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Eight Steps To Practical Problem Solving

Problem solving

The Toyota Way To Problem Solving

The art of problem solving is constantly trying to evolve and be re-branded by folks in various industries. While the new way might very well be an effective method in certain applications. A tried and true way of identifying and solving problems is the eight steps to practical problem solving developed by Toyota, years ago. The system is structured, but simple and practical enough to handle problems of the smallest nature, to the most complex issues.

Using a fundamental and strategic way to solve problems creates consistency within an organization. When you base your results off facts, experience and common sense, the results form in a rational and sustainable way.

Problem Solving Solution

The Eight Step Problem Solving Process

  • Clarify the Problem
  • Breakdown the Problem
  • Set the Target
  • Analyze the Root Cause
  • Develop Countermeasures
  • Implement Countermeasures
  • Monitor Results and Process
  • Standardize and Share Success

The eight steps to practical problem solving also include the Plan, Do, Check and Act (PDCA) cycle. Steps one through five are the planning process. The doing is found in step six. Step seven is the checking . Step eight involves acting out the results of the new standard.

This practical problem solving can be powerful tool to issues facing your organization. It allows organizations to have a common understanding of what defines a problem and what steps are going to be taken in order to overcome the problem efficiently.

The Eight Steps Broken Down:

Step 1: clarify the problem.

A problem can be defined in one of three ways. The first being, anything that is a deviation from the standard. The second could be the gap between the actual condition and the desired condition. With the third being an unfilled customer need.

In order to best clarify the problem, you have to see the problem with your own eyes. This gives you the details and hands-on experience that will allow you to move forward in the process.

Step 2: Breakdown the Problem

Once you’ve seen the problem first hand, you can begin to breakdown the problem into more detailed and specific problems. Remember, as you breakdown your problem you still need to see the smaller, individual problems with your own eyes. This is also a good time to study and analyze the different inputs and outputs  of the process so that you can effectively prioritize your efforts. It is much more effective to manage and solve a bunch of micro-problems one at a time, rather than try and tackle a big problem with no direction.

Step 3: Set the Target

setting goals, root cause analysis

Step three is all about commitment and focus. Your attention should now turn towards focusing on what is needed to complete the project and how long it will take to finish. You should set targets that are challenging, but within limits and don’t put a strain on the organization that would hinder the improvement process.

Step 4: Analyze the Root Cause

This is a vital step when problem solving, because it will help you identify the actual factors that caused the issue in the first place. More often than not, there are multiple root causes to analyze. Make sure you are considering all potential root causes and addressing them properly. A proper root cause analysis, again involves you actually going to the cause itself instead of simply relying on reports.

Step 5: Develop Countermeasures

Once you’ve established your root causes, you can use that information to develop the countermeasures needed to remove the root causes. Your team should develop as many countermeasures needed to directly address any and all root causes. Once you’ve developed your countermeasures, you can begin to narrow them down to the most practical and effective based off your target.

Step 6: Implement Countermeasures

Now that you have developed your countermeasures and narrowed them down, it is time to see them through in a timely manner. Communication is extremely important in step six. You’ll want to seek ideas from the team and continue to work back through the PDCA cycle to ensure nothing is being missed along the way. Consider implementing one countermeasure at a time to monitor the effectiveness of each.

You will certainly make mistakes in throughout your problem solving processes, but your persistence is key, especially in step six.

Step 7: Monitor Results and Process

As mistakes happen and countermeasures fail, you need a system in place to review and modify them to get the intended result. You can also determine if the intended outcome was the result of the action of the countermeasure, or was it just a fluke? There is always room for improvement in the problem solving process, but you need to be able to recognize it when it comes to your attention.

Step 8: Standardize and Share Success

Now that you’ve encountered success along your problem solving path, it is time to set the new processes as the new standard within the organization and share them throughout the organization. It is also a good time to reflect on what you’ve learned and address any possible unresolved issues or troubles you have along the way. Ignoring unresolved issues will only lead to more problems down the road.

Finally, because you are a true Lean organization who believes continuous improvement never stops, it is time to tackle the next problem. Start the problem solving process over again and continue to work towards perfection.

Additional Resources

  • 8D for Problem Solving – creativesafetysupply.com
  • Training to Use 8D Problem-Solving Tactics – blog.creativesafetysupply.com
  • The Great Root Cause Problem Solving Debate – realsafety.org
  • Design Thinking: Empathy and Iteration for Innovation and Problem-Solving – creativesafetypublishing.com
  • 10 Commandments to Continuous Improvement – lean-news.com
  • Lean Manufacturing Implementation – The First 5 Steps – iecieeechallenge.org
  • No Problem is a Problem – jakegoeslean.com
  • The Transitional Steps Involved In The 5s Principles During Implementation – 5snews.com
  • The Tools of Kaizen – blog.5stoday.com

Related posts:

  • 3P and Lean
  • The Vacation Paradox
  • Why Single Minute Exchange of Die (SMED)?
  • Total Quality Management And Kaizen Principles In Lean Management
  • An Engaged Employee is a Productive Employee
  • Jim Womack’s Top Misconceptions of the Lean Movement
  • Muda, Mura, and Muri: The Three Wastes


Toyota Practical Problem Solving (PPS)—Introduction

a practical problem solving

The Framework: PDCA

PDCA Circle

  • Plan is to identify and clarify the problem, including collecting data to understand the problem, setting a target, and doing a root-cause analysis.
  • Do is the development and implementation of countermeasures.
  • Check verifies whether these countermeasures were effective and the target has been reached.
  • Act is to re-do and further improve if the targets have not been met (yet). If it was successful, the Act part looks for other locations and applications where this solution could be used (e.g., if it was a smaller trial to be rolled out on a larger scale). Toyota also shares these yokoten on an internal website with other plants.


Toyota practical problem solving consists of the steps as listed below. Note that sometimes you have a step more if you decide to split a step into two.

  • Clarify the Problem
  • Break Down the Problem
  • Set a Target
  • Root-Cause Analysis
  • Develop Countermeasures and Implement
  • Monitor Process and Results
  • Standardize and Share

I will explain all these steps in much more detail, including the risks and difficulties, throughout this small series of posts. But before explaining these steps in detail, let me also show you the structure.

The Structure: A3

You probably know the structure already, or at least have heard of it: it is the famous A3 . This report, named after the standard A3 paper size, is commonly used at Toyota to tackle medium-sized problems. The A3 format was chosen because it was a good compromise between getting lots of data on a single page and also having a page small enough to be carried around on the shop floor. (And, as legend has it, A3 was supposedly the largest format to fit though a fax machine back in the day).

You will find all the steps from above again in this A3 format, an example of which is shown below, plus the obligatory header row with organizational data like title, date, and so on.

a practical problem solving

The A3 is intended to be filled out in pencil (not pen), which makes changing content easy by using an eraser. Nowadays digital tools are also often used, although Toyota still does this mostly by hand using pencil on paper. Digital A3s are easier to share and look prettier, but they are harder to make and much more effort is needed in creating the A3. If you have ever created an A3 in Microsoft Excel, you know what I am talking about (as Excel is wholly unsuited for such graphical work…Ugh!)

a practical problem solving

The “Do” part is actually quite small. If you understand the problem well, the solutions are rather easy. If you don’t understand the problem, you still may have a solution, but it will probably be an inferior one, if it works at all. Similarly, the Check and Act are also rather small.

In my experience, this is often done differently (and in my opinion worse) in many other Western companies. The focus is all on doing something, implementing some sort of solution. There is a bit of planning, but the vast majority of the effort goes into the “Do” part. The “Check” and “Act” parts are quite underdeveloped, if they exist at all.

A fancy presentation often substitutes for “Check,” resulting in many supposedly successful projects that did not improve much or even made it worse. Below I compared the normal representation of the PDCA circle having four equal quadrants with a PDCA circle based on the effort by Japanese or Toyota standards, and another PDCA circle based on the effort of (way too many) Western companies. I’ll let you be the judge on how this is in your company.

a practical problem solving

Over and over again I guide people through the practical problem-solving process, and at every single step they jump to a solution. Let’s take a (fictitious) example for the steps of the problem solving, where every step is going right for the solution, ignoring the initial purpose of the step:

  • Clarify the Problem: Well, we need kanban!
  • Break Down the Problem: Okay, how many kanban do we need?
  • Set a Target: That’s how many kanban we need!
  • Root-Cause Analysis: Um… we did this already. It’s the lack of kanban…
  • Develop Countermeasures and Implement: Add kanban!
  • Monitor Process and Results: Do we have kanban now? Yes, we do. Case closed.
  • Standardize and Share: Hey, guys, use kanban!

a practical problem solving

PS: Many thanks to the team from the Toyota Lean Management Centre at the Toyota UK Deeside engine plant in Wales, where I participated in their 5-day course. This course gave us a lot of access to the Toyota shop floor, and we spent hours on the shop floor looking at processes. In my view, this the only generally accessible course by Toyota that gives such a level of shop floor involvement.

6 thoughts on “Toyota Practical Problem Solving (PPS)—Introduction”

Great ‘ Flow ‘ and easy to understand , specially for many who have limited exposure. Thanks

Thank you for sharing. PDCA is applicable on the shop floor, logistics, service industry – wherever Problems are accurately defined

Nice blog. I’m working in an NHS Production System (NHSps) design based on the Toyota and VMI Production Systems. Do you have any experience in this area?

