sample of routine problem solving

35 problem-solving techniques and methods for solving complex problems

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How do you identify problems?

How do you identify the right solution.

Tips for more effective problem-solving

Complete problem-solving methods

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

Problem-solving warm-up activities

Closing activities for a problem-solving process.

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

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

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

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

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

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

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

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

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

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

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

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

Tips for more effective problem solving

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

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

Clearly define the problem

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

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

Don’t jump to conclusions

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

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

Try different approaches

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

Don’t take it personally

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

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

Get the right people in the room

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

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

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

Document everything

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

Bring a facilitator

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

Develop your problem-solving skills

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

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

Design a great agenda

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

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

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

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

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

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

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

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

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

2. Lightning Decision Jam

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

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

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

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

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

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

3. Problem Definition Process

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

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

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

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

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

4. The 5 Whys

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

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

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

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

5. World Cafe

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

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

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

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

6. Discovery & Action Dialogue (DAD)

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

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

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

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

7. Design Sprint 2.0

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

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

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

8. Open space technology

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

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

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

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

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

Techniques to identify and analyze problems

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

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

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

Let’s take a look!

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

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

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

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

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

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

10. The Creativity Dice

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

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

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

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

11. Fishbone Analysis

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

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

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

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

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

12. Problem Tree

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

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

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

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

13. SWOT Analysis

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

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

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

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

14. Agreement-Certainty Matrix

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

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

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

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

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

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

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

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

16. Speed Boat

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

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

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

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

17. The Journalistic Six

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

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

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

18. LEGO Challenge

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

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

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

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

19. What, So What, Now What?

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

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

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

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

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

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

20. Journalists

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

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

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

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

Problem-solving techniques for developing solutions

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

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

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

21. Mindspin

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

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

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

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

22. Improved Solutions

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

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

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

23. Four Step Sketch

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

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

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

24. 15% Solutions

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

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

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

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

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

25. How-Now-Wow Matrix

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

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

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

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

26. Impact and Effort Matrix

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

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

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

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

27. Dotmocracy

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

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

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

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

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

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

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

28. Check-in / Check-out

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

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

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

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

29. Doodling Together

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

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

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

30. Show and Tell

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

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

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

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

31. Constellations

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

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

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

32. Draw a Tree

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

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

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

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

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

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

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

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

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

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

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

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

33. One Breath Feedback

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

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

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

34. Who What When Matrix

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

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

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

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

35. Response cards

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

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

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

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

Save time and effort discovering the right solutions

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

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

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

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

Over to you

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

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

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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

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Culture Development

Workplace problem-solving examples: real scenarios, practical solutions.

March 11, 2024

In today’s fast-paced and ever-changing work environment, problems are inevitable. From conflicts among employees to high levels of stress, workplace problems can significantly impact productivity and overall well-being. However, by developing the art of problem-solving and implementing practical solutions, organizations can effectively tackle these challenges and foster a positive work culture. In this article, we will delve into various workplace problem scenarios and explore strategies for resolution. By understanding common workplace problems and acquiring essential problem-solving skills, individuals and organizations can navigate these challenges with confidence and success.

Understanding Workplace Problems

Before we can effectively solve workplace problems , it is essential to gain a clear understanding of the issues at hand. Identifying common workplace problems is the first step toward finding practical solutions. By recognizing these challenges, organizations can develop targeted strategies and initiatives to address them.

Identifying Common Workplace Problems

One of the most common workplace problems is conflict. Whether it stems from differences in opinions, miscommunication, or personality clashes, conflict can disrupt collaboration and hinder productivity. It is important to note that conflict is a natural part of any workplace, as individuals with different backgrounds and perspectives come together to work towards a common goal. However, when conflict is not managed effectively, it can escalate and create a toxic work environment.

In addition to conflict, workplace stress and burnout pose significant challenges. High workloads, tight deadlines, and a lack of work-life balance can all contribute to employee stress and dissatisfaction. When employees are overwhelmed and exhausted, their performance and overall well-being are compromised. This not only affects the individuals directly, but it also has a ripple effect on the entire organization.

Another common workplace problem is poor communication. Ineffective communication can lead to misunderstandings, delays, and errors. It can also create a sense of confusion and frustration among employees. Clear and open communication is vital for successful collaboration and the smooth functioning of any organization.

The Impact of Workplace Problems on Productivity

Workplace problems can have a detrimental effect on productivity levels. When conflicts are left unresolved, they can create a tense work environment, leading to decreased employee motivation and engagement. The negative energy generated by unresolved conflicts can spread throughout the organization, affecting team dynamics and overall performance.

Similarly, high levels of stress and burnout can result in decreased productivity, as individuals may struggle to focus and perform optimally. When employees are constantly under pressure and overwhelmed, their ability to think creatively and problem-solve diminishes. This can lead to a decline in the quality of work produced and an increase in errors and inefficiencies.

Poor communication also hampers productivity. When information is not effectively shared or understood, it can lead to misunderstandings, delays, and rework. This not only wastes time and resources but also creates frustration and demotivation among employees.

Furthermore, workplace problems can negatively impact employee morale and job satisfaction. When individuals are constantly dealing with conflicts, stress, and poor communication, their overall job satisfaction and engagement suffer. This can result in higher turnover rates, as employees seek a healthier and more supportive work environment.

In conclusion, workplace problems such as conflict, stress, burnout, and poor communication can significantly hinder productivity and employee well-being. Organizations must address these issues promptly and proactively to create a positive and productive work atmosphere. By fostering open communication, providing support for stress management, and promoting conflict resolution strategies, organizations can create a work environment that encourages collaboration, innovation, and employee satisfaction.

The Art of Problem Solving in the Workplace

Now that we have a clear understanding of workplace problems, let’s explore the essential skills necessary for effective problem-solving in the workplace. By developing these skills and adopting a proactive approach, individuals can tackle problems head-on and find practical solutions.

Problem-solving in the workplace is a complex and multifaceted skill that requires a combination of analytical thinking, creativity, and effective communication. It goes beyond simply identifying problems and extends to finding innovative solutions that address the root causes.

Essential Problem-Solving Skills for the Workplace

To effectively solve workplace problems, individuals should possess a range of skills. These include strong analytical and critical thinking abilities, excellent communication and interpersonal skills, the ability to collaborate and work well in a team, and the capacity to adapt to change. By honing these skills, individuals can approach workplace problems with confidence and creativity.

Analytical and critical thinking skills are essential for problem-solving in the workplace. They involve the ability to gather and analyze relevant information, identify patterns and trends, and make logical connections. These skills enable individuals to break down complex problems into manageable components and develop effective strategies to solve them.

Effective communication and interpersonal skills are also crucial for problem-solving in the workplace. These skills enable individuals to clearly articulate their thoughts and ideas, actively listen to others, and collaborate effectively with colleagues. By fostering open and honest communication channels, individuals can better understand the root causes of problems and work towards finding practical solutions.

Collaboration and teamwork are essential for problem-solving in the workplace. By working together, individuals can leverage their diverse skills, knowledge, and perspectives to generate innovative solutions. Collaboration fosters a supportive and inclusive environment where everyone’s ideas are valued, leading to more effective problem-solving outcomes.

The ability to adapt to change is another important skill for problem-solving in the workplace. In today’s fast-paced and dynamic work environment, problems often arise due to changes in technology, processes, or market conditions. Individuals who can embrace change and adapt quickly are better equipped to find solutions that address the evolving needs of the organization.

The Role of Communication in Problem Solving

Communication is a key component of effective problem-solving in the workplace. By fostering open and honest communication channels, individuals can better understand the root causes of problems and work towards finding practical solutions. Active listening, clear and concise articulation of thoughts and ideas, and the ability to empathize are all valuable communication skills that facilitate problem-solving.

Active listening involves fully engaging with the speaker, paying attention to both verbal and non-verbal cues, and seeking clarification when necessary. By actively listening, individuals can gain a deeper understanding of the problem at hand and the perspectives of others involved. This understanding is crucial for developing comprehensive and effective solutions.

Clear and concise articulation of thoughts and ideas is essential for effective problem-solving communication. By expressing oneself clearly, individuals can ensure that their ideas are understood by others. This clarity helps to avoid misunderstandings and promotes effective collaboration.

Empathy is a valuable communication skill that plays a significant role in problem-solving. By putting oneself in the shoes of others and understanding their emotions and perspectives, individuals can build trust and rapport. This empathetic connection fosters a supportive and collaborative environment where everyone feels valued and motivated to contribute to finding solutions.

In conclusion, problem-solving in the workplace requires a combination of essential skills such as analytical thinking, effective communication, collaboration, and adaptability. By honing these skills and fostering open communication channels, individuals can approach workplace problems with confidence and creativity, leading to practical and innovative solutions.

Real Scenarios of Workplace Problems

Now, let’s explore some real scenarios of workplace problems and delve into strategies for resolution. By examining these practical examples, individuals can develop a deeper understanding of how to approach and solve workplace problems.

