rather than a place filled mostly with ordinary people who are merely trying to get through the day. The vast majority of Americans (87 percent) view North Korea as mostly or very unfavorable, and the only foreign policy item that American Democrats and Republicans can seem to agree upon is the importance of limiting the power and influence of North Korea.

Both sides have justifiable reasons to think the other has done them wrong in prior agreements. One needs look no further than the 1994 Agreed Framework , the first major nuclear deal. North Korea complains that the United States failed to deliver on promised fuel oil and dragged its feet on the construction of light water reactors. The United States claims that North Korea broke the spirit if not the letter of the agreement by secretly pursuing a uranium path to the bomb. Several stalled attempts later, both sides have accumulated a laundry list of complaints about the infidelities of the other. Neither is in the mood to leap first to break the impasse, although precedent suggests this may be necessary.

Historically, diplomatic progress has been undercut by system incompatibility, multilateral misalignment, and geopolitics. American domestic politics have complicated the ability of the U.S. president to follow up on commitments. For example, Republicans in Congress opposed the transfer of heavy fuel oil to North Korea during the Agreed Framework. North Korea’s top-down system has made it difficult for diplomats at the working level to make serious headway in the nuclear issue. American negotiators came prepared for detailed talks in the run-up to the Hanoi summit, but their North Korean interlocutors simply did not have permission to discuss nuclear weapons.

The sheer number and variety of attempts to make a deal work have led to a state of learned helplessness. At this point, we’ve tried bilateral and multilateral negotiations. We’ve tried talks that start with working group–level negotiations and talks that are catalyzed by early leader-level summits. We’ve tried economic incentives and negative security assurances. We’ve tried having South Korea and China serve core roles in the process and otherwise. Both sides have given up trying to improve the very bad situation because we’ve become conditioned that it’s not within their power. This is of course understandable but wrong.

Looking Forward

Long-time North Korea watchers tend to believe that North Korea may make tactical adjustments along the way, but its strategic goals remain unchanged. An offshoot of this thinking is that the North Korean leadership continues to view the United States as indispensable for regime security . That is certainly what prompted Kim Il Sung to improve relations with Washington in the 1990s and Kim Jong Il and Kim Jong Un to continue this policy. But are we confident that this remains Kim Jong Un’s priority? As explained above, the signaling from North Korea indicates otherwise. There is a real threat of failing to recognize that North Korea is changing and thus failing to recalibrate U.S. policy accordingly.

Additionally, it’s crucial to acknowledge that the offer at the core of former strategies — the lifting of sanctions or provision of economic aid packages in return for North Korea’s steps toward denuclearization — do not have the same allure for Pyongyang as they once did. For one, the strides North Korea has made in its weapons programs since the collapse of the Hanoi summit mean the terms of negotiations will not be the same as they were in 2018 or 2019. Let’s not forget that Kim has effectively drawn the line: no denuclearization. Next, North Korea’s calculus vis-á-vis the United States, China, and Russia has changed. Additionally, the growing rift between the United States and both China and Russia, combined with North Korea’s improved relations with Beijing and Moscow, have facilitated Pyongyang’s illicit economy. Notably, Russia recently vetoed a U.N. group tasked with monitoring North Korea’s sanctions evasions. The horse has truly left the barn.

The current state of the policy debate pits deterrence against engagement and assurance, ignoring the fact that all three will be needed to solve the problem. One dilemma is that it’s counter-productive to reward or incentivize bad behavior, but it’s also necessary to provide an off-ramp from this negative cycle the United States and North Korea are stuck in. The challenge is to pursue a policy that moves the ball in the right direction whether or not Pyongyang is in the mood to work on the relationship. The current debate also fails to address the reality that North Korea’s intransigence stems from regional division and global competition between rival blocs. So long as China and Russia continue to be at odds with the United States and even benefit from North Korea’s confrontation with Washington, it’s foolhardy to expect them to abandon their ally of convenience.

A great deal of intellectual and political capital has been expended on showy summits and grand bargains that simply don’t pan out. Victor Cha has written that “all the past denuclearization policies have arguably left the United States worse off than before.” To surmount the dilemmas inherent to North Korea policy, Washington should first break through the limitations in its own thinking. Policymakers should follow William Perry’s advice to “deal with the North Korean government as it is, not as we might wish it to be.”