Hi Tom, sorry, I am completely unfamiliar with the NHS production system. if you mean the National Health Service in the UK, I do have a bit of experience with lean Hospital.

Might I suggest a dry erase marker and a whiteboard? After a few times when the document structure is mostly stable, you can add lines with a permanent marker to fix the format in place. That way you’re not creating extra friction for the process.

As for actual A3, that works best when the A3 paper and printers that can print it are already readily available. I’m sure you ran across more than one business where just about every single printer on site can’t print anything larger than A4 or A3 paper simply isn’t available due to A4 used for everything.

Hi Andrey, I am a great fan of erasable notes, and use dry erase whiteboard markers a lot myself. An A3 printer is also really helpful, but just as you said, not every (small) business has one. For example, I only have an A4 printer in my office…

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Home > Learn Lean > Learn A3 8 Step Practical Problem Solving

Learn A3 8 Step Practical Problem Solving

a practical problem solving

What is A3 8 Step Practical Problem Solving?

A3 8 Step Practical Problem Solving (PPS) is a structured and effective problem-solving process used by individuals and teams to solve challenging, medium term, business and operational problems, originally pioneered by Toyota. Learn about the 8-step process, including clarifying the problem, containment, analysing & breaking it down, target setting, analysing the root cause(s), developing & planning countermeasures, confirming the results and standardising & sharing. Improve your problem-solving skills, preventing the reoccurrence of issues whilst improving results by applying the A3 8 Step Practical Problem Solving (PPS) process.

a practical problem solving

A3 8 Step Practical Problem Solving – Skill Level 1: Knowledge

This is a self-paced 2 hour course that is hosted on our online Learning Platform . By completeting this course you will gain the basic Purpose, Process and People knowledge about A3 Practical Problem Solving.

a practical problem solving

A3 8 Step Practical Problem Solving – Skill Level 2: Understanding

– 12 Hours Online, On-Demand, Self Paced Learning

– Purpose, Process, People & Method of Practical Problem Solving

– Teach Poster, 31 Teach Videos, A3 Case Study and Evaluation Method

– Learning Confirmation & Certificate of Completion

a practical problem solving

A3 8 Step Practical Problem Solving – Skill Level 3: Capable

This is an on-the-job coached course where a Senior Lean Coach will help you to become Capable in A3 8 Step Practical Problem Solving. Available online or face-to-face.

a practical problem solving

A3 8 Step Practical Problem Solving – Skill Level 4: Teach & Coach Others

Want to access all our online courses and webinars all in one place? Starting at just £99.99+VAT/year, our Learning Platform Subscription provides all current and future materials developed by the Lean Enterprise Academy. Click on the subscription logo to find out more information.

a practical problem solving

Supporting Materials

A3 Problem Solving - Capability Development Workshop 2024

A3 Problem Solving: On-Demand Webinar

This is a video recording of our A3 Problem Solving webinar. Included is access to a video of the webinar, a copy of the presentation slides, a transcript of the webinar, our Lean A3 Problem Solving Teach Poster presented during the webinar.

a practical problem solving

35 problem-solving techniques and methods for solving complex problems

Problem solving workshop

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

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

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

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

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

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

  • Tips for more effective problem-solving

Complete problem-solving methods

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

Problem-solving warm-up activities

Closing activities for a problem-solving process.

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

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

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

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

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

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

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

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

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

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

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

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

a practical problem solving

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!

a practical problem solving

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! 

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thank you very much for these excellent techniques

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Certainly wonderful article, very detailed. Shared!

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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."

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

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

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

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

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

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

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

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

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

National Alliance on Mental Illness. Warning signs and symptoms .

Mayer RE. Thinking, problem solving, cognition, 2nd ed .

Schooler JW, Ohlsson S, Brooks K. Thoughts beyond words: When language overshadows insight. J Experiment Psychol: General . 1993;122:166-183. doi:10.1037/0096-3445.2.166

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


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The Problem-Solving Process

Looking at the basic problem-solving process to help keep you on the right track.

By the Mind Tools Content Team

Problem-solving is an important part of planning and decision-making. The process has much in common with the decision-making process, and in the case of complex decisions, can form part of the process itself.

We face and solve problems every day, in a variety of guises and of differing complexity. Some, such as the resolution of a serious complaint, require a significant amount of time, thought and investigation. Others, such as a printer running out of paper, are so quickly resolved they barely register as a problem at all.

a practical problem solving

Despite the everyday occurrence of problems, many people lack confidence when it comes to solving them, and as a result may chose to stay with the status quo rather than tackle the issue. Broken down into steps, however, the problem-solving process is very simple. While there are many tools and techniques available to help us solve problems, the outline process remains the same.

The main stages of problem-solving are outlined below, though not all are required for every problem that needs to be solved.

a practical problem solving

1. Define the Problem

Clarify the problem before trying to solve it. A common mistake with problem-solving is to react to what the problem appears to be, rather than what it actually is. Write down a simple statement of the problem, and then underline the key words. Be certain there are no hidden assumptions in the key words you have underlined. One way of doing this is to use a synonym to replace the key words. For example, ‘We need to encourage higher productivity ’ might become ‘We need to promote superior output ’ which has a different meaning.

2. Analyze the Problem

Ask yourself, and others, the following questions.

  • Where is the problem occurring?
  • When is it occurring?
  • Why is it happening?

Be careful not to jump to ‘who is causing the problem?’. When stressed and faced with a problem it is all too easy to assign blame. This, however, can cause negative feeling and does not help to solve the problem. As an example, if an employee is underperforming, the root of the problem might lie in a number of areas, such as lack of training, workplace bullying or management style. To assign immediate blame to the employee would not therefore resolve the underlying issue.

Once the answers to the where, when and why have been determined, the following questions should also be asked:

  • Where can further information be found?
  • Is this information correct, up-to-date and unbiased?
  • What does this information mean in terms of the available options?

3. Generate Potential Solutions

When generating potential solutions it can be a good idea to have a mixture of ‘right brain’ and ‘left brain’ thinkers. In other words, some people who think laterally and some who think logically. This provides a balance in terms of generating the widest possible variety of solutions while also being realistic about what can be achieved. There are many tools and techniques which can help produce solutions, including thinking about the problem from a number of different perspectives, and brainstorming, where a team or individual write as many possibilities as they can think of to encourage lateral thinking and generate a broad range of potential solutions.

4. Select Best Solution

When selecting the best solution, consider:

  • Is this a long-term solution, or a ‘quick fix’?
  • Is the solution achievable in terms of available resources and time?
  • Are there any risks associated with the chosen solution?
  • Could the solution, in itself, lead to other problems?

This stage in particular demonstrates why problem-solving and decision-making are so closely related.

5. Take Action

In order to implement the chosen solution effectively, consider the following:

  • What will the situation look like when the problem is resolved?
  • What needs to be done to implement the solution? Are there systems or processes that need to be adjusted?
  • What will be the success indicators?
  • What are the timescales for the implementation? Does the scale of the problem/implementation require a project plan?
  • Who is responsible?

Once the answers to all the above questions are written down, they can form the basis of an action plan.

6. Monitor and Review

One of the most important factors in successful problem-solving is continual observation and feedback. Use the success indicators in the action plan to monitor progress on a regular basis. Is everything as expected? Is everything on schedule? Keep an eye on priorities and timelines to prevent them from slipping.

If the indicators are not being met, or if timescales are slipping, consider what can be done. Was the plan realistic? If so, are sufficient resources being made available? Are these resources targeting the correct part of the plan? Or does the plan need to be amended? Regular review and discussion of the action plan is important so small adjustments can be made on a regular basis to help keep everything on track.

Once all the indicators have been met and the problem has been resolved, consider what steps can now be taken to prevent this type of problem recurring? It may be that the chosen solution already prevents a recurrence, however if an interim or partial solution has been chosen it is important not to lose momentum.

Problems, by their very nature, will not always fit neatly into a structured problem-solving process. This process, therefore, is designed as a framework which can be adapted to individual needs and nature.

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

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

What Is Problem Solving?

Definition and importance.

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

Problem-Solving Steps

The problem-solving process typically includes the following steps:

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

Defining the Problem

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

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

Generating Solutions

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

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

Evaluating and Selecting Solutions

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

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

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

Implementing and Monitoring the Solution

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

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

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

Problem-Solving Techniques

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

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


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

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

When brainstorming, remember to:

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

Root Cause Analysis

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

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

SWOT Analysis

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

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

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

Mind Mapping

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

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

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

Examples of Problem Solving in Various Contexts

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

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

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

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

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

  • Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
  • Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
  • Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
  • How to Resolve Employee Conflict at Work [Steps, Tips, Examples]
  • How to Write Inspiring Core Values? 5 Steps with Examples
  • 30 Employee Feedback Examples (Positive & Negative)

How To Solve The Problems? Practical Problem Solving Skills

A woman in a white shirt is looking down and holding her head in her hands. She has long blonde hair and blue eyes. Her lips are slightly pursed, and her eyebrows are slightly furrowed. She looks sad and contemplative, as if she is lost in thought. Her arms are crossed in front of her chest, and her head is slightly tilted to the side. Her expression is thoughtful and her posture is relaxed. She is standing in front of a plain white wall, and the light casts shadows on her face. She appears to be alone in the room, and her posture conveys a sense of loneliness and introspection.