Conflict Resolution in the Workplace

Imagine a scenario where two team members have conflicting ideas on how to approach a project. The disagreement becomes heated, leading to a tense work environment. To resolve this conflict, it is crucial to encourage open dialogue between the team members. Facilitating a calm and respectful conversation can help uncover underlying concerns and find common ground. Collaboration and compromise are key in reaching a resolution that satisfies all parties involved.

In this particular scenario, let’s dive deeper into the dynamics between the team members. One team member, let’s call her Sarah, strongly believes that a more conservative and traditional approach is necessary for the project’s success. On the other hand, her colleague, John, advocates for a more innovative and out-of-the-box strategy. The clash between their perspectives arises from their different backgrounds and experiences.

As the conflict escalates, it is essential for a neutral party, such as a team leader or a mediator, to step in and facilitate the conversation. This person should create a safe space for both Sarah and John to express their ideas and concerns without fear of judgment or retribution. By actively listening to each other, they can gain a better understanding of the underlying motivations behind their respective approaches.

During the conversation, it may become apparent that Sarah’s conservative approach stems from a fear of taking risks and a desire for stability. On the other hand, John’s innovative mindset is driven by a passion for pushing boundaries and finding creative solutions. Recognizing these underlying motivations can help foster empathy and create a foundation for collaboration.

As the dialogue progresses, Sarah and John can begin to identify areas of overlap and potential compromise. They may realize that while Sarah’s conservative approach provides stability, John’s innovative ideas can inject fresh perspectives into the project. By combining their strengths and finding a middle ground, they can develop a hybrid strategy that incorporates both stability and innovation.

Ultimately, conflict resolution in the workplace requires effective communication, active listening, empathy, and a willingness to find common ground. By addressing conflicts head-on and fostering a collaborative environment, teams can overcome challenges and achieve their goals.

Dealing with Workplace Stress and Burnout

Workplace stress and burnout can be debilitating for individuals and organizations alike. In this scenario, an employee is consistently overwhelmed by their workload and experiencing signs of burnout. To address this issue, organizations should promote a healthy work-life balance and provide resources to manage stress effectively. Encouraging employees to take breaks, providing access to mental health support, and fostering a supportive work culture are all practical solutions to alleviate workplace stress.

In this particular scenario, let’s imagine that the employee facing stress and burnout is named Alex. Alex has been working long hours, often sacrificing personal time and rest to meet tight deadlines and demanding expectations. As a result, Alex is experiencing physical and mental exhaustion, reduced productivity, and a sense of detachment from work.

Recognizing the signs of burnout, Alex’s organization takes proactive measures to address the issue. They understand that employee well-being is crucial for maintaining a healthy and productive workforce. To promote a healthy work-life balance, the organization encourages employees to take regular breaks and prioritize self-care. They emphasize the importance of disconnecting from work during non-working hours and encourage employees to engage in activities that promote relaxation and rejuvenation.

Additionally, the organization provides access to mental health support services, such as counseling or therapy sessions. They recognize that stress and burnout can have a significant impact on an individual’s mental well-being and offer resources to help employees manage their stress effectively. By destigmatizing mental health and providing confidential support, the organization creates an environment where employees feel comfortable seeking help when needed.

Furthermore, the organization fosters a supportive work culture by promoting open communication and empathy. They encourage managers and colleagues to check in with each other regularly, offering support and understanding. Team members are encouraged to collaborate and share the workload, ensuring that no one person is overwhelmed with excessive responsibilities.

By implementing these strategies, Alex’s organization aims to alleviate workplace stress and prevent burnout. They understand that a healthy and balanced workforce is more likely to be engaged, productive, and satisfied. Through a combination of promoting work-life balance, providing mental health support, and fostering a supportive work culture, organizations can effectively address workplace stress and create an environment conducive to employee well-being.

Practical Solutions to Workplace Problems

Now that we have explored real scenarios, let’s discuss practical solutions that organizations can implement to address workplace problems. By adopting proactive strategies and establishing effective policies, organizations can create a positive work environment conducive to problem-solving and productivity.

Implementing Effective Policies for Problem Resolution

Organizations should have clear and well-defined policies in place to address workplace problems. These policies should outline procedures for conflict resolution, channels for reporting problems, and accountability measures. By ensuring that employees are aware of these policies and have easy access to them, organizations can facilitate problem-solving and prevent issues from escalating.

Promoting a Positive Workplace Culture

A positive workplace culture is vital for problem-solving. By fostering an environment of respect, collaboration, and open communication, organizations can create a space where individuals feel empowered to address and solve problems. Encouraging teamwork, recognizing and appreciating employees’ contributions, and promoting a healthy work-life balance are all ways to cultivate a positive workplace culture.

The Role of Leadership in Problem Solving

Leadership plays a crucial role in facilitating effective problem-solving within organizations. Different leadership styles can impact how problems are approached and resolved.

Leadership Styles and Their Impact on Problem-Solving

Leaders who adopt an autocratic leadership style may make decisions independently, potentially leaving their team members feeling excluded and undervalued. On the other hand, leaders who adopt a democratic leadership style involve their team members in the problem-solving process, fostering a sense of ownership and empowerment. By encouraging employee participation, organizations can leverage the diverse perspectives and expertise of their workforce to find innovative solutions to workplace problems.

Encouraging Employee Participation in Problem Solving

To harness the collective problem-solving abilities of an organization, it is crucial to encourage employee participation. Leaders can create opportunities for employees to contribute their ideas and perspectives through brainstorming sessions, team meetings, and collaborative projects. By valuing employee input and involving them in decision-making processes, organizations can foster a culture of inclusivity and drive innovative problem-solving efforts.

In today’s dynamic work environment, workplace problems are unavoidable. However, by understanding common workplace problems, developing essential problem-solving skills, and implementing practical solutions, individuals and organizations can navigate these challenges effectively. By fostering a positive work culture, implementing effective policies, and encouraging employee participation, organizations can create an environment conducive to problem-solving and productivity. With proactive problem-solving strategies in place, organizations can thrive and overcome obstacles, ensuring long-term success and growth.

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Pentathlon Institute

Active Problem-Solving

Learning to resolve problems that are continually undergoing change.

The Mathematics Pentathlon ® Program provides experiences in thought processes necessary for Active Problem Solving. The series of 20 Mathematics Pentathlon games provide K-7 students with experiences in deductive and inductive reasoning through the repeated use of sequential thought as well as nonlinear, intuitive thinking. Exposure to such forms of thought helps students relate to real-life problem-solving situations and learn to “think on their feet.”

The Four Sections below explain the following: Active Problem Solving Defined, What is Mathematics, Three Types of Mathematical Thought, and Conceptual Understanding Using Concrete and Pictorial Models.

Active-Problem Solving Defined

Problem solving can be divided into two categories:, routine & non-routine.

Routine Problem Solving , stresses the use of sets of known or prescribed procedures (algorithms) to solve problems. The strength of this approach is that it is easily assessed by paper-pencil tests. Since today’s computers and calculators can quickly and accurately perform the most complex arrangements of algorithms for multi-step routine problems, the typical workplace does not require a high level of proficiency in Routine Problem Solving. However, today’s workplace does require many employees to be proficient in Nonroutine Problem Solving.

Nonroutine Problem Solving , stresses the use of heuristics and often requires little to no use of algorithms. Unlike algorithms, heuristics are procedures or strategies that do not guarantee a solution to a problem but provide a more highly probable method for discovering a solution. Building a model and drawing a picture of a problem are two basic problem-solving heuristics. Studying end-of-game situations provides students with experiences in using the heuristics of reducing the problem to a similar but simpler problem and working a problem backwards, i.e. from its resolution to its initial state. Other heuristics include describing the problem situation, classifying information, and finding irrelevant information.

There Are Two Categories of Nonroutine Problem Solving:

Static and active.

Static-Nonroutine problems have a fixed, known goal and fixed, known elements that are used to resolve the problem. Solving a jigsaw puzzle is an example of a Static- Nonroutine problem. Given all pieces to a puzzle and a picture of the goal, learners are challenged to arrange the pieces to complete the picture. Various heuristics such as classifying the pieces by color, connecting the pieces that form the border, or connecting the pieces that form a salient feature to the puzzle, such as a flag pole, are typical ways in which people attempt to resolve such problems.

Active-Nonroutine problems may have a fixed goal with changing elements, a changing goal or alternative goals with fixed elements, or changing or alternative goals with changing elements. The heuristics used in this form of problem-solving are known as strategies. People who study such problems must learn to change or adapt their strategies as the problem unfolds.

What is Mathematics?

There is a growing belief in the mathematics community, as well as society in general, that the study of mathematics must develop in all students an understanding of mathematics that continues throughout one’s lifetime and evolves to meet ever-changing situations and variables. From our perspective, mathematics is an area of investigation that develops the ability to critically observe, classify, describe, and analyze data in a logical manner using both inductive and deductive methods. In contrast to the sterilized and unrelated manner in which school mathematics has often been taught, mathematics is a creative and aesthetic study of patterns and geometric and numerical relationships. It is dynamic rather than passive in nature and should involve students in strategic thinking by exploring multiple possibilities and variables that continually change, much like life.