Given the nature of the problem — one so firmly rooted in wider regional rivalries — it is necessary to take the long view. That means preparing for sudden change while also girding for stasis or deterioration and proactively working to create conditions for favorable improvement. Sudden change could come in the form of an unanticipated two-front war in Asia involving the United States, both Koreas, China, Japan, and Taiwan. It could begin with a North Korean provocation or miscalculation that spirals out of control. It could be triggered by famine , regime instability , a coup, or a nuclear accident . Preventing and preparing for these eventualities involve painstaking planning, cooperation with our allies, and crisis management with our adversaries.

All too often, in stalemates, only a crisis can convince policymakers to invest the political capital needed for change. To that end, deterrence, assurance, and engagement will all be needed — as well as a healthy dose of pragmatism. When it comes to tough cases like North Korea, incremental progress doesn’t get the fanfare it deserves.

Modest Measures

Given the paucity of progress and the fait accompli that denuclearization is virtually impossible, some are calling for the United States and South Korea to make concessions to kick-start a peace process with an arms control deal or an end-of-war declaration . But without the proper verification measures and mutual trust-building, an arms control deal that stops short of full denuclearization could actually make the peninsula a more dangerous and unstable place. While an end-of-war declaration would be politically symbolic, it could lead to increased calls by Pyongyang to halt U.S.-South Korean joint military exercises or pull out U.S. military personnel and assets from South Korea, which could be more destabilizing for the region. Both objectives are worth pursuing in the long term, but only as part of a holistic and parallel process with reciprocity and snapbacks.

Both the United States and North Korea will need to demonstrate good faith. That’s worth working toward but shouldn’t be expected overnight, especially so long as China and Russia continue to bankroll the Kim regime’s intransigence. On the diplomatic front, rather than the unrealistic fantasy of a sweeping solution through a grand bargain, efforts should be focused on building out overlapping and supporting layers of initiatives that stave off disaster and precipitate positive outcomes.

First, Washington should invest serious political capital in crisis communications and confidence-building measures in Northeast Asia. It’s ideal if Pyongyang participates but nonetheless meaningful if similar dialogues can take place with the other regional players, especially China, the United States, South Korea, and Japan. The door will remain open for North Korea’s subsequent participation.

Next, the United States and South Korea have nothing to lose by trying to rekindle trust through humanitarian assistance, academic exchange, and people-to-people ties.

Simultaneously, the U.S.-Korean alliance should improve its deterrence posture by enhancing ballistic missile defenses , increasing trilateral cooperation with Japan, and developing and deploying assets and doctrines to meet the advancing threat. However, instead of emphasizing deterrence by punishment, which tends to be louder than it is effective, the alliance can focus on deterrence by denial “to undermine North Korea’s confidence in escalatory options without further threatening the regime.”

Over time, North Korea will come to understand that Washington and Seoul’s strategy is a reflection of its own. When Pyongyang turns down the temperature, stops provocations, and engages in reciprocal trust-building, it will find ready and willing partners. When it insists on proliferation, weapons testing, and provocations, the United States and South Korea will improve their deterrence posture and lead an international pressure coalition. Washington can hold out hope that North Korea comes around, but if it relies on this, it passes up the opportunity for more modest and pragmatic achievements. At the very least, Washington can take proactive measures to prevent the worst possible outcome, no matter what path the Kim regime decides to take.

Jonathan Corrado is director of policy for The Korea Society, where he produces programming and conducts research on the U.S.-Korea alliance and the Korean Peninsula. He teaches a class on North Korea at the School of International and Public Affairs (SIPA) at Columbia University and the State University of New York Stony Brook University. He was previously a Korean-English translator for Daily NK, a South Korean news service collecting information from North Korean sources.

Rachel Minyoung Lee is a senior fellow with the 38 North Program at the Stimson Center. She was a North Korea collection expert and analyst with the Open Source Enterprise of the U.S. government from 2000 to 2019.

Image: Wikimedia

Mid-Afternoon Map: Why North is Up, Part Two

Coming to terms with the loss of turkey, horns of a dilemma, sweden, finland, and the meaning of alliance membership.