Problem solving is a process in which problems can break down into three steps: identify the problem, generate solutions, and evaluate and choose one of the developed solutions as an appropriate solution for this specific situation. Breaking the problem solving process down into these three steps makes it easier to understand and follow.

The first step in problem solving is to identify the problem. This may seem like a simple task, but it can be challenging to accurately determine the situation when multiple issues are involved. Once the problem has been identified, it is important to understand what the problem is and what needs to be done to fix it.

The second step in problem-solving is to generate possible solutions. Many different strategies can be used when developing these potential solutions. One strategy is brainstorming, where each person in a group shares all of their ideas no matter how ridiculous they may seem. Another strategy involves using a Venn diagram and either expanding or reducing it as you start considering more or less possible solutions.

The third step in problem-solving is to evaluate and choose one of the generated solutions appropriate for this specific situation. This step can be difficult, as it can be hard to determine which solution is best. A few different factors can be considered when making this decision, such as how realistic the answer is, how effective it will be in solving the problem, and whether or not it will make things better or worse. Some other factors include how much time and effort it will take to implement the solution and whether or not there are any laws or regulations that must be considered.

Once a problem has been properly identified, possible solutions have been generated, and a decision has been made as to which possible explanation is the most appropriate for this specific situation, it can be put into action. If issues with this solution or other problems arise, the problem solving process must start over. This process can take place many times before a final resolution is reached.

Understanding and following the three steps of problem solving can be easier to identify and fix problems. However, it is essential to note that these steps are not always linear and that different solutions may need to be tried to find the best one. The key is to stay focused on solving the problem and not give up until a resolution is reached.

Creative Solutions For Better Resolving The Issues

Sometimes, reasoning with others works wonders. However, you may find yourself up against a brick wall at other times. And if that happens, there are ways to do things the right way, so the next time someone tries to hold their ground stubbornly, your side of the story comes across as being more persuasive than theirs does. For example, instead of arguing with someone and resorting to insults or name-calling, you can try coming up with a creative solution to the problem at hand.

That's because when it comes to problem-solving, creativity is key. If you can think of a unique way to resolve the situation, then there's a good chance that things will go more smoothly than if you try to overpower the other person or take a more traditional route. Granted, there's no guarantee that things will work out in your favor, but it's always worth a shot, especially if the alternative is an all-out war.

Being creative with your problem-solving skills can mean the difference between coming across as professional or childish. Sure, there are certain situations where you'll want to be respectful of others even if they're being difficult, but when it comes down to brass tacks. Someone is refusing to budge on an issue that needs to be resolved (or an argument needs to end). Creativity can work wonders in getting what you want. So the next time you find yourself in a sticky situation, try thinking outside the box and see if that helps resolve things more positively. Who knows? You may be surprised at how well it works.

There are many different types of problems; however, you should follow some general guidelines when trying to solve any problem.

Problems come in all shapes and sizes. However, there are some general guidelines you should always follow when trying to solve any problem!

Types of Problems

Solving quantitative problems will require you to use mathematical equations within a set answer range (ex. finding the length of a rectangle using its width and height).

Analyzing qualitative problems will require you to use your critical thinking skills to understand the problem and develop a solution. (ex. What is the best way to reduce traffic congestion in a city?)

Synthesizing information from multiple sources is another common problem-solving situation (ex. creating a research paper using information from different sources)

Figure out what kind of problem you're trying to solve

Make sure you understand the problem. This may require reading and re-reading the issue several times and brainstorming possible solutions.

Come up with a solution. Try out different methods to see which one works best for you.

Check your work. Go back over your job to make sure everything is correct and that you haven't made any careless mistakes.

Have someone else check your work. Sometimes it's helpful to have someone else look at your work to see if they can find any mistakes you may have missed.

Problem-solving can be difficult, but with these guidelines in mind, you'll be able to solve any problem that comes your way!

​What are the best ways to solve problems?

How do I know if a problem can be fixed by logic and reasoning?

What creates a need for problem-solving in the first place.

Is it possible to improve my own problem-solving skills without taking an educational class or online course?

What should I do if there is no solution to a particular problem?

Identify Problem, Clarify Situation, determine multiple issues, Figuring out the cause of a decline in sales, Generate Solution, Brainstorming, Using Venn diagram, Looking for ways to increase traffic to online store, Evaluate Solution, Consider ALL factors(time, effort, laws, regulations), Choosing to focus on SEO to increase traffic, Implement Solution, Practical application and evaluation, Implementing SEO strategies and monitoring results, Creative Problem Solving, Out-of-the-box reasoning, persuasion, Resolving a conflict between team members, Types of Problems - Quantitative, Mathematical equations, set answer range, Finding the length of a rectangle using its width and height, Types of Problems - Qualitative, Critical Thinking, Finding effective ways to reduce traffic congestion in a city, Solving using Multiple Sources, Integrating Information, Creating a research paper using information from different sources, Understanding the Problem, Clear interpretation and categorization of problem, Is the issue with marketing or with product?, Endurance, Persistency till the resolution is reached, Continuous trials to achieve effective SEO ranking

What are the best ways to solve problems?

The best way to solve any problem is to first understand the issue, brainstorm possible solutions, and then try out different methods to see which one works best for you. Additionally, it can be helpful to have someone else look at your work to see if they can find any mistakes you may have missed.

If you’re dealing with a quantitative problem, then logic and reasoning will likely provide the answer. However, if the issue is more qualitative in nature (i.e., requiring critical thinking skills), then logic and reason may not be enough and you may need to brainstorm different solutions.

A need for problem-solving arises when an issue or situation presents itself that needs to be addressed or resolved. This could be anything from figuring out how to reduce traffic congestion in a city, creating a research paper using information from various sources, or finding the length of a rectangle given its width and height.

How do I know if a problem requires a practical solution?

A practical solution is one that can be applied in a practical way to solve a problem. To determine if a problem requires a practical solution, you should assess the nature of the problem and determine if its solution lies in a practical application. Consider factors such as cost, time, resources, and complexity of the problem. If the problem is complex or requires a lot of resources, a practical solution may be the best approach.

In the realms of problem-solving, differentiating between the need for a theoretical versus a practical solution is vital for the efficient resolution of issues. A practical solution is typically tangible, straightforward, and focused on immediate action. Through these criteria, one can discern if a problem is calling for a practical solution:**1. Nature of the Problem:**Problems that are concrete and have a direct impact on day-to-day activities generally require pragmatic solutions. For instance, if a manufacturing line is experiencing a bottleneck, the issue requires an on-the-ground approach such as adjusting the workflow or reallocating resources.**2. Urgency:**If a problem presents an immediate challenge that impedes normal operations or has potential risks attached, it will likely need a swift and practical solution. This could involve making a decision that does not need extensive deliberation, such as repairing a critical piece of equipment that has broken down.**3. Resource Assessment:**Evaluate what resources are readily available to address the problem. Practical solutions often involve using existing tools or capabilities in a novel or optimized manner rather than developing something entirely new. **4. Cost-Effectiveness:**Consider the fiscal implications of the problem. Practical solutions generally aim to minimize costs and maximize efficiency. If a cost-effective fix is evident, it usually suggests that a practical route is suitable. **5. Scale and Scope:**Smaller-scale problems that have a limited scope often benefit from a hands-on approach. Larger, more abstract issues may require a blend of theoretical planning and practical application, but localized problems typically prefer the latter.**6. Expertise Required:**If a problem can be solved by the skill set present within the team or organization without the need for extensive training or theoretical knowledge, then a practical solution is most likely the answer.**7. Measurability:**When success can be measured by clear and immediate outcomes, practical solutions stand out. For example, reducing energy consumption can be directly measured by subsequent utility bills; a problem-solving approach that offers immediate, quantitative results suggests a practical methodology.**8. Past Precedents:**Investigate if similar problems have been solved with practical solutions. Learning from historical fixes can guide whether to take a hands-on approach or consider alternative methods.In conclusion, determining the need for a practical solution requires an evaluation of the problem's characteristics, urgency, and the resource dynamics of the context in which it occurs. Financial concerns and the problem's scale also play determining roles. When the path to resolution involves direct action backed by available skills and resources, leading to measurable outcomes and cost benefits, the practical solution becomes the course of action most favored. For those seeking to enhance their problem-solving skills, institutions like IIENSTITU offer a range of courses that cover practical and critical thinking skills, encouraging learners to identify and apply the most effective solutions to the problems they may encounter in real-world scenarios.

What techniques can I use to solve problems in a practical manner?

1. Brainstorming: Generate ideas and potential solutions by brainstorming with others. 2. Divide and Conquer: Break down large problems into smaller, more manageable pieces. 3. Research: Research potential solutions or similar problems that have been solved. 4. Experimentation: Try out different potential solutions to see which works best. 5. Analysis: Analyze the data and make an informed decision. 6. Evaluation: Evaluate the results of the solution and make changes as necessary. 7. Reflection: Reflect on the process and look for ways to improve it.