The Mathematics Pentathlon® Program, which integrates Adventures in Problem Solving, Activity Books I & II, the Mathematics Pentathlon® Games and Investigation Exercises, Books I & II was designed to implement the definition of mathematics described above. The games are organized into four division levels by grade, K-1, 2-3, 4- 5, and 6-7 with five games at each level. The name of the Program, Mathematics Pentathlon®, was coined to liken it to a worldwide series of athletic events, the Decathlon component of the Olympics. In the world of athletics the Decathlon is appreciated for valuing and rewarding individuals who have developed a diverse range of athletic abilities. In contrast, the mathematics community as a whole has rarely valued or rewarded individuals with a diverse range of mathematics abilities. The Mathematics Pentathlon® Games promote diversity in mathematical thinking by integrating spatial/ geometric, arithmetic/computational, and logical/scientific reasoning at each division level. Since each of the 5 games requires students to broaden their thought processes, it attracts students from a wide range of ability levels, from those considered “gifted and talented” to “average” to “at-risk.”

The format of games was chosen for two reasons. First, games that are of a strategic nature require students to consider multiple options and formulate strategies based on expected countermoves from the other player. The Mathematics Pentathlon® further promotes this type of thought by organizing students into groups of four and teams of two. Teams alternate taking turns and team partners alternate making decisions about particular plays by discussing aloud the various options and possibilities. In this manner, all group members grow in their understanding of multiple options and strategies. As students play these games over the course of time, they learn to make a plan based on better available options as well as to reassess and adjust this plan based on what the other team acted upon to change their prior ideas. Through this interactive process of sharing ideas and possibilities, students learn to think many steps ahead, blending both inductive and deductive thinking. Second, games were chosen as a format since they are a powerful motivational tool that attracts students from a diverse range of abilities and interest levels to spend more time on task developing basic skills as well as problem-solving skills. While race-type games based on chance are commonly used in classrooms, they do not typically capture students’ curiosity for long periods of time. Students may play such games once or twice, but then lose interest since they are not seriously challenged. The Mathematics Pentathlon® Games have seriously challenged students to mature in their ability to think strategically and resolve problems that are continually undergoing change. As a result, we view active-problem solving and strategic thinking as described above as a critical focal point of the mathematics curriculum.

3 Types of Mathematical Thought

Integration of spatial/geometric, computational, and logical/scientific reasoning.

Most mathematics instruction stresses students’ knowledge of basic arithmetic facts. While the Mathematics Pentathlon Program provides a great deal of practice with mastery of the basic facts, it goes far beyond learning arithmetic skills. The Mathematics Content and Standards Chart for the 20 Mathematics Pentathlon Games shows how each game addresses several mathematical content and process objectives (see inside back cover of manual). These objectives have been clustered into logical/scientific reasoning, computational reasoning, and spatial/geometric reasoning. Each of these categories is described below.

Spatial/Geometric Reasoning

Spatial visualization involves the ability to image objects and pictures in the mind’s eye and to be able to mentally transform the positions and examine the properties of these objects/pictures. A large body of mathematics research concludes that spatial reasoning ability is highly related to higher-level mathematical problem-solving and geometric skills as well as students’ overall achievement in mathematics. Many of the Mathematics Pentathlon Games stress spatial reasoning and several integrate this form of thinking with logical and computational reasoning.

Computational Reasoning

Many of the Mathematics Pentathlon Games incorporate computation into the game structure. More time-on-task practicing arithmetic skills does indeed result in students’ increased performance in the classroom as well as on standardized tests. But in the Mathematics Pentathlon Games that stress computation, it is not sufficient to rely on arithmetic skills alone. To be successful in these games, students must also use their logical reasoning abilities to consider several options and to decide which ones will maximize their ability to reach the game’s goal(s).

Logical/Scientific Reasoning

One of the most important life skills, not to mention mathematical skills, is the ability to think logically. The process of observation, classification, hypothesizing, experimentation, and inductive and deductive thought are required for logical reasoning. Yet where do children learn these fundamental life skills? Strategic games provide students the opportunity to develop this form of thinking. Each of the Mathematics Pentathlon Games is a strategy game that develops students’ logical reasoning skills through the process of investigating a variety of options and choosing better options. At the same time students develop scientific reasoning skills by learning how to be better observers of game-playing variables and options. Playing the games over the course of time allows for hypothetical reasoning to evolve since students analyze sequences of “if-then” situations and make choices based on linking inductive and deductive thought.

While each of the 20 games may stress one form of the mathematical thinking over another, each game integrates at least two categories of mathematical thinking. Furthermore, the five games at each Divisional level balance the three types of reasoning.

Conceptual Understanding Using Concrete and Pictorial Models Understanding

Since its inception, the National Council of Teachers of Mathematics (NCTM) has called for a conceptually-based curriculum in schools throughout the country. The most recent psychological and educational research has shown that conceptual understanding is a key attribute of individuals who are proficient in mathematics. Furthermore, a large body of research over the last four decades suggests that effective use of physical and pictorial models of mathematics concepts improves students’ conceptual understanding, problem-solving skills, and overall achievement in mathematics. Research also indicates that the use of concrete and pictorial models improves spatial visualization and geometric thinking.

The Mathematics Pentathlon ® Program incorporates a variety of concrete and pictorial models to develop students’ conceptual understanding of many important mathematics concepts that involve computational, spatial, and logical reasoning. In addition, by playing these games in cooperative groups, as suggested in this publication, students also improve their oral and written communication skills through their discussion of mathematical ideas and relationships.

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10 Problem-solving strategies to turn challenges on their head

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What is an example of problem-solving?

What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.

Problems come in all shapes and sizes — from workplace conflict to budget cuts.

Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge.

Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem .

Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.

Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.

To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high.

Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one.

Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions.

This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.

They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.

The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.

Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving.

Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.

1. Identify the problem

The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem.

The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions.

Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .

2. Break the problem down

Identifying the problem allows you to see which steps need to be taken to solve it.

First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage.

3. Generate potential solutions

At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible.

Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.

Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.

4. Evaluate the possible solutions

Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist.

There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:

Will my team be on board with the proposition?
Does the solution align with organizational goals ?
Is the solution likely to achieve the desired outcomes?
Is the solution realistic and possible with current resources and constraints?
Will the solution solve the problem without causing additional unintended problems?

woman-helping-her-colleague-problem-solving-strategies

5. Implement and monitor the solutions

Once you’ve identified your solution and got buy-in from your team, it’s time to implement it.

But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem.

Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.

If the solution doesn’t achieve your desired results, start this step-by-step process again.

There are many different ways to approach problem-solving. Each is suitable for different types of problems.

The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.

Here are 10 effective problem-solving strategies for you to try:

Use a solution that worked before
Brainstorming
Work backward
Use the Kipling method
Draw the problem
Use trial and error
Sleep on it
Get advice from your peers
Use the Pareto principle
Add successful solutions to your toolkit

Let’s break each of these down.

1. Use a solution that worked before

It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.

2. Brainstorming

The more people you enlist to help solve the problem, the more potential solutions you can come up with.

Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.

3. Work backward

Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.

Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.

4. Use the Kipling method

This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .”

What is the problem?
Why is the problem important?
When did the problem arise, and when does it need to be solved?
How did the problem happen?
Where is the problem occurring?
Who does the problem affect?

Answering these questions can help you identify possible solutions.

5. Draw the problem

Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.

This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.

woman-drawing-mind-map-problem-solving-strategies

6. Use trial-and-error

A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.

7. Sleep on it

Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.

A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level.

If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.

8. Get advice from your peers

Getting input from a group of people can help you find solutions you may not have thought of on your own.

For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group.

For leaders , it might be consulting other members of the leadership team or working with a business coach .

It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone.

9. Use the Pareto principle

The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.

Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales.

You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.

10. Add successful solutions to your toolkit

Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit.

These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.

three-colleagues-looking-at-computer-problem-solving-strategies

Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:

Critical thinking and analytical skills
Communication skills , including active listening
Decision-making
Planning and prioritization
Emotional intelligence , including empathy and emotional regulation
Time management
Data analysis
Research skills
Project management

And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.

Ready to work on your problem-solving abilities? Get started with these seven tips.

1. Build your problem-solving skills

One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .

2. Practice

Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life.

Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.

3. Don’t try to find a solution right away

Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.

Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking.

two-colleagues-talking-at-corporate-event-problem-solving-strategies

4. Ask for feedback

Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve.

5. Learn new approaches and methodologies

There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject.

We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman.

6. Experiment

Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches.

Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.

7. Analyze the success of your competitors

Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem.

For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster.

But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007.

If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.

Use problem-solving strategies to uplevel your business

When facing a problem, it’s worth taking the time to find the right solution.

Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.

Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.

If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.

Boost your productivity

Maximize your time and productivity with strategies from our expert coaches.

Elizabeth Perry, ACC

Elizabeth Perry is a Coach Community Manager at BetterUp. She uses strategic engagement strategies to cultivate a learning community across a global network of Coaches through in-person and virtual experiences, technology-enabled platforms, and strategic coaching industry partnerships. With over 3 years of coaching experience and a certification in transformative leadership and life coaching from Sofia University, Elizabeth leverages transpersonal psychology expertise to help coaches and clients gain awareness of their behavioral and thought patterns, discover their purpose and passions, and elevate their potential. She is a lifelong student of psychology, personal growth, and human potential as well as an ICF-certified ACC transpersonal life and leadership Coach.

8 creative solutions to your most challenging problems

5 problem-solving questions to prepare you for your next interview, what are metacognitive skills examples in everyday life, what is lateral thinking 7 techniques to encourage creative ideas, 31 examples of problem solving performance review phrases, learn what process mapping is and how to create one (+ examples), leadership activities that encourage employee engagement, how much do distractions cost 8 effects of lack of focus, can dreams help you solve problems 6 ways to try, similar articles, the pareto principle: how the 80/20 rule can help you do more with less, thinking outside the box: 8 ways to become a creative problem solver, 3 problem statement examples and steps to write your own, contingency planning: 4 steps to prepare for the unexpected, learn to sweat the small stuff: how to improve attention to detail, stay connected with betterup, get our newsletter, event invites, plus product insights and research..

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10 minute read

Problem Solving

Cognitive processing aimed at figuring out how to achieve a goal is called problem solving. In problem solving, the problem solver seeks to devise a method for transforming a problem from its current state into a desired state when a solution is not immediately obvious to the problem solver. Thus, the hallmark of problem solving is the invention of a new method for addressing a problem. This definition has three parts: (1) problem solving is cognitive –that is, it occurs internally in the mind (or cognitive system) and must be inferred indirectly from behavior; (2) problem solving is a process –it involves the manipulation of knowledge representations (or carrying out mental computations); and (3) problem solving is directed –it is guided by the goals of the problem solver.

The definition of problem solving covers a broad range of human cognitive activities, including educationally relevant cognition–figuring out how to manage one's time, writing an essay on a selected topic, summarizing the main point of a textbook section, solving an arithmetic word problem, or determining whether a scientific theory is valid by conducting experiments.

A problem occurs when a problem solver has a goal but initially does not know how to achieve the goal. This definition has three parts: (1) the current state –the problem begins in a given state; (2) the goal state –the problem solver wants the problem to be in a different state, and problem solving is required to transform the problem from the current (or given) state into the goal state, and (3) obstacles –the problem solver does not know the correct solution and an effective solution method is not obvious to the problem solver.

According to this definition a problem is personal, so that a situation that is a problem for one person might not be a problem for another person. For example, "3 + 5 = ___" might be a problem for a six-year-old child who reasons, "Let's see. I can take one from the 5 and give it to the 3. That makes 4 plus 4, and I know that 4 plus 4 is 8." However, this equation is not a problem for an adult who knows the correct answer.

Types of Problems

Routine and nonroutine problems. It is customary to distinguish between routine and nonroutine problems. In a routine problem, the problem solver knows a solution method and only needs to carry it out. For example, for most adults the problem "589 × 45 = ___" is a routine problem if they know the procedure for multicolumn multiplication. Routine problems are sometimes called exercises, and technically do not fit the definition of problem stated above. When the goal of an educational activity is to promote all the aspects of problem solving (including devising a solution plan), then nonroutine problems (or exercises) are appropriate.

In a nonroutine problem, the problem solver does not initially know a method for solving the problem. For example, the following problem (reported by Robert Sternberg and Janet Davidson) is nonroutine for most people: "Water lilies double in area every twenty-four hours. At the beginning of the summer, there is one water lily on the lake. It takes sixty days for the lake to be completely covered with water lilies. On what day is the lake half covered?" In this problem, the problem solver must invent a solution method based on working backwards from the last day. Based on this method, the problem solver can ask what the lake would look like on the day before the last day, and conclude that the lake is half covered on the fifty-ninth day.

Well-defined and ill-defined problems. It is also customary to distinguish between well-defined and ill-defined problems. In a well-defined problem, the given state of the problem, the goal state of the problem, and the allowable operators (or moves) are each clearly specified. For example, the following water-jar problem (adapted from Abrahama Luchins) is an example of a well defined problem: "I will give you three empty water jars; you can fill any jar with water and pour water from one jar into another (until the second jar is full or the first one is empty); you can fill and pour as many times as you like. Given water jars of size 21, 127, and 3 units and an unlimited supply of water, how can you obtain exactly 100 units of water?" This is a well-defined problem because the given state is clearly specified (you have empty jars of size 21, 127, and 3), the goal state is clearly specified (you want to get 100 units of water in one of the jars), and the allowable operators are clearly specified (you can fill and pour according to specific procedures). Well-defined problems may be either routine or nonroutine; if you do not have previous experience with water jar problems, then finding the solution (i.e., fill the 127, pour out 21 once, and pour out 3 twice) is a nonroutine problem.

In an ill-defined problem, the given state, goal state, and/or operations are not clearly specified. For example, in the problem, "Write a persuasive essay in favor of year-round schools," the goal state is not clear because the criteria for what constitutes a "persuasive essay" are vague and the allowable operators, such as how to access sources of information, are not clear. Only the given state is clear–a blank piece of paper. Ill-defined problems can be routine or nonroutine; if one has extensive experience in writing then writing a short essay like this one is a routine problem.

Processes in Problem Solving

The process of problem solving can be broken down into two major phases: problem representation, in which the problem solver builds a coherent mental representation of the problem, and problem solution, in which the problem solver devises and carries out a solution plan. Problem representation can be broken down further into problem translation, in which the problem solver translates each sentence (or picture) into an internal mental representation, and problem integration, in which the problem solver integrates the information into a coherent mental representation of the problem (i.e., a mental model of the situation described in the problem). Problem solution can be broken down further into solution planning, in which the problem solver devises a plan for how to solve the problem, and solution execution, in which the problem solver carries out the plan by engaging in solution behaviors. Although the four processes of problem solving are listed sequentially, they may occur in many different orderings and with many iterations in the course of solving a problem.

For example, consider the butter problem described by Mary Hegarty, Richard Mayer, and Christopher Monk: "At Lucky, butter costs 65 cents per stick. This is two cents less per stick than butter at Vons. If you need to buy 4 sticks of butter, how much will you pay at Vons?" In the problem translation phase, the problem solver may mentally represent the first sentence as "Lucky = 0.65," the second sentence as "Lucky = Vons - 0.02," and the third sentence as "4 × Vons = ___." In problem integration, the problem solver may construct a mental number line with Lucky at 0.65 and Vons to the right of Lucky (at 0.67); or the problem solver may mentally integrate the equations as "4 × (Lucky + 0.02) = ____." A key insight in problem integration is to recognize the proper relation between the cost of butter at Lucky and the cost of butter at Vons, namely that butter costs more at Vons (even though the keyword in the problem is "less"). In solution planning, the problem solver may break the problem into parts, such as: "First add 0.02 to 0.65, then multiply the result by 4." In solution executing, the problem solver carries out the plan: 0.02 + 0.65 =0.67, 0.67 × 4 = 2.68. In addition, the problem solver must monitor the problem-solving process and make adjustments as needed.

Teaching for Problem Solving

A challenge for educators is to teach in ways that foster meaningful learning rather than rote learning. Rote instructional methods promote retention (the ability to solve problems that are identical or highly similar to those presented in instruction), but not problem solving transfer (the ability to apply what was learned to novel problems). For example, in 1929, Alfred Whitehead used the term inert knowledge to refer to learning that cannot be used to solve novel problems. In contrast, meaningful instructional methods promote both retention and transfer.

In a classic example of the distinction between rote and meaningful learning, the psychologist Max Wertheimer (1959) described two ways of teaching students to compute the area of a parallelogram. In the rote method, students learn to measure the base, measure the height, and then multiply base times height. Students taught by the A = b × h method are able to find the area of parallelograms shaped like the ones given in instruction (a retention problem) but not unusual parallelograms or other shapes (a transfer problem). Wertheimer used the term reproductive thinking to refer to problem solving in which one blindly carries out a previously learned procedure. In contrast, in the meaningful method, students learn by cutting the triangle from one end of a cardboard parallelogram and attaching it to the other end to form a rectangle. Once students have the insight that a parallelogram is just a rectangle in disguise, they can compute the area because they already know the procedure for finding the area of a rectangle. Students taught by the insight method perform well on both retention and transfer problems. Wertheimer used the term productive thinking to refer to problem solving in which one invents a new approach to solving a novel problem.