Brian Chen holding a notebook with math problems, a pen and a smartphone open to the new ChatGPT app.

The New ChatGPT Offers a Lesson in A.I. Hype

OpenAI released GPT-4o, its latest chatbot technology, in a partly finished state. It has much to prove.

ChatGPT-4o trying to solve a geometry problem Credit... Arsenii Vaselenko for The New York Times

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By Brian X. Chen

Brian X. Chen is the author of Tech Fix , a weekly column about the societal implications of the tech we use.

May 31, 2024

When OpenAI unveiled the latest version of its immensely popular ChatGPT chatbot this month, it had a new voice possessing humanlike inflections and emotions. The online demonstration also featured the bot tutoring a child on solving a geometry problem.

To my chagrin, the demo turned out to be essentially a bait and switch. The new ChatGPT was released without most of its new features, including the improved voice (which the company told me it postponed to make fixes). The ability to use a phone’s video camera to get real-time analysis of something like a math problem isn’t available yet, either.

Amid the delay, the company also deactivated the ChatGPT voice that some said sounded like the actress Scarlett Johansson, after she threatened legal action , replacing it with a different female voice.

For now, what has actually been rolled out in the new ChatGPT is the ability to upload photos for the bot to analyze. Users can generally expect quicker, more lucid responses. The bot can also do real-time language translations, but ChatGPT will respond in its older, machine-like voice.

Nonetheless, this is the leading chatbot that upended the tech industry , so it was worth reviewing. After trying the sped-up chatbot for two weeks, I had mixed feelings. It excelled at language translations, but it struggled with math and physics. All told, I didn’t see a meaningful improvement from the last version, ChatGPT-4. I definitely wouldn’t let it tutor my child.

This tactic, in which A.I. companies promise wild new features and deliver a half-baked product, is becoming a trend that is bound to confuse and frustrate people. The $700 Ai Pin , a talking lapel pin from the start-up Humane, which is funded by OpenAI’s chief executive, Sam Altman, was universally panned because it overheated and spat out nonsense. Meta also recently added to its apps an A.I. chatbot that did a poor job at most of its advertised tasks , like web searches for plane tickets.

Companies are releasing A.I. products in a premature state partly because they want people to use the technology to help them learn how to improve it. In the past, when companies unveiled new tech products like phones, what we were shown — features like new cameras and brighter screens — was what we were getting. With artificial intelligence, companies are giving a preview of a potential future, demonstrating technologies that are being developed and working only in limited, controlled conditions. A mature, reliable product might arrive — or might not.

The lesson to learn from all this is that we, as consumers, should resist the hype and take a slow, cautious approach to A.I. We shouldn’t be spending much cash on any underbaked tech until we see proof that the tools work as advertised.

The new version of ChatGPT, called GPT-4o (“o” as in “omni”), is now free to try on OpenAI’s website and app . Nonpaying users can make a few requests before hitting a timeout, and those who have a $20 monthly subscription can ask the bot a larger number of questions.

OpenAI said its iterative approach to updating ChatGPT allowed it to gather feedback to make improvements.

“We believe it’s important to preview our advanced models to give people a glimpse of their capabilities and to help us understand their real-world applications,” the company said in a statement.

(The New York Times sued OpenAI and its partner, Microsoft , last year for using copyrighted news articles without permission to train chatbots.)

Here’s what to know about the latest version of ChatGPT.

Geometry and Physics

To show off ChatGPT-4o’s new tricks, OpenAI published a video featuring Sal Khan, the chief executive of the Khan Academy, the education nonprofit, and his son, Imran. With a video camera pointed at a geometry problem, ChatGPT was able to talk Imran through solving it step by step.

Even though ChatGPT’s video-analysis feature has yet to be released, I was able to upload photos of geometry problems. ChatGPT solved some of the easier ones correctly, but it tripped up on more challenging problems.

For one problem involving intersecting triangles, which I dug up on an SAT preparation website , the bot understood the question but gave the wrong answer.

Taylor Nguyen, a high school physics teacher in Orange County, Calif., uploaded a physics problem involving a man on a swing that is commonly included on Advanced Placement Calculus tests. ChatGPT made several logical mistakes to give the wrong answer, but it was able to correct itself with feedback from Mr. Nguyen.