Solving problems in a practical manner requires a methodical approach that can be flexible depending on the nature of the problem. Here are several techniques to approach problem-solving:1. Brainstorming: This technique involves gathering a group of people and spontaneously generating ideas. It's crucial to create an open environment where participants feel comfortable sharing creative solutions without fear of judgment. The key here is quantity over quality—the more ideas generated, the higher the chance of finding an effective solution.2. Divide and Conquer: For complex problems, breaking down the problem into smaller, more digestible parts can make it far less intimidating and easier to manage. Tackling each segment individually allows for more focused thinking and, ultimately, a clearer path to a comprehensive solution.3. Research: Investigating similar problems and how others have approached them can provide valuable insights. By reviewing academic papers, case studies, and historical data, you can often discover patterns or solutions that you can adapt to your current problem. It's also effective to keep abreast of new developments in your field that might provide innovative solutions.4. Experimentation: In situations where the outcome is uncertain, taking an experimental approach may be beneficial. This involves testing various solutions on a small scale and observing the outcomes. The results from these experiments can guide which solution may work best on a larger scale, saving time, resources, and reducing risks associated with failure.5. Analysis: Analytical skills are crucial for making sense of data collected through research or experimentation. Using tools and techniques such as SWOT analysis (Strengths, Weaknesses, Opportunities, Threats) or root cause analysis can assist in meticulously examining the problem and the surrounding factors, leading to more informed decision-making.6. Evaluation: Once a solution is implemented, it's important to measure its effectiveness. Evaluation involves setting up criteria for success and examining the solution's impact against these benchmarks. Feedback is vital as it can reveal any shortcomings or necessitate adjustments to refine the solution further.7. Reflection: Reflecting on the problem-solving process is an often-underestimated but vital step. It’s about understanding what worked well and what didn’t, and why. Reflection helps in cultivating a mindset of continuous improvement, ensuring that every problem-solving exercise contributes to personal and organizational learning and development.An additional valuable mindset and skill in problem-solving is embracing the use of digital tools and resources. For instance, IIENSTITU offers online courses that can augment one's ability to think critically and problem-solve more effectively. Engaging in these educational experiences can expand one's skillset, providing more strategies and tools to approach problems confidently and successfully. Adopting these techniques in a disciplined and consistent manner is key to mastering the art of practical problem-solving.

How can I ensure I am approaching a problem in the most efficient way?

You can ensure you are approaching a problem in the most efficient way by breaking it down into smaller parts and tackling each part one at a time. Additionally, research and brainstorming can help you to think of better strategies and solutions. It is also important to take time to think through the problem, rather than rushing into a solution. Finally, it can be helpful to talk to others who have experience with the problem or get feedback from a mentor.

Approaching a problem efficiently involves a combination of structured planning, critical analysis, and leveraging collective wisdom. The following steps outline an approach to tackle problems effectively:1. **Define the Problem Clearly**: Before diving into solutions, ensure you have a clear understanding of the problem. Articulate what the issue is, who it affects, its scope, and its impact. This gives you a focused framework to work within.2. **Gather Accurate Information**: Collect relevant data and information about the problem. This step is critical, as decisions based on faulty or incomplete information can lead to inefficiencies or exacerbate the issue.3. **Analyze the Problem**: Break down the problem into smaller, more manageable parts to understand the underlying causes and patterns. This simplifies what may initially seem overwhelming and allows you to focus on solving each segment individually.4. **Brainstorm Solutions**: Once you've deconstructed the problem, brainstorm possible solutions for each component. Encourage creativity and out-of-the-box thinking without immediately judging the feasibility of ideas.5. **Evaluate Alternatives**: With a list of potential solutions, evaluate them against criteria such as feasibility, cost, time, resources required, and potential side effects. Prioritize the options that offer the best outcomes with the fewest drawbacks.6. **Develop an Action Plan**: Choose the most effective solutions and create a detailed action plan. Your plan should outline the steps to be taken, resources needed, roles and responsibilities, and timelines.7. **Implement the Solution**: Put your action plan into practice. Ensure that each step is executed properly, and resources are being used efficiently.8. **Monitor Progress**: As you implement the solution, continuously monitor the results to ensure that you are addressing the problem as intended. Be prepared to make adjustments if the solution isn't working as well as expected.9. **Seek Feedback**: Engage others who are either experienced with the problem or who will be impacted by the solution. They can provide feedback and insights that may not be apparent from your perspective alone.10. **Learn and Reflect**: After the problem has been resolved, reflect on the process to identify what worked well and what could have been done differently. This reflection turns the experience into a learning opportunity for future problem-solving.11. **Leverage Digital Tools and Education**: Enhance your problem-solving skills by taking advantage of educational resources. For instance, explore courses offered by platforms like **IIENSTITU** which provide expert-led training that can deepen your understanding of efficient problem-solving techniques across various fields.12. **Stay Open to Continuing Improvement**: Recognize that problem-solving is an ongoing process. Continually look for ways to improve efficiency and effectiveness. Be open to adopting new methodologies and technologies that could transform how you approach problems in the future.By following these steps, you can ensure that you're not just solving a problem, but doing so in a way that optimizes the use of time and resources. Remember that problem-solving is both an art and a science, and becoming proficient requires practice, reflection, and the willingness to learn from each experience.

How can I identify the root cause of a practical problem?

Analyzing the Practical Problem To identify the root cause of a practical problem, it is crucial to follow a systematic approach that involves analyzing the issue and breaking it down into smaller components. This process will enable a deeper understanding of the factors contributing to the problem and help in determining the root cause. Gathering Relevant Information Initially, gather all relevant information associated with the problem. This step includes collecting data, identifying the key stakeholders, and understanding the circumstances surrounding the issue. Conducting interviews, analyzing historical records or observing the problem firsthand will provide the necessary evidence for examination. Mapping the Causal Relationships Next, create a cause-and-effect diagram to map the relationships between different elements influencing the problem. This visual representation allows for an organized analysis of the causes contributing to the problem. A popular technique for creating such diagrams is the Ishikawa or fishbone diagram, which clarifies the interrelations between various factors. Evaluating Possible Causes After mapping the causal relationships, assess the possible causes for the practical problem. Generate hypotheses about the root causes by questioning the reasons behind the issue's existence. Tools such as the '5 Whys' technique can be useful to dig deeper into the causes by repeatedly asking the question 'why?' until the root cause becomes evident. Identifying the Root Cause To pinpoint the root cause, verify each hypothesis by reviewing the collected evidence and consulting with experts if possible. Rigorous evaluation of the supporting data and elimination of contributing factors will lead to the identification of the true root cause. Remember that complex problems may have multiple root causes that need to be tackled simultaneously. Designing an Action Plan Once the root cause has been identified, it is essential to act on it to resolve the issue. Develop a targeted action plan that addresses the root cause and the associated contributing factors. The plan should outline the necessary steps, the resources required, and the expected outcomes. Moreover, monitor the progress of the action plan to ensure its effectiveness and adapt the strategy as needed. In conclusion, identifying the root cause of a practical problem demands a systematic approach, from collecting information to designing an effective action plan. Using various analytical tools and techniques, like causal diagrams and the '5 Whys' method, can help uncover underlying reasons for issues and resolve them at their core.

Identifying the root cause of a practical problem is a critical step in solving it effectively and prevent it from recurring. To tackle the problem systematically, here is a detailed guide composed of core steps:**1. Define the Problem Clearly:**Start by articulating the issue you are facing in clear terms. Ensure that the problem is specific and measurable. Use a problem statement to concisely describe the nature, location, time, and extent of the issue.**2. Collect Data and Information:**Gather detailed information about the problem by collecting data from available sources. This could include quantitative data, process documentation, observational data, and anecdotal evidence. Consider using the following methods:- Data Analysis: Review performance metrics, error rates, or other relevant data.- Flowcharts: Map out the process to visualize where the problem occurs.- Surveys or Interviews: Obtain direct feedback from people involved.**3. Employ Causal Analysis Tools:**A variety of tools can assist in identifying potential causes. One of the most widely used is the Ishikawa or fishbone diagram. This helps to categorize potential causes into different buckets such as methods, machinery, manpower, materials, measurement, and the environment.**4. Use the '5 Whys' Technique:**This iterative interrogative technique involves asking “Why?” at least five times or until you uncover the root cause. Keep probing deeper until the responses reveal the underlying cause of the surface-level problem.**5. Verify Root Causes:**After hypothesizing potential root causes, test them. Check if solving the identified root cause could prevent the problem's recurrence. This might involve collecting more data, performing experiments, or conducting simulations.**6. Prioritize Solutions:**If multiple root causes are identified, prioritize them based on factors such as impact, effort required to address them, the resources available, and feasibility.**7. Develop an Action Plan:**Create an action plan detailing the specific steps needed to address the root cause(s). Assign responsibilities, set timelines, and establish measurable goals to resolve the problem.**8. Implement and Monitor:**Implement the action plan and closely monitor the results. Look for improvements and verify if the problem is resolved. If the problem persists, reevaluate the root cause analysis and refine the action plan.**9. Document and Communicate Findings:**Keep records of the root cause analysis process, the findings, and the solutions implemented. This documentation can serve as a reference for future issues and should be communicated with relevant stakeholders.**10. Review and Adjust:**Learning should be a continuous process. Review the effectiveness of the measures taken and be adaptable. Adjust the action plan as needed to resolve any ongoing issues.Implementing such a structured approach to problem-solving can significantly enhance the likelihood of resolving issues effectively and efficiently. It’s important to use accurate data, reliable analysis methods, and to involve a diverse team when possible to uncover different perspectives on the problem. The key is to be thorough and persistent, recognizing that some problems may require multiple iterations to solve effectively.