Educationally Relevant Advances in Problem Solving

Recent advances in educational psychology point to the role of domain-specific knowledge in problem solving–such as knowledge of specific strategies or problem types that apply to a particular field. Three important advances have been: (1) the teaching of problem-solving processes, (2) the nature of expert problem solving, and (3) new conceptions of individual differences in problem-solving ability.

Teaching of problem-solving processes. An important advance in educational psychology is cognitive strategy instruction, which includes the teaching of problem-solving processes. For example, in Project Intelligence, elementary school children successfully learned the cognitive processes needed for solving problems similar to those found on intelligence tests. In Instrumental Enrichment, students who had been classified as mentally retarded learned cognitive processes that allowed them to show substantial improvements on intelligence tests.

Expert problem solving. Another important advance in educational psychology concerns differences between what experts and novices know in given fields, such as medicine, physics, and computer programming. For example, expert physicists tend to store their knowledge in large integrated chunks, whereas novices tend to store their knowledge as isolated fragments; expert physicists tend to focus on the underlying structural characteristics of physics word problems, whereas novices focus on the surface features; and expert physicists tend to work forward from the givens to the goal, whereas novices work backwards from the goal to the givens. Research on expertise has implications for professional education because it pinpoints the kinds of domain-specific knowledge that experts need to learn.

Individual differences in problem-solving ability. This third advance concerns new conceptions of intellectual ability based on differences in the way people process information. For example, people may differ in cognitive style–such as their preferences for visual versus verbal representations, or for impulsive versus reflective approaches to problem solving. Alternatively, people may differ in the speed and efficiency with which they carry out specific cognitive processes, such as making a mental comparison or retrieving a piece of information from memory. Instead of characterizing intellectual ability as a single, monolithic ability, recent conceptions of intellectual ability focus on the role of multiple differences in information processing.

See also: C REATIVITY ; L EARNING , subentry on A NALOGICAL R EASONING ; M ATHEMATICS L EARNING, subentry on C OMPLEX P ROBLEM S OLVING .

BIBLIOGRAPHY

C HI , M ICHELENE T. H.; G LASER , R OBERT ; and F ARR , M ARSHALL J., eds. 1988. The Nature of Expertise. Hillsdale, NJ: Erlbaum.

D UNKER , K ARL . 1945. On Problem Solving. Washington, DC: American Psychological Association.

F EUERSTEIN , R EUVEN . 1980. Instrumental Enrichment. Baltimore: University Park Press.

H EGARTY , M ARY ; M AYER , R ICHARD E.; and M ONK , C HRISTOPHER A. 1995. "Comprehension of Arithmetic Word Problems: Evidence from Students' Eye Fixations." Journal of Educational Psychology 84:76–84.

H UNT , E ARL ; L UNNEBORG , C LIFF ; and L EWIS , J. 1975. "What Does It Mean to Be High Verbal?" Cognitive Psychology 7:194–227.

L ARKIN , J ILL H.; M C D ERMOTT , J OHN ; S IMON , D OROTHEA P.; and S IMON , H ERBERT A. 1980. "Expert and Novice Performance in Solving Physics Problems." Science 208:1335–1342.

L UCHINS , A BRAHAMA S. 1942. Mechanization in Problem Solving: The Effect of Einstellung. Evanston, IL: American Psychological Association.

M AYER , R ICHARD E. 1992. Thinking, Problem Solving, Cognition, 2nd edition. New York: Freeman.

M AYER , R ICHARD E. 1999. The Promise of Educational Psychology. Upper Saddle River, NJ: Prentice-Hall.

N ICKERSON , R AYMOND S. 1995. "Project Intelligence." In Encyclopedia of Human Intelligence, ed. Robert J. Sternberg. New York: Macmillan.

P RESSLEY , M ICHAEL J., and W OLOSHYN , V ERA . 1995. Cognitive Strategy Instruction that Really Improves Children's Academic Performance. Cambridge, MA: Brookline Books.

S TERNBERG , R OBERT J., and D AVIDSON , J ANET E. 1982. "The Mind of the Puzzler." Psychology Today 16:37–44.

S TERNBERG , R OBERT J., and Z HANG , L I -F ANG , eds. 2001. Perspectives on Thinking, Learning, and Cognitive Styles. Mahwah, NJ: Erlbaum.

W ERTHEIMER , M AX . 1959. Productive Thinking. New York: Harper and Row.

W HITEHEAD , A LFRED N ORTH . 1929. The Aims of Education. New York: Macmillan.

R ICHARD E. M AYER

Additional topics

Learning - Reasoning
Learning - Perceptual Processes

Education - Free Encyclopedia Search Engine Education Encyclopedia Learning - Causal Reasoning, Conceptual Change, Knowledge Acquisition, Representation, And Organization, Neurological Foundation, Perceptual Processes - ANALOGICAL REASONING

26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter.

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
Tailor your interview answer with the specific skills and qualifications outlined in the job description.
Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills?

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation.

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

Critical thinking
Analytical skills
Decision making
Research skills
Technical skills
Communication skills
Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow.

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve.

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams.

Examples of Problem-Solving in the Workplace

Correcting a mistake at work, whether it was made by you or someone else
Overcoming a delay at work through problem solving and communication
Resolving an issue with a difficult or upset customer
Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
Troubleshooting and resolving technical issues
Handling and resolving a conflict with a coworker
Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
Taking initiative when another team member overlooked or missed something important
Taking initiative to meet with your superior to discuss a problem before it became potentially worse
Solving a safety issue at work or reporting the issue to those who could solve it
Using problem solving abilities to reduce/eliminate a company expense
Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
Changing how a process, team, or task is organized to make it more efficient
Using creative thinking to come up with a solution that the company hasn’t used before
Performing research to collect data and information to find a new solution to a problem
Boosting a company or team’s performance by improving some aspect of communication among employees
Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

Coordinating work between team members in a class project
Reassigning a missing team member’s work to other group members in a class project
Adjusting your workflow on a project to accommodate a tight deadline
Speaking to your professor to get help when you were struggling or unsure about a project
Asking classmates, peers, or professors for help in an area of struggle
Talking to your academic advisor to brainstorm solutions to a problem you were facing
Researching solutions to an academic problem online, via Google or other methods
Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them.

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description.

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities.

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution.

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce.

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

3 Answers to “How Do You Handle Stress?”
How to Answer “How Do You Handle Conflict?” (Interview Question)
Sample Answers to “Tell Me About a Time You Failed”

About the Author

Biron Clark is a former executive recruiter who has worked individually with hundreds of job seekers, reviewed thousands of resumes and LinkedIn profiles, and recruited for top venture-backed startups and Fortune 500 companies. He has been advising job seekers since 2012 to think differently in their job search and land high-paying, competitive positions. Follow on Twitter and LinkedIn .

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5 Steps to Teaching Students a Problem-Solving Routine

By Jeff Heyck-Williams, the director of curriculum and instruction for Two Rivers Public Charter School

When I visited a 5th grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

There were students on the rug modeling people with Unifix cubes. There were kids at one table vigorously shaking each other’s hand. There were kids at another table writing out a diagram with numbers. At yet another table, students were working on creating a numeric expression. What was common across this class was that all of the students were productively grappling around the problem.

On a different day, I was out at recess with a group of kindergartners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher, they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics, which they took to Capitol Hill to share with legislators. Through the process, students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios and is an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in the District of Columbia, we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem-solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School on Vimeo .

Before Problem-Solving: The KWI

The three steps before problem-solving: We call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above, students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine, the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

The “I” stands for “ideas” and refers to ideas that a student brings to the table to solve a problem effectively. In this portion of the routine, students list the strategies that they will use to solve a problem. In the example from the math class, this step involved all of the different ways that students tackled the problem from Unifix cubes to creating mathematical expressions.

This KWI routine before problem-solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem-solving.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem-solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem-solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits, they also consider if their path to a solution was efficient and how it compares with other students’ solutions.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them. This empowers students to be the problem-solvers that we know they can become.

The opinions expressed in Next Gen Learning in Action are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.

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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.

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

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

New Designs for School 5 Steps to Teaching Students a Problem-Solving Routine

Jeff Heyck-Williams (He, His, Him) Director of the Two Rivers Learning Institute in Washington, DC

We’ve all had the experience of truly purposeful, authentic learning and know how valuable it is. Educators are taking the best of what we know about learning, student support, effective instruction, and interpersonal skill-building to completely reimagine schools so that students experience that kind of purposeful learning all day, every day.

Students can use the 5 steps in this simple routine to solve problems across the curriculum and throughout their lives.

When I visited a fifth-grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

On a different day, I was out at recess with a group of kindergarteners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics which they took to Capitol Hill to share with legislators. Through the process students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios, and an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in Washington, D.C., we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School

Before Problem-Solving: The KWI

The three steps before problem solving: we call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

This KWI routine before problem solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem solving.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits they also consider if their path to a solution was efficient and how it compares to other students’ solutions.

Jeff Heyck-Williams (He, His, Him)

Director of the two rivers learning institute.