“I was able to coach it, but I’m a teacher,” he said. “How is a student supposed to pick out those mistakes? They’re making this assumption that the chatbot is right.”

I did notice that ChatGPT-4o succeeded at some division calculations that its predecessors did incorrectly, so there are signs of slow improvement. But it also failed at a basic math task that past versions and other chatbots, including Meta AI and Google’s Gemini, have flunked at: the ability to count. When I asked ChatGPT-4o for a four-syllable word starting with the letter “W,” it responded, “Wonderful.”

OpenAI said it was constantly working to improve its systems’ responses to complex math problems.

Mr. Khan, whose company uses OpenAI’s technology in its tutoring software Khanmigo, did not respond to a request for comment on whether he would leave ChatGPT the tutor alone with his son.

OpenAI also highlighted that the new ChatGPT was better at reasoning, or using logic to come up with responses. So I ran it through one of my favorite tests: I asked it to generate a Where’s Waldo? puzzle. When it showed an image of a giant Waldo standing in a crowd, I said that the point is that he’s supposed to be hard to find.

The bot then generated an even larger Waldo.

Subbarao Kambhampati, a professor and researcher of artificial intelligence at Arizona State University, also put the chatbot through some tests and said he saw no noticeable improvement in reasoning compared with the last version.

He presented ChatGPT a puzzle involving blocks:

If block C is on top of block A, and block B is separately on the table, can you tell me how I can make a stack of blocks with block A on top of block B and block B on top of block C, but without moving block C?

The answer is that it’s impossible to arrange the blocks under these conditions, but, just as with past versions, ChatGPT-4o consistently came up with a solution that involved moving block C. With this and other reasoning tests, ChatGPT was occasionally able to take feedback to get the correct answer, which is antithetical to how artificial intelligence is supposed to work, Mr. Kambhampati said.

“You can correct it, but when you do that you’re using your own intelligence,” he said.

OpenAI pointed to test results that showed GPT-4o scored about two percentage points higher at answering general knowledge questions than previous versions of ChatGPT, illustrating that its reasoning skills had slightly improved.

OpenAI also said the new ChatGPT could do real-time language translation, which could help you converse with someone speaking a foreign language.

I tested ChatGPT with Mandarin and Cantonese and confirmed that it was OK at translating phrases, such as “I’d like to book a hotel room for next Thursday” and “I want a king-size bed.” But the accents were slightly off. (To be fair, my broken Chinese is not much better.) OpenAI said it was still working to improve accents.

ChatGPT-4o also excelled as an editor. When I fed it paragraphs that I wrote, it was fast and effective at removing excessive words and jargon. ChatGPT’s decent performance with language translation gives me confidence that this will soon become a more useful feature.

Bottom Line

A major thing OpenAI got right with ChatGPT-4o is making the technology free for people to try. Free is the right price: Since we are helping to train these A.I. systems with our data to improve, we shouldn’t be paying for them.

The best of A.I. has yet to come, and it might one day be a good math tutor that we want to talk to. But we should believe it when we see it — and hear it.

Brian X. Chen is the lead consumer technology writer for The Times. He reviews products and writes Tech Fix , a column about the social implications of the tech we use. More about Brian X. Chen

Explore Our Coverage of Artificial Intelligence

News and Analysis

Federal regulators have reached a deal that allows them to proceed with antitrust investigations into the dominant roles that Microsoft, OpenAI and Nvidia play in the A.I. industry.

Google appears to have rolled back its new A.I. Overviews after the technology produced a litany of untruths and errors.

OpenAI said that it has begun training a new flagship A.I. model that would succeed the GPT-4 technology that drives its popular online chatbot, ChatGPT.

The Age of A.I.

After some trying years during which Mark Zuckerberg could do little right, many developers and technologists have embraced the Meta chief as their champion of “open-source” A.I.

D’Youville University in Buffalo had an A.I. robot speak at its commencement . Not everyone was happy about it.

A new program, backed by Cornell Tech, M.I.T. and U.C.L.A., helps prepare lower-income, Latina and Black female computing majors for A.I. careers.

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