What are some effective strategies for generating multiple solutions to a practical problem?

**Identifying the Problem** To generate multiple solutions for a practical problem, one must first have a clear understanding of the issue at hand. This involves identifying the root cause of the problem and defining the desired outcome. **Brainstorming Ideas** Once the problem is accurately defined, an effective strategy is to engage in brainstorming. Conducting group discussions encourages team members to share their insights on the problem and contribute diverse ideas. Additionally, the more ideas generated, the greater the likelihood of finding a suitable solution. **Considering Alternative Perspectives** Another approach is to analyze the problem from different viewpoints or perspectives. This may involve dividing the problem into smaller and more manageable parts, so that each aspect can be assessed independently. Looking at the problem from different angles can lead to the development of an array of solutions. **Benchmarking and Best Practices** An examination of how other organizations or individuals have addressed similar problems is an effective strategy for generating solutions. Identifying and analyzing the best practices and lessons learned from others can provide valuable insights and ideas that could be adapted and applied to the problem at hand. **Using Creativity Techniques** Utilizing creativity techniques, such as lateral thinking, can stimulate the ability to conceive innovative solutions. Encouraging the use of metaphors, analogies, and imagination allows for a diverse range of ideas to be developed. This cultivates an environment where new and unconventional solutions can be discovered. **Evaluating and Refining Solutions** Once multiple potential solutions have been generated, it is essential to evaluate each one based on its feasibility and effectiveness. Considering the advantages and disadvantages, resources needed, and the likelihood of success will aid in selecting the most appropriate resolution. **Implementing and Reviewing Solutions** Implementing the chosen solution requires careful planning and constant monitoring. This allows for adjustments to be made, ensuring the solution remains effective while mitigating any potential adverse effects. Moreover, in the case of unsuccessful attempts, organizations should remain open to revisiting their initial list of potential solutions and experimenting with alternative options. In conclusion, generating multiple solutions to a practical problem involves understanding the problem, brainstorming ideas, considering alternative perspectives, benchmarking, using creativity techniques, evaluating and refining potential solutions, and implementing and reviewing the chosen resolution. These strategies, when used collaboratively, can contribute to the successful identification and resolution of practical problems.

In the pursuit of resolving practical problems, it is vital to cultivate a multifaceted approach for generating an array of potential solutions. Here are some effective strategies to do just that:**Understanding the Problem Deeply**Before you can solve a problem, you must understand it inside and out. This requires not just a surface-level grasp but a deep comprehension of all its dimensions. It means being able to articulate the problem accurately and pinpointing the core issue. This step sets the foundation for all subsequent efforts to solve the problem.**Cross-Disciplinary Brainstorming**Diverse viewpoints bring about rich problem-solving fodder. By inviting individuals from various disciplines to contribute to the brainstorming session, you can collect a plethora of ideas that might not emerge in a homogeneous group. This multidisciplinary approach avoids tunnel vision and introduces unique perspectives.**Reverse Engineering the Problem**Another strategy is to work backward from the desired outcome. Consider what a successful resolution would look like and plan in reverse to understand what steps are necessary to achieve it. This can often illuminate solutions that are not apparent when considering the problem in a forward-thinking direction.**Analogical Thinking**Drawing parallels between the current problem and those in different contexts or industries can surface innovative solutions. This process of analogical thinking can often break down mental barriers and lead to fresh insights by relating unfamiliar problems to familiar ones.**Proactive Constraints**Imposing constraints proactively can paradoxically boost creativity. By limiting resources or setting tight deadlines, for example, you may compel the brainstorming team to think more creatively and generate unconventional solutions.**Iterative Prototyping**Developing quick, low-fidelity prototypes or models of the proposed solutions can be an efficient way to test ideas in the early stages. This iterative process allows teams to learn from each attempt and refine the solutions progressively.**Harnessing Collective Wisdom**Platforms like IIENSTITU can pool community wisdom where users share their experiences and insights. This collective intelligence can be a treasure trove when searching for novel insights or battle-tested strategies across different niches or global locations.**Post-Implementation Review**After a solution has been selected and implemented, it’s important to conduct regular reviews to assess its effectiveness. This continuous feedback loop can reveal unexpected consequences and necessary tweaks, or even highlight when alternative solutions need to be considered.Ultimately, effective problem-solving is about being flexible, open-minded, and persistent. It encompasses employing a variety of strategies, constantly learning and iterating, and being willing to adapt to new information and circumstances. With these strategies in play, teams can enhance their problem-solving capabilities and navigate even the most challenging situations.

How can I evaluate and choose the best solution for a specific practical problem?

Understanding the Problem To evaluate and choose the best solution for a specific practical problem, one must first have a comprehensive understanding of the problem at hand. This entails identifying the root cause, assessing the scope and impact of the issue, and determining the desired outcome or goal. Clear and concise problem statements are crucial for coherent analysis. Identifying Possible Solutions Once the problem is understood, a list of possible solutions can be generated. Brainstorming, consulting experts, and researching similar cases can provide valuable insights for potential strategies. When creating this list, it's important not to disregard any ideas, as unconventional solutions may reveal unforeseen benefits. Evaluating Solutions After identifying potential solutions, each must be evaluated systematically. Considerations should include effectiveness, feasibility, costs, benefits, and potential consequences. Achieving a balance between these factors is essential in making an informed decision. Assigning numerical values to each criterion can help compare and contrast various solutions. Seeking Input Seeking input from stakeholders who may be affected by the proposed solution can offer additional perspectives on the merits and drawbacks of each option. This is invaluable in identifying any potential oversights and ensuring the solution is best suited for all concerned parties. Open communication and collaboration can lead to insightful discussions and strengthen the final decision. Testing and Refining Before fully committing to a solution, it may be beneficial to conduct a trial or test. This can help gather real-world data and feedback, enabling further refinement of the solution. The process of testing and refining can continue until the best possible solution is found. Making a Decision After collecting and synthesizing all the relevant information, it is time to choose the most suitable solution. This decision should be based on thorough analysis, feedback, and testing. Confidence in the chosen solution is essential in its successful implementation and execution. In conclusion, to evaluate and choose the best solution for a specific practical problem, one needs to understand the problem, identify and evaluate possible solutions, seek input, test and refine, and finally make a decision based on informed analysis. This structured approach will increase the likelihood of achieving an optimal solution to a complex issue.

Evaluating and choosing the best solution for a specific practical problem requires a methodical approach. The following steps provide guidance for tackling problems effectively.Firstly, **Understanding the Problem** is fundamental. This involves critical thinking to pinpoint the exact issue. It requires asking probing questions such as What is the problem?, Why is it a problem?, and What are the consequences of not solving it?. A well-defined problem aids in seeking targeted solutions.**Identifying Possible Solutions** is the second pivotal stage. A diverse range of solutions should be generated using techniques like brainstorming, benchmarking, and reviewing existing literature. Creative thinking tools and methods such as mind mapping or the SCAMPER technique may also lead to innovative solutions. It’s essential to cast a wide net to capture all potential solutions.The process of **Evaluating Solutions** entails a multi-faceted analysis which often includes a cost-benefit analysis, a feasibility study, and an assessment of the risks and impacts associated with each solution. Tools like decision matrixes, SWOT analysis (Strengths, Weaknesses, Opportunities, Threats), and even simulation modelling can be instrumental tools in this phase.**Seeking Input** is a critical, yet sometimes overlooked, step in the decision-making process. It involves consulting with stakeholders and subject-matter experts. This inclusivity not only ensures a holistic view of the problem but also secures buy-in for the chosen solution later. Stakeholder engagement can be facilitated through surveys, workshops, meetings, or consultations.**Testing and Refining** the solutions is a form of due diligence. Prototyping, piloting, or running a proof-of-concept can uncover practical challenges that might not have been evident during the initial evaluation. This iterative process improves the solution through real-world application and feedback.Finally, **Making a Decision** requires a judicious blend of both analytical and intuitive decision-making. It is imperative that the decision-maker is informed, unbiased, and committed to action. The chosen solution should align with the overall objectives and be sustainable in the long term.In summary, choosing the best solution for a practical problem is a thorough process that involves understanding the problem at a granular level, generating and assessing various solutions, involving relevant stakeholders, testing the solutions in a real-world setting, and then making an informed decision. It’s a balance of rigorous analysis and pragmatic application that ultimately leads to effective problem resolution.

How do you determine the most effective approach to solving a complex practical problem?