Jeff Heyck-Williams is the director of the Two Rivers Learning Institute and a founder of Two Rivers Public Charter School. He has led work around creating school-wide cultures of mathematics, developing assessments of critical thinking and problem-solving, and supporting project-based learning.

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Inside Problem Solving

The Inside Problem Solving problems are non-routine math problems designed to promote problem-solving in your classroom. Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity. The problems were developed by the Silicon Valley Mathematics Initiative and are aligned to the Common Core standards.

To request the Inside Problem Solving Solutions Guide, please get in touch with us via the feedback form .

Courtney’s Collection Cut It Out Cutting a Cube Digging Dinosaurs Diminishing Return First Rate Friends You Can Count On Game Show Got Your Number Growing Staircases Measuring Mammals Measuring Up Miles of Tiles Movin ‘n Groovin On Balance Once Upon A Time Part and Whole Party Time Piece it Together Polly Gone Rod Trains Surrounded and Covered Squirreling It Away The Shape of Things The Wheel Shop Through the Grapevine Tri-Triangles What’s Your Angle?

Cutting a Cube (K.G.B.4) Digging Dinosaurs (K.OA.A.2) First Rate (K.CC.B.5, K.CC.C.6) Growing Staircases (K.CC.B.5) On Balance (K.MD.A.2)

Cutting a Cube (1.G.A.1) Growing Staircases (1.OA.A.1) Rod Trains (1.MD.A.2, 1.OA.C.6) Measuring Mammals (1.MD.A.1) Miles of Tiles (1.OA.A.1) Movin ‘n Groovin (1.OA.A.1) Piece it Together (1.G.A.2)

Courtney’s Collection (2.MD.C.8) Digging Dinosaurs (2.MD.C.8) Got Your Number (2.OA.B.2, 2.NBT.A.1, 2.NBT.A.4, 2.NBT.B.5) Miles of Tiles (2.NBT.B.5) Part and Whole (2.G.A.3) Piece it Together (2.G.A.1) Squirreling It Away (2.OA.1) The Shape of Things (2.G.A.1) Through the Grapevine (2.MD.D.9, 2.MD.D.10) What’s Your Angle? (2.G.A.1)

Measuring Up (3.OA.A.3) Once Upon A Time (3.MD.A.1) Part and Whole (3.G.A.2, 3.NF.A.1, 3.MD.C.6) Party Time (3.OA.A.3) Piece it Together (3.MD.C.5, 3.MD.D.8) Polly Gone (3.MD.D.8) Surrounded and Covered (3.MD.C.6, 3.MD.D.8) The Wheel Shop (3.OA.A.1, 3.OA.A.2) Tri-Triangles (3.OA.A.3)

Courtney’s Collection (4.MD.A.2) Digging Dinosaurs (4.MD.A.2) Diminishing Return (4.OA.A.3, 4.MD.A.2) Friends You Can Count On (4.OA.A.3) Game Show (4.OA.C.5) Growing Staircases (4.OA.C.5) Measuring Mammals (4.OA.A.2) Measuring Up (4.OA.A.3) Once Upon A Time (4.OA.A.3) Part and Whole (4.G.A.3) Party Time (4.NF.B.4c) Piece it Together (4.G.A.2, 4.MD.C.6) Squirreling It Away (4.OA.3) The Shape of Things (4.G.A.3) The Wheel Shop (4.OA.A.3) Tri-Triangles (4.OA.C.5)

Digging Dinosaurs (5.NBT.B.7) Movin ‘n Groovin (5.NF.B.4)

Courtney’s Collection (6.NS.B.4) Cutting a Cube (6.G.A.4, 6.RP.A.3c) Diminishing Return (6.RP.A.3a, 6.RP.A.3b) First Rate (6.RP.A.3b, 6.RP.A.2) Measuring Up (6.RP.A.3c, 6.EE.A.1, 6.EE.B.7) On Balance (6.EE.B.5, 6.EE.B.6, 6.EE.B.8) Once Upon A Time (6.NS.B.2, 6.NS.B.4) Movin ‘n Groovin (6.RP.A.3d) Part and Whole (6.G.A.1) Piece it Together (6.G.A.4) Polly Gone (6.G.A.1) Surrounded and Covered (6.RP.A.2, 6.RP.A.3b) Tri-Triangles (6.EE.A.1, 6.EE.B.6, 6.EE.C.9)

Courtney’s Collection (7.SP.C.8b) First Rate (7.RP.A.2b, 7.RP.A.3, 7.EE.B.4a) Friends You Can Count On (7.SP.C.7a, 7.SP.C.8a, 7.SP.C.8b) Game Show (7.SP.C.8a, 7.SP.C.8b) Got Your Number (7.NS.A.3) Measuring Mammals (7.RP.A.2a, 7.RP.A.2b, 7.RP.A.2c 7.RP.A.1) Measuring Up (7.RP.A.2b, 7.RP.A.2c, 7.RP.A.3, 7.EE.B.4) Movin ‘n Groovin (7.RP.A.2c, 7.RP.A.3) Part and Whole (7.NS.A.1D) Piece it Together (7.G.B.6) Polly Gone (7.G.B.6, 7.G.B.4) Rod Trains (7.SP.C.8b) Squirreling It Away (7.SP.8b) Surrounded and Covered (7.G.B.4, 7.G.B.6) Through the Grapevine (7.SP.A.2)

Cutting a Cube (8.G.A.1a) Digging Dinosaurs (8.EE.C.7b, 8.F.B.4) Diminishing Return (8.EE.C.7.b) Miles of Tiles (8.EE.C.8b, 8.EE.C.8c) Movin ‘n Groovin (8.EE.B5) On Balance (8.EE.C.8b, 8.EE.C.8c) Once Upon A Time (8.EE.C.8b) Squirreling It Away (8-F.1) Through the Grapevine (8.SP.A.1, 8.SP.A.2) The Wheel Shop (8.EE.C.8b, 8.EE.C.8c)

Courtney’s Collection (A-CED.A.2) Digging Dinosaurs (A-CED.A.2) Diminishing Return (A-CED.A.1) Growing Staircases (A-CED.A.2) Measuring Mammals (A-CED.A.2, A-REI.B.3, A-REI.C.6) Measuring Up (A-CED.2) Miles of Tiles (A-APR.A.1, A-SSE.A.1a, A-SSE.A.2) On Balance (A-CED.A.2, A-REI.C.6) Once Upon A Time (A-CED.A.1) Part and Whole (A-APR.D.6) Polly Gone (A-REI.C.6) Squirreling It Away (A-CED.2, A-CED.3, A-REI.6, A-REI.8, A-REI.10) The Wheel Shop (A-REI.C.6, A-REI.D.12) Tri-Triangles (A-CED.A.1, A-REI.B.4b, A-SSE.A.2)

Cut It Out (F-BF.A.1a) Digging Dinosaurs (F-IF.C.7b, F-IF.C.7e) Diminishing Return (F-BF.A.1a) First Rate (F-IF.B.6, F-BF.A.1a) Growing Staircases (F-LE.A.2, F-BF.A.2, F-BF.A.1a) Movin ‘n Groovin (F.BF. A.1a) Rod Trains (F-BF.A.1a) Squirreling It Away (F.LE.2, F-BF.1a, F-BF.2) Surrounded and Covered (F-BF.A.1a) Tri-Triangles (F-BF.A.1a) What’s Your Angle? (F-BF.A.1a)

Cut It Out (G-CO.B.6) Growing Staircases (G-MG.1) First Rate (G-SRT.C.8) Measuring Mammals (G-SRT.B.5) Miles of Tiles (G-MG.A.3) Once Upon A Time (G-C.A.2) Piece it Together (G.MG.A.1, G-MG.A.3, G.GMD.A.1, G.SRT.C.8) Polly Gone (G-CO.B.7, G-GPE.B.7, G-MG.A.3, G-GPE.B.4) The Shape of Things (G-C.A.2, G-CO.C.10, G-CO.C.11, G-SRT.B.5, G-MG.A.1) What’s Your Angle? (G-MG.A.3, G-C.A.2)

Digging Dinosaurs (S-ID.6.a) Diminishing Return (S-CP.A.2, S-CP.B.8) Friends You Can Count On (S-CP.A.4, S-CP.A.5, S-CP.B.6) Game Show (S-MD.A.1, S-MD.A.2, S-MD.A.3) Growing Staircases (S-ID.6a) Party Time (S-CP.A.1, S-CP.B.9, S-CP.B.8) Squirreling It Away (S-ID.6a) Through the Grapevine (S-IC.B.4, S-ID.A.1, S-ID.A.2, S-ID.A.3, S-ID.B.5, S-ID.B.6c) The Wheel Shop (S-CP.A.1)

Why Problem Solving?