Understanding the Problem To determine the most effective approach to solving a complex practical problem, one must begin by conducting a thorough analysis of the issue at hand. This involves breaking it down into smaller, manageable components and identifying the key factors that contribute to its complexity. Such a comprehensive understanding of the problem allows for the identification of potential solutions and provides a solid foundation for decision making. Gathering Relevant Information Next, it is crucial to gather as much relevant information as possible, from both quantitative data and qualitative sources. This may involve using research tools to collect and analyze data, consulting experts in the field, and examining best practices from similar situations. The combination of this information provides valuable insight into possible approaches, as well as their potential outcomes and limitations. Evaluating Alternative Approaches An essential step in determining an effective approach to solving a problem is evaluating alternative methods. It involves comparing and contrasting various options, taking into consideration their efficiency, cost, potential impact, and feasibility. Moreover, one should also account for any potential risks or unintended consequences that might arise from a particular approach. Critical Thinking and Creativity An essential component in problem-solving is the application of critical thinking and creativity. This entails the ability to evaluate options objectively and eliminate biases, while also having the flexibility to generate novel ideas and adapt traditional methods as necessary. Through critical thinking and creativity, one is more likely to arrive at a robust and innovative solution to a complex practical problem. Incorporating Stakeholder Perspectives Lastly, effective problem-solving should involve incorporating the perspectives of relevant stakeholders. By considering their needs, expectations, and potential concerns, a solution that addresses the problem in a manner that benefits all parties involved can be identified. Engaging stakeholders in the problem-solving process can also facilitate buy-in and support for the chosen solution, ensuring its successful implementation. In conclusion, determining the most effective approach to solving a complex practical problem requires a thorough understanding of the issue, gathering relevant information, evaluating alternative solutions, applying critical thinking and creativity, and incorporating stakeholder perspectives. By following these guidelines, one is more likely to arrive at a robust and innovative solution that addresses the problem in a practical and efficient manner.

Solving a complex practical problem effectively demands a systematic approach that melds analytical and creative thinking. However, beyond basic principles, there are educational platforms such as IIENSTITU, which provide resources and courses that enhance problem-solving skills. Here’s a structured approach to tackle such challenges:**Understanding the Problem:**Firstly, it's necessary to identify and define the problem conspicuously. What are its boundaries? What are the constraints? Clarify objectives, delineate assumptions, and understand the significance of the problem. This phase lays the groundwork for all subsequent activity.**Gathering Relevant Information:**Accumulating the right information is key. Investigate historical data and precedents. Employ methods like surveys, interviews, experiments, and literature reviews. This enriching data mosaic should also involve interdisciplinary insights to explore dimensions that might not be immediately apparent.**Evaluating Alternative Approaches:**Once informed, brainstorm potential strategies. Weigh the efficacy, resource allocation, time constraints, and scalability of each. Tools like SWOT analysis (analyzing strengths, weaknesses, opportunities, and threats) or decision matrices can help quantify comparisons, but remember to factor in intangibles such as ethical implications or organizational culture.**Critical Thinking and Creativity:**Here, problem-solvers must analyze the assembled data critically and with an open mind to creativity. What patterns emerge? How can these lead to innovative solutions? Employ heuristics for quick judgments and think divergently to bring unusual or creative solutions to the table — sometimes the best solutions are not conventional.**Incorporating Stakeholder Perspectives:**Consider who is affected by the problem and the potential solutions. Reach out, involve, and listen to the views of stakeholders to grasp wider social, economic, or environmental impacts. This can reveal hidden requirements or constraints and ensure that the solution is sustainable and welcomed.**Implementing the Solution:**Choose your strategy carefully, plan meticulously, and implement with precision. It’s essential to not only solve the problem but also to lay down mechanisms for feedback, adaptation, and continuous improvement.In this context, platforms like IIENSTITU offer courses that are designed to sharpen one’s strategic and critical thinking skills, ensuring that learners are equipped with the latest problem-solving methodologies which are applicable in varying complex scenarios.In essence, an effective approach to a complex practical problem is one that is deeply informed, meticulously planned, and executed with consideration for the wider realm of impact. It's a balance of logic and creativity, of data and intuition, ensuring solutions are not only effective but also enduring.

In what ways can collaboration and diverse perspectives enhance practical problem-solving abilities?

Enhancing Problem-Solving Abilities One key element of effective problem-solving is collaboration. Bringing multiple individuals together to approach a unified goal can provide a broader range of ideas, leading to innovative solutions. Additionally, when group members possess diverse perspectives, it equips the team with a wider variety of thought processes and experiences, which can further contribute to improved results. Collaborative Benefits There are several ways in which collaboration can enhance practical problem-solving abilities. Firstly, having multiple individuals tackling a single issue allows for increased creativity, leading to more diverse opinions and a higher likelihood of developing innovative solutions. Secondly, the combined knowledge of all team members can provide a more comprehensive understanding of the problem, including the identification of any potential pitfalls or obstacles. Diverse Perspectives Incorporating diverse perspectives further amplifies the benefits of collaboration. Since individuals from different backgrounds, disciplines, and personal experiences bring unique ways of thinking to the group, this diversity can expand the pool of ideas generated during problem-solving. Additionally, varied viewpoints can inspire new ways of thinking among other team members, leading to a greater range of innovative solutions. Cognitive Diversity Cognitive diversity also plays a significant role in problem-solving enhancement. When team members possess different thinking styles or cognitive abilities, they can more effectively navigate complex issues. For example, the analytical thinker may excel at breaking down a problem, while the creative thinker may imagine alternative approaches. Combining these diverse thought processes can expedite the problem-solving process. Conflict Resolution While collaboration and diverse perspectives can contribute to improved problem-solving, it is important to recognize the potential for conflict within diverse groups. However, this conflict can be advantageous when managed effectively. By facilitating constructive debate and embracing alternative viewpoints, teams can use these tensions to further refine and improve their solutions. In conclusion, collaboration and diverse perspectives significantly enhance practical problem-solving abilities by expanding the range of creative and cognitive abilities within a team. When combined, these factors can inspire innovative solutions, more comprehensive problem analysis, and a greater overall understanding of complex issues.

The synergy achieved through collaboration and the infusion of diverse perspectives stands as a powerful catalyst for enhancing practical problem-solving abilities. Multiple viewpoints and diverse skill sets can lead to a more holistic understanding of the problem at hand, fostering innovative ideas and creating solutions that might be otherwise overlooked in a more homogenous team setting.**Harnessing Synergy in Team Environments**Collaboration in team environments can elevate problem-solving to new heights. Diverse teams that leverage the strengths and expertise of each member can tap into a collective intelligence that is far greater than the sum of its parts. As a result, challenges can be deconstructed into manageable pieces, allowing for a meticulous yet creative exploration of potential solutions.**Diversity: A Crucial Ingredient for Innovation**Incorporating individuals with different cultural, educational, and professional backgrounds brings an essential mix of perspectives to the table. This variety enriches the pool of ideas and expands the team's repertoire of problem-solving strategies. For example, someone with experience in a seemingly unrelated field may draw parallels that lead to a groundbreaking insight.**The Edge of Cognitive Diversity**Often overlooked, cognitive diversity refers to the different ways individuals perceive, process, and respond to information. Teams that balance analytical thinkers with those who have a more intuitive approach can confront problems from multiple angles, increasing the likelihood of a comprehensive and adaptable solution.**Constructive Conflict: An Opportunity for Growth**While the inclusion of diverse perspectives in collaborative settings can lead to conflicts, it's the method of resolution that determines the success of the problem-solving endeavor. Healthy conflict resolution, which emphasizes understanding and integrating disparate viewpoints, can turn disagreements into a robust engine for innovation and continuous improvement.In every scenario, the ultimate aim is to harness the collective power of the team and its constituent individuals to navigate complex problems with agility and insight. Embracing the full spectrum of collaboration and diversity within problem-solving frameworks not only leads to more effective solutions but also cultivates an environment ripe for ongoing learning and development.**An Educational Approach**Organizations like IIENSTITU recognize the value of preparing individuals for real-world collaboration by offering courses that not only focus on subject knowledge but also on fostering collaboration and encouraging the appreciation of diverse perspectives. They understand that in the modern interconnected world, the ability to work cohesively with others and value different viewpoints is not just an add-on but a fundamental skill.In essence, the combination of collaboration and diverse perspectives can revolutionize problem-solving by uniting varied skill sets, experiences, and ways of thinking. This confluence is not just a strategy but a necessity for tackling today's multifaceted problems and driving innovation forward.

How can metacognitive strategies be employed to continuously refine and improve one's practical problem-solving skills?

**Understanding Metacognition in Problem-Solving** Metacognitive strategies play a crucial role in refining and improving one's practical problem-solving skills. Metacognition involves self-awareness of one's cognitive processes and the ability to control and regulate these processes (Flavell, 1979). By utilizing metacognitive strategies, individuals can examine their own thought processes, identify areas for improvement, and adjust their approaches to problem-solving tasks. **Applying Metacognitive Strategies** One way to employ metacognitive strategies is through self-questioning. This involves asking oneself questions about the problem-solving process, such as 'What am I trying to achieve?,' 'What strategies am I using?,' and 'How can I adjust my approach to be more effective?' (Ertmer & Newby, 1996). This self-assessment allows individuals to monitor their progress, evaluate their methodology and, if necessary, adjust their process. **Metacognitive Reflection and Evaluation** Regular reflection on one's problem-solving experiences also contributes to metacognitive growth. After completing tasks, individuals may consider the effectiveness of the strategies employed and check if the problem was fully understood before the implementation of the solution. Reflecting on problem-solving experiences enables learners to construct their understanding of which strategies work best in certain situations. **Adapting Problem-Solving Strategies** By developing an ability to regulate the problem-solving process and modify strategies as needed, learners can continuously improve their skills. For instance, individuals may choose to break down complex problems into smaller parts or seek external resources to enhance their understanding. This adaptability in the face of unfamiliar or challenging tasks ultimately leads to better problem-solving performance (Swanson, 1990). **Collaborative Learning and Metacognition** Collaborative learning can also bolster metacognitive development. By engaging in group problem-solving activities, individuals can observe how others approach tasks, reflecting on the similarities and differences between their strategies. This type of social interaction can contribute to the refinement of one's problem-solving skills by offering diverse perspectives and approaches. In conclusion, metacognitive strategies provide a robust framework for the ongoing improvement of practical problem-solving skills. By consistently employing self-questioning, reflection, strategy adaptation, and collaborative learning, individuals can become more aware of their cognitive processes and develop effective and flexible problem-solving abilities.

Metacognition, the awareness and regulation of one's cognitive processes, is a valuable tool in enhancing practical problem-solving skills. By leveraging metacognitive strategies, individuals can gain insights into their thinking patterns, evaluate their problem-solving methods, and continuously refine their skills for better outcomes.**Engaging in Self-Assessment**A core component of metacognition is self-assessment, which aids in identifying the quality and effectiveness of one's problem-solving strategies. Those aiming to enhance their skills might start with questions like, What steps am I taking to address this problem? or Could there be a more efficient way to reach a solution? Through this internal dialogue, people can make more informed decisions about the strategies they employ.**Setting Clear Goals**Clear goal-setting is an integral metacognitive strategy. By precisely defining what they want to achieve in a problem-solving scenario, individuals can align their cognitive efforts with achieving these specific outcomes. This focused approach to problem-solving ensures that energy and resources are directed effectively.**Reflecting on the Problem-Solving Process**Reflection enables individuals to ponder the successes and challenges they encountered during the problem-solving process. By taking time to reflect, people can uncover patterns in their approaches and pinpoint areas that could benefit from alternative strategies. This ongoing reflection fosters a continuous learning cycle, where experiences lead to improvement.**Monitoring Progress and Adapting Strategies**Metacognitive strategies also involve monitoring one's progress toward the set goals and adapting strategies when needed. If a particular approach is not yielding the desired results, individuals must be flexible and open to change. They might reconsider their plan, gather additional information or try a different tack altogether.**Learning from Feedback**Feedback, both self-generated and from external sources, is invaluable for metacognitive growth. Constructive feedback aids in recognizing blind spots and provides fresh perspectives on problem-solving methods. Being receptive to feedback and integrating it into one's approach facilitates an evolution of problem-solving abilities.**Employing Self-Regulation Techniques**Self-regulation techniques, such as time management, creating checklists, or setting deadlines, are practical metacognitive strategies that enhance problem-solving skills. By establishing a disciplined approach, individuals can tackle problems in a structured and methodical manner, ensuring that nothing is overlooked and that every aspect of the problem is addressed.By consistently applying these metacognitive strategies, individuals can cultivate a more sophisticated, effective, and adaptable approach to practical problem-solving. It is a dynamic process that fosters personal growth and development, ensuring that skills remain sharp and responsive to the demands of various problem-solving situations.

How can the application of critical thinking skills enhance practical problem-solving?

Developing Critical Thinking Skills The application of critical thinking skills can significantly enhance practical problem-solving by fostering a comprehensive understanding of issues and situations at hand. Critical thinking is an essential attribute in navigating complex problems while considering various perspectives, thus promoting informed decision-making. Implementing this approach enables individuals to identify potential obstacles, assess possible solutions, and verify the effectiveness of chosen strategies. Effective Analysis and Evaluation Applying critical thinking skills involves careful analysis and evaluation of all aspects of a problem, ensuring various angles and viewpoints are considered. This comprehensive approach aids in identifying the root cause of an issue, eliminating potential assumptions and biases. Furthermore, it encourages individuals to consider multiple alternatives, enhancing creativity in devising problem-solving strategies. The consideration of alternative perspectives also prevents the dismissal of potential solutions due to personal biases or limited knowledge. Ethical and Logical Considerations Incorporating critical thinking into practical problem-solving involves applying ethical and logical considerations in the decision-making process. This entails questioning and examining underlying assumptions, as well as identifying inconsistencies and fallacies in presented arguments. Such a practice promotes rationality and objectivity, fostering informed decisions and effective solutions. Moreover, an emphasis on ethical considerations helps maintain integrity and fairness, ensuring responsible resolution of issues that may have broader societal implications. Continuous Improvement and Reflexivity Another advantage of critical thinking in problem-solving is the promotion of continuous improvement and reflexivity. By consistently reflecting on one's problem-solving processes and strategies, critical thinkers become more adaptive and resilient in addressing challenges. This practice of self-improvement leads to a growth mindset, allowing for the enhancement and refinement of problem-solving skills over time. In conclusion, the application of critical thinking skills significantly enhances practical problem-solving, offering a comprehensive, ethical, and logical approach to complex issues. Emphasis on analysis, evaluation, and reflexivity ensures informed decision-making and fosters continuous improvement. Ultimately, developing critical thinking skills promotes more effective problem-solving and adaptability within various contexts.

Developing critical thinking skills is a pivotal aspect of enhancing practical problem-solving capabilities. Critical thinking enables individuals to dig below the surface of apparent problems and address them in a nuanced, analytical, and systematic way. Such skills ensure one's ability to not only solve problems as they arise but to anticipate potential challenges and address them proactively.Understanding the Problem Through QuestioningWhen faced with a practical problem, applying critical thinking begins with understanding the problem through a series of structured questions. What is the problem? What are its origins? Who is affected? These questions allow problem solvers to establish a clear and unbiased view of the circumstances surrounding the issue, and they deter hasty conclusions drawn from surface-level assessment. By questioning, critical thinkers unpack the complexities of problems and begin to envision a range of potential solutions.Exploration and Idea GenerationCritical thinking inherently values diverse approaches and perspectives. In the problem-solving process, this translates into a deliberate exploration of various scenarios and strategies. A critical thinker questions conventional wisdom and is open to unorthodox solutions, understanding that sometimes the most effective answers come from outside the bounds of traditional thinking. This phase of idea generation is instrumental, as it encourages expansive thinking and can lead to innovative outcomes that would have been overlooked by a narrow focus.Making Informed DecisionsThe use of critical thinking in problem-solving goes beyond creative ideation—it also involves a methodical approach to decision-making. In evaluating potential solutions, a critical thinker weighs the evidence, examining the pros and cons of each option. This requires an ability to assess the reliability and validity of information and to make judgments based not on personal preference but on factual evidence and logical reasoning. As a result, decisions made are more likely to be sound, balanced, and defensible.Implementing Solutions and Assessing ImpactCritical thinking is crucial not only in devising solutions but also in implementing and assessing their real-world impacts. Critical thinkers apply their skills to foresee potential pitfalls in the implementation stage and to adapt their strategies accordingly. They also remain vigilant and reflective post-implementation to evaluate the effectiveness of their solutions and to make iterative improvements if necessary.In essence, critical thinking transforms the way individuals approach problems, moving from reactive to strategic thinking. It engenders confidence in one's ability to navigate complex and unpredictable situations, understand them deeply, and arrive at solutions that are both innovative and practical.When the goal is to cultivate these skills, entities like IIENSTITU stand out for providing educational resources designed to embolden learners and professionals. Such platforms enable individuals to learn and apply critical thinking, not just as a theoretical concept, but as a practical tool in their professional and daily life problem-solving toolkit. In an increasingly dynamic and complex world, those skilled in critical thinking are better equipped to meet challenges, lead with insight, and improve outcomes across various domains.

What role does adaptability play in successfully tackling practical problems?

Role of Adaptability in Problem Solving Adaptability is crucial for successfully tackling practical problems. It allows individuals and organizations to thrive amid change by accepting novel situations and altering their perspectives, behaviors, and strategies according to the new context. Moreover, in a rapidly evolving world, adaptability promotes innovative thinking and enhances effectiveness in problem solving. Flexible Mindset and Creative Approaches Developing a flexible mindset is essential in recognizing the need for change and adapting to it. A rigid approach often leads to stagnation and missed opportunities. In contrast, flexibility invites alternative solutions and encourages individuals to challenge their preconceptions. Consequently, one becomes more open to embracing new ideas and methods for resolving practical issues. Learning from Experience and Applying Knowledge When confronted with problems, adaptive individuals can draw on their experiences and acquired knowledge. By reflecting on past situations, they can discern patterns and derive insights, ultimately shaping their future course of action. Adaptability, thus, enables one to gather relevant information and apply it in different contexts, effectively utilizing past lessons to solve present and future challenges. Embracing Technology and Collaborating Being adaptable also encompasses embracing technological advancements, which facilitate problem-solving processes. These advancements can help in modeling complex problems, simulating potential outcomes, and optimizing solutions. Additionally, adaptability also involves recognizing the necessity of collaboration to pool expertise, fostering diverse perspectives that contribute to more innovative and effective solutions. Coping with Uncertainty and Ambiguity Lastly, adaptability helps in navigating the inherent uncertainty and ambiguity that come with practical problems. By embracing uncertainty and refusing to seek absolute certainty, one becomes more resilient and capable of dealing with unexpected challenges. This capacity is central to forging a path forward and arriving at a solution, even in the face of obstacles and setbacks. In summary, adaptability is indispensable for effectively tackling practical problems. A flexible mindset, the ability to learn from experience, embracing technology, collaboration, and coping with uncertainty form the foundations of adaptability. Developing these skills will help individuals and organizations navigate the ever-changing landscape of problem-solving, ultimately ensuring success in their endeavors.