Problem solving is the cornerstone of doing mathematics. George Polya, a famous mathematician from Stanford, once said, "A problem is not a problem if you can solve it in 24 hours." His point was that a problem that you can solve in less than a day is usually a problem that is similar to one that you have solved before, or at least is one where you recognize that a certain approach would lead to the solution. Bu t in real life, a problem is a situation that confronts you and you don’t have an idea of where to even start. Mathematics is the toolbox that solves so many problems. Whether it is calculating an estimate measure, modeling a complex situation, determining the probability of a chance event, transforming a graphical image or proving a case using deductive reasoning, mathematics is used. If we want our student s to be problem solvers and mathematically powerful, we must model perseverance and challenge students with non-routine problems.

Problem Solving in Math

Math Problem Solving, non-routine math problems

What is non-routine problem-solving in math?

A non-routine problem is any complex problem that requires some degree of creativity or originality to solve. Non-routine problems typically do not have an immediately apparent strategy for solving them. Often times, these problems can be solved in multiple ways.

Incorporating non-routine problem solving into your math program is one of the most impactful steps you can take as an educator. By consistently allowing your students to grapple with these challenging problems, you are helping them acquire essential problem-solving skills and the confidence needed to successfully execute them.

One of the best ways to prepare students for solving non-routine problems is by familiarizing them with the four steps of problem-solving. I have a set of questions and/or guides for each step, that students can use to engage in an inner-dialogue as they progress through the steps. You can download this free Steps to Non-Routine Problem Solving Flip-Book {HERE}.

1. Understand:

This is a time to just think! Allow yourself some time to get to know the problem. Read and reread. No pencil or paper necessary for this step. Remember, you cannot solve a problem until you know what the problem is!

Does the problem give me enough information (or too much information)?
What question is being asked of me?
What do I know and what do I need to find out?
What should my solution look like?
What type of mathematics might be required?
Can I restate the problem in my own words?
Are there any terms or words that I am unfamiliar with?

Now it’s time to decide on a plan of action! Choose a reasonable problem-solving strategy. Several are listed below. You may only need to use one strategy or a combination of strategies.

draw a picture or diagram
make an organized list
make a table
solve a simpler related problem
find a pattern
guess and check
act out a problem
work backward
write an equation
use manipulatives
break it into parts
use logical reasoning

3. Execute:

Alright! You understand the problem. You have a plan to solve the problem. Now it’s time to dig in and get to work! As you work, you may need to revise your plan. That’s okay! Your plan is not set in stone and can change anytime you see fit.

Am I checking each step of my plan as I work?
Am I keeping an accurate record of my work?
Am I keeping my work organized so that I could explain my thinking to others?
Am I going in the right direction? Is my plan working?
Do I need to go back to Step 2 and find a new plan?
Do I think I have the correct solution? If so, it’s time to move on to the next step!

4. Review:

You’ve come so far, but you’re not finished just yet! A mathematician must always go back and check his/her work. Reviewing your work is just as important as the first 3 steps! Before asking yourself the questions below, reread the problem and review all your work.

Is my answer reasonable?
Can I use estimation to check if my answer is reasonable?
Is there another way to solve this problem?
Can this problem be extended? Can I make a change to this problem to create a new one?
I didn’t get the correct answer. What went wrong? Where did I make a mistake?

My Brain Power Math resources are the perfect compliment to this free flip-book. Each book has a collection of non-routine math problems in a variety of formats.

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How to Solve Math Problems: Non-Routine Problems

Nonroutine Problem Solving , stresses the use of heuristics [3] and often requires little to no use of algorithms. Unlike algorithms, heuristics are procedures or strategies that do not guarantee a solution to a problem but provide a more highly probable method for discovering a solution. Building a model and drawing a picture of a problem are two basic problem-solving heuristics. Studying end-of-game situations provides students with experiences in using the heuristics of reducing the problem to a similar but simpler problem and working a problem backwards, i.e. from its resolution to its initial state. Other heuristics include describing the problem situation, classifying information, and finding irrelevant information. [1]

There Are Two Categories of Nonroutine Problem Solving: Static and Active

What is non-routine problem-solving in math?

Step 1: Understand

Does the problem give me enough information (or too much information)?
What question is being asked of me?
What do I know and what do I need to find out?
What should my solution look like?
What type of mathematics might be required?
Can I restate the problem in my own words?
Are there any terms or words that I am unfamiliar with?

Step 2: Plan

Now it’s time to decide on a plan of action! Choose a reasonable problem-solving strategy. Several are listed below. You may only need to use one strategy or a combination of strategies.

Draw a picture or diagram
Make an organized list
Make a table
Solve a simpler related problem
Find a pattern
Guess and check
Act out a problem
Work backward
Write an equation
Use manipulatives
Break it into parts
Use logical reasoning

Step 3: Execute

Am I checking each step of my plan as I work?
Am I keeping an accurate record of my work?
Am I keeping my work organized so that I could explain my thinking to others?
Am I going in the right direction? Is my plan working?
Do I need to go back to Step 2 and find a new plan?
Do I think I have the correct solution? If so, it’s time to move on to the next step!

Step 4: Review

Is my answer reasonable?
Can I use estimation to check if my answer is reasonable?
Is there another way to solve this problem?
Can this problem be extended? Can I make a change to this problem to create a new one?
I didn’t get the correct answer. What went wrong? Where did I make a mistake?

[1] “Pentathlon Institute Active Problem-Solving”. 2023. mathpentath.org . https://www.mathpentath.org/active-problem-solving/ .

[2] Tallman, Melissa. 2015. “Problem Solving In Math • Teacher Thrive”. Teacher Thrive. https://teacherthrive.com/non-routine-problem-solving/ .

[3] A heuristic is a mental shortcut commonly used to simplify problems and avoid cognitive overload .

Additional Reading

“101 Great Higher-Order Thinking Questions for Math”. 2023. elementaryassessments.com . https://elementaryassessments.com/higher-order-thinking-questions-for-math/ .

⭐ “Developing Mathematics Thinking with HOTS (Higher Order Thinking Skills) Questions”. 2023. saydel.k12.ia.us . https://www.saydel.k12.ia.us/cms_files/resources/Developing%20Mathematics%20Thinking%20with%20HOTS%20Questions%20(from%20classroom%20observations)PDF.pdf .

“Higher Order Thinking Skills in Maths”. 2017. education.gov.Scot . https://education.gov.scot/resources/higher-order-thinking-skills-in-maths/ .

“How to Increase Higher Order Thinking”. 2023. Reading Rockets . https://www.readingrockets.org/topics/comprehension/articles/how-increase-higher-order-thinking .

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.

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Linear algebra ( numpy.linalg ) #

The NumPy linear algebra functions rely on BLAS and LAPACK to provide efficient low level implementations of standard linear algebra algorithms. Those libraries may be provided by NumPy itself using C versions of a subset of their reference implementations but, when possible, highly optimized libraries that take advantage of specialized processor functionality are preferred. Examples of such libraries are OpenBLAS , MKL (TM), and ATLAS. Because those libraries are multithreaded and processor dependent, environmental variables and external packages such as threadpoolctl may be needed to control the number of threads or specify the processor architecture.

The SciPy library also contains a linalg submodule, and there is overlap in the functionality provided by the SciPy and NumPy submodules. SciPy contains functions not found in numpy.linalg , such as functions related to LU decomposition and the Schur decomposition, multiple ways of calculating the pseudoinverse, and matrix transcendentals such as the matrix logarithm. Some functions that exist in both have augmented functionality in scipy.linalg . For example, scipy.linalg.eig can take a second matrix argument for solving generalized eigenvalue problems. Some functions in NumPy, however, have more flexible broadcasting options. For example, numpy.linalg.solve can handle “stacked” arrays, while scipy.linalg.solve accepts only a single square array as its first argument.

The term matrix as it is used on this page indicates a 2d numpy.array object, and not a numpy.matrix object. The latter is no longer recommended, even for linear algebra. See the matrix object documentation for more information.

The @ operator #

Introduced in NumPy 1.10.0, the @ operator is preferable to other methods when computing the matrix product between 2d arrays. The numpy.matmul function implements the @ operator.

Matrix and vector products #

(a, b[, out])	Dot product of two arrays.
(arrays, *[, out])	Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order.
(a, b, /)	Return the dot product of two vectors.
(a, b, /)	Inner product of two arrays.
(a, b[, out])	Compute the outer product of two vectors.
(x1, x2, /[, out, casting, order, ...])	Matrix product of two arrays.
(a, b[, axes])	Compute tensor dot product along specified axes.
(subscripts, *operands[, out, dtype, ...])	Evaluates the Einstein summation convention on the operands.
(subscripts, *operands[, optimize])	Evaluates the lowest cost contraction order for an einsum expression by considering the creation of intermediate arrays.
(a, n)	Raise a square matrix to the (integer) power .
(a, b)	Kronecker product of two arrays.

Decompositions #

(a)	Cholesky decomposition.
(a[, mode])	Compute the qr factorization of a matrix.
(a[, full_matrices, compute_uv, ...])	Singular Value Decomposition.

Matrix eigenvalues #

(a)	Compute the eigenvalues and right eigenvectors of a square array.
(a[, UPLO])	Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.
(a)	Compute the eigenvalues of a general matrix.
(a[, UPLO])	Compute the eigenvalues of a complex Hermitian or real symmetric matrix.

Norms and other numbers #

(x[, ord, axis, keepdims])	Matrix or vector norm.
(x[, p])	Compute the condition number of a matrix.
(a)	Compute the determinant of an array.
(A[, tol, hermitian])	Return matrix rank of array using SVD method
(a)	Compute the sign and (natural) logarithm of the determinant of an array.
(a[, offset, axis1, axis2, dtype, out])	Return the sum along diagonals of the array.

Solving equations and inverting matrices #

(a, b)	Solve a linear matrix equation, or system of linear scalar equations.
(a, b[, axes])	Solve the tensor equation x = b for x.
(a, b[, rcond])	Return the least-squares solution to a linear matrix equation.
(a)	Compute the (multiplicative) inverse of a matrix.
(a[, rcond, hermitian])	Compute the (Moore-Penrose) pseudo-inverse of a matrix.
(a[, ind])	Compute the 'inverse' of an N-dimensional array.

Exceptions #

Generic Python-exception-derived object raised by linalg functions.

Linear algebra on several matrices at once #

New in version 1.8.0.

Several of the linear algebra routines listed above are able to compute results for several matrices at once, if they are stacked into the same array.

This is indicated in the documentation via input parameter specifications such as a : (..., M, M) array_like . This means that if for instance given an input array a.shape == (N, M, M) , it is interpreted as a “stack” of N matrices, each of size M-by-M. Similar specification applies to return values, for instance the determinant has det : (...) and will in this case return an array of shape det(a).shape == (N,) . This generalizes to linear algebra operations on higher-dimensional arrays: the last 1 or 2 dimensions of a multidimensional array are interpreted as vectors or matrices, as appropriate for each operation.

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35 problem-solving techniques and methods for solving complex problems
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.
Workplace Problem-Solving Examples: Real Scenarios, Practical Solutions
Problem-solving in the workplace is a complex and multifaceted skill that requires a combination of analytical thinking, creativity, and effective communication. It goes beyond simply identifying problems and extends to finding innovative solutions that address the root causes. Essential Problem-Solving Skills for the Workplace
Routine and non routine problems
AI-enhanced description. rey castro. Follow. This document discusses and provides examples of routine and non-routine problem solving. Routine problems involve using arithmetic operations to solve practical problems and have clear, straightforward procedures. Non-routine problems require more creativity, originality, and higher-order thinking ...
Pentathlon Institute Active Problem-Solving
Routine & Non-Routine. Routine Problem Solving, stresses the use of sets of known or prescribed procedures (algorithms) to solve problems. The strength of this approach is that it is easily assessed by paper-pencil tests. ... Solving a jigsaw puzzle is an example of a Static- Nonroutine problem. Given all pieces to a puzzle and a picture of the ...
10 Problem-solving strategies to turn challenges on their head
One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training, shadowing a mentor, or working with a coach. 2. Practice. Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life.
Learning
In a routine problem, the problem solver knows a solution method and only needs to carry it out. For example, for most adults the problem "589 × 45 = ___" is a routine problem if they know the procedure for multicolumn multiplication. Routine problems are sometimes called exercises, and technically do not fit the definition of problem stated ...
Chapter 2 Routine and Non Routine Problem
Routine problems can be solved using a direct application of learned algorithms and involve a single arithmetic operation. Non-routine problems require strategies and creative thinking as the procedure for solving is unknown, involving consideration of multiple facts and information to solve in distinct ways. Examples of non-routine problems include estimating the number of hairs on one's head ...
26 Expert-Backed Problem Solving Examples
The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate. 1. Analytical Thinking. Situation: In my previous role as a data analyst, our team encountered a significant drop in website traffic.
5 Steps to Teaching Students a Problem-Solving Routine
The three steps before problem-solving: We call them the K-W-I. The "K" stands for "know" and requires students to identify what they already know about a problem. The goal in this step of ...
Problem-Solving Strategies and Obstacles
Problem-solving is a vital skill for coping with various challenges in life. This webpage explains the different strategies and obstacles that can affect how you solve problems, and offers tips on how to improve your problem-solving skills. Learn how to identify, analyze, and overcome problems with Verywell Mind.
Activity Sheets
The document contains instructions for solving routine and non-routine mathematics problems. For routine problems, students are given two examples: calculating the teacher-pupil ratio given the number of teachers and pupils, and calculating the cost of 2.5 meters of cloth given the cost of 1 meter. For non-routine problems, students are given two examples: finding a three-digit number based on ...
5 Step Problem Solving Process Model for Students
The three steps before problem solving: we call them the K-W-I. The "K" stands for "know" and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem.
What Are Critical Thinking Skills and Why Are They Important?
Examples of common critical thinking skills. ... Problem-solving: Problem-solving is perhaps the most important skill that critical thinkers can possess. The ability to solve issues and bounce back from conflict is what helps you succeed, be a leader, and effect change. One way to properly solve problems is to first recognize there's a ...
Inside Problem Solving
The Inside Problem Solving problems are non-routine math problems designed to promote problem-solving in your classroom. Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity. The problems were developed by the Silicon ...
Routine and Non-Routine Problems
Routine Problem Solving - From the curricular point of view, routine problem solving. involves using at least one of the four arithmetic operations and/or ratio to solve problems that are practical in nature. Problems: How many cubic centimeters are there in 1; 1. 2 liters? Answer: 1500 cm 3. Daniella bought 12; 1.
Conceptual Knowledge, Procedural Knowledge, and ...
When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of doubt, mediate interactions between procedural and ...
Lesson 81 Routine and Non-Routine Problems Involving Areas of ...
1. The lesson plan provides activities to teach students how to solve routine and non-routine problems involving the areas of squares and rectangles. 2. Students will identify shapes, solve word problems, and create their own word problems involving the area of squares and rectangles. 3. The activities include identifying shapes from descriptions, calculating areas of squares and rectangles ...
The Difference of Routine and Non-routine Problems in Mathematics
This video shows the difference between routine and Non-routine Problems in Mathematics with some examples for each type of problem.Routine problem is a type...
The relationship between routine and non-routine problem solving and
This study aims to investigate the relationship between learning styles and the efficacy of routine and non-routine problem solving. It also compares these relationships with respect to routine and non-routine problem types. The study sample consisted of 356 eighth-grade students in four different schools. In this study, correlational and ...
Differences between routine and non-routine problems
The study sample was divided into two groups which were the treatment group and the control group. ... teachers rarely emphasised on non-routine problem solving in classrooms as well (Silver et al ...
Problem Solving in Math • Teacher Thrive
Incorporating non-routine problem solving into your math program is one of the most impactful steps you can take as an educator. By consistently allowing your students to grapple with these challenging problems, you are helping them acquire essential problem-solving skills and the confidence needed to successfully execute them.
7 Problem-Solving Skills That Can Help You Be a More ...
Although problem-solving is a skill in its own right, a subset of seven skills can help make the process of problem-solving easier. These include analysis, communication, emotional intelligence, resilience, creativity, adaptability, and teamwork. 1. Analysis. As a manager, you'll solve each problem by assessing the situation first.
PDF Non-routine problem solving and strategy flexibility: A quasi
Demetriou (2004), for example, flexibility refers to the amount of diversity in mental operations and concepts a person has. On the other hand, strategic flexibility is the ability to use multiple ... Non-routine problem-solving strategies can be defined as procedures used to explore, analyze
How to Solve Math Problems: Non-Routine Problems
Step 2: Plan. Now it's time to decide on a plan of action! Choose a reasonable problem-solving strategy. Several are listed below. You may only need to use one strategy or a combination of strategies. Draw a picture or diagram. Make an organized list. Make a table. Solve a simpler related problem.
More effective solutions? Senior managers and non‐routine problem solving
Importantly, while including in the sample instances of problem solving that had already ended is a necessary condition to assess solution effectiveness, the firm's closure of the problem-solving project does not equate to effective problem solving. In fact, the problem-solving projects in our sample varied in their outcomes. 3.2 Data collection
Transferable Skills: How to Use Them to Land Your Next Job
Here are six common transferable skills, with examples of how they might show up in different roles. Use this list to help identify your own transferrable skills. 1. Critical thinking. Critical thinking is the ability to evaluate, synthesize, and analyze information in an objective manner in order to produce an original insight or judgement.
Linear algebra (numpy.linalg)
For example, scipy.linalg.eig can take a second matrix argument for solving generalized eigenvalue problems. Some functions in NumPy, however, have more flexible broadcasting options. For example, numpy.linalg.solve can handle "stacked" arrays, while scipy.linalg.solve accepts only a single square array as its first argument.
FAR
FAC Number Effective Date HTML DITA PDF Word EPub Apple Books Kindle; 2024-05: 05/22/2024