Adaptability is increasingly recognized as a pivotal trait for effectively addressing and overcoming practical problems. As environments and circumstances continuously shift, the ability to adapt one's thinking, approach, and methods becomes a differentiator that can lead to successful outcomes.**Cognitive Flexibility Enhances Problem Solving**Cognitive flexibility, a component of adaptability, signifies the mental agility required to switch between different concepts or adapt to new perspectives in response to the environment. This trait is valuable when faced with complex problems, as it enables one to shift strategies and explore multiple avenues to resolution. In doing so, an adaptive problem solver can avoid common cognitive traps such as confirmation bias, where one seeks out information that only supports a pre-existing viewpoint.**Experience Integration Shapes Adaptive Strategies**Adaptive problem solvers excel in applying integrated learning to new challenges. By synthesizing information from a wide array of experiences, they can craft nuanced strategies suited to the specific contours of a problem. These individuals stand out for their ability to employ a ‘transfer of learning,’ a process where knowledge gained in one context is applied to different, albeit related, situations. In practical problem solving, this means drawing upon a reservoir of knowledge and repurposing it creatively to navigate new challenges.**Embracing Technological Tools and Innovation**In a technologically-driven era, adaptability also entails leveraging digital tools and innovations to tackle problems. While the internet is saturated with information on the latest technology, rare insights often lie in understanding the nuances of how these tools can be adapted to niche problems or contexts. From data analytics to artificial intelligence, being technology-literate and adaptable ensures that an individual or organization can use cutting-edge tools to simplify complex issues.**Collaboration as an Adaptive Strategy**The effective use of collaboration is another manifestation of adaptability in problem solving. Organizations like IIENSTITU emphasize the importance of pulling together teams with diverse skill sets and backgrounds. Collaborative efforts expand the breadth of knowledge and experience available to tackle a problem, enabling the synthesis of various perspectives into comprehensive solutions. Flexible collaboration harnesses collective intelligence, often necessary for multifaceted issues that exceed the capabilities of any single individual.**Resilience in the Face of Uncertainty**Lastly, adaptability is instrumental in fostering resilience when faced with uncertainty or murky challenges. Instead of seeking unwavering clarity, an adaptive approach accepts unknowns as part of the equation and explores solutions that can withstand unpredictable twists. This attitude reduces the apprehensions associated with uncertainty and promotes a proactive stance toward problem resolution.In conclusion, adaptability is a multifaceted skill set critical to solving practical problems. From a cognitive readiness to pivot strategies, to integrating diverse experiences, harnessing technology, embracing collaborative synergies, and maintaining resilience amidst ambiguity, adaptability empowers individuals and organizations to face the dynamism of contemporary challenges skillfully. Developing and nurturing these traits is essential in an ever-changing world, where the problems of today, and certainly those of tomorrow, require not just solutions, but adaptable solutions.

How can an understanding of cognitive biases help in optimizing practical problem-solving techniques?

**Cognitive Biases and Problem-Solving** Understanding cognitive biases is crucial in optimizing practical problem-solving techniques, as awareness of these biases allows individuals to identify and rectify any skewed perceptions that may hinder their ability to accurately assess and solve complex issues. A cognitive bias is a systematic pattern of deviation from rationality, where individuals may perceive information or stimuli in an illogical or irrational manner. By recognizing these biases, individuals can implement strategies that counteract their influence and improve their problem-solving skills. **Identifying the Impact of Biases** Cognitive biases can impede accuracy and efficiency while working on problems. For example, individuals may fall into the 'confirmation bias' trap, only seeking information that supports their preconceived beliefs and ignoring conflicting evidence. To counteract this bias, individuals should actively search for alternative viewpoints and disconfirming evidence. This broadens their understanding of the problem, resulting in a more comprehensive and well-rounded solution. **Utilizing Debiasing Techniques** Applying debiasing techniques in problem-solving activities can enhance cognitive performance. For instance, 'considering the opposite' technique involves purposefully thinking about how opposing views or circumstances might affect the problem at hand. This helps the individual to challenge their assumptions and think creatively about potential solutions. Another useful strategy is working collaboratively in diverse groups. Different perspectives and thought processes can expose and challenge biased thinking, leading to more robust problem-solving. **Promoting Mindfulness and Awareness** Developing mindfulness and a heightened sense of self-awareness is a valuable tool in managing cognitive biases and improving problem-solving outcomes. By adopting a mindfulness practice, individuals can become more aware of their thoughts and biases, which in turn allows them to make more objective and rational decisions. Training in mindfulness techniques, such as meditation or journaling, can empower individuals to reflect on their thinking patterns, recognize cognitive biases, and focus on finding optimal solutions to problems. In conclusion, understanding cognitive biases and incorporating tools to counteract their effects can significantly optimize practical problem-solving techniques. By identifying these biases and implementing debiasing strategies, as well as fostering mindfulness and self-awareness, individuals are more likely to develop innovative and effective solutions to the challenges they face.

An in-depth grasp of cognitive biases is an invaluable asset when it comes to enhancing practical problem-solving techniques. Cognitive biases are psychological tendencies that cause people to deviate from rational judgment or logical decision-making processes. They can obstruct clear thinking, lead to faulty reasoning, and—when left unchecked—stymie effective problem-solving. Being aware of and proactively managing these cognitive distortions can refine our approach to tackling complex issues, leading to better outcomes.**Recognizing Cognitive Biases**The first step in leveraging knowledge of cognitive biases is recognizing their presence and influence within problem-solving contexts. Confirmation bias, for instance, can cause individuals to focus on information that reaffirms their existing beliefs and discount evidence to the contrary. This bias can result in a narrowed view of the issue and potentially lead to suboptimal solutions. Being cognizant of confirmation bias encourages problem solvers to seek out and consider disconfirming evidence, providing a more rounded analysis and basis for decision-making.**Strategic Deployment of Debiasing Techniques**Debiasing techniques can actively mitigate the effects of cognitive biases. For example, the pre-mortem strategy, where problem solvers envision failure and then work backward to determine possible causes, helps counteract overconfidence and planning fallacy biases. This proactive approach facilitates the identification of potential risks and roadblocks, allowing for more strategic and comprehensive planning.Another powerful debiasing strategy is 'red teaming', wherein another group critiques and provides different perspectives on the proposed solution. This adversarial approach challenges prevailing assumptions and examines the problem from distinct angles, often uncovering blind spots in the original problem-solving process.**Harnessing Mindfulness to Improve Decision-Making**Developing a practice of mindfulness can significantly bolster the ability to recognize and control cognitive biases. Mindfulness cultivates a heightened awareness of present-moment thoughts and feelings without immediate judgment, which can illuminate biased thinking in its early stages. Incorporating mindfulness into routine activities can train the brain to maintain objectivity and enhances the capacity to reflect critically on automatic judgments. It's a proactive measure for consistently checking and adjusting cognitive processes to support sound problem-solving.To sum up, a deep-seated awareness and understanding of cognitive biases are key to optimizing problem-solving techniques. The synthesis of recognizing the various biases that could compromise problem analyses, applying targeted debiasing strategies, and fostering mindfulness fosters a more analytical and comprehensive approach to solving problems. Such an enhanced problem-solving methodology aligns closely with the aim of IIENSTITU—to facilitate learning and development through innovative education strategies, enabling individuals to tackle challenges with insight, precision, and creativity.

How can I improve my practical problem-solving skills?

Develop a Problem-Solving Mindset Aiming to improve practical problem-solving skills requires a shift in mindset. Embrace problems as opportunities for growth and learning rather than obstacles. Practice Critical Thinking Integrating critical thinking into your daily routine can help. This involves considering different perspectives, evaluating logical connections, and drawing conclusions based on evidence. Boost Creativity Creative thinking helps generate insightful solutions to problems. Engage in activities that stimulate creativity, such as brainstorming, mind mapping, or doing arts and crafts. Learn from Others Look for individuals or groups who are renowned for their problem-solving skills. Observe how they approach issues. Pull lessons from their methods and apply them to your own problem-solving processes. Apply Problem-Solving Frameworks Implementing recognized problem-solving frameworks, like SWOT analysis, root cause analysis, or design thinking, can structure your approach. This structured approach enhances the effectiveness of problem-solving endeavors. Reflect on Past Experiences Consider past situations where problem-solving was required. Reflect on the approach used, the results achieved, and the lessons learned. This introspection can inform future actions. Invest in Self-Improvement Continuous education promotes growth in all areas, including problem-solving. Consider enrolling in online courses or attending workshops aimed at enhancing such skills. Solve Puzzles and Games Solving puzzles and engaging in brain games builds cognitive capabilities, enhancing problem-solving skills. They also test your ability to strategize, think creatively, and make decisions under pressure. Encourage Feedback Feedback helps pinpoint areas of improvement. Encourage others to provide constructive criticism on your problem-solving strategies and refine them accordingly. Persistently Practice Like any skill, practical problem-solving becomes stronger through consistent practice. Dedicate time regularly to tackle problems, persevere in finding solutions, and learn from each experience. In conclusion, improving practical problem-solving skills requires a multimodal approach. By fostering a forward-thinking mindset and continuously engaging in strategies to stimulate cognitive growth, you can considerably enhance your problem-solving abilities.

To enhance practical problem-solving skills, it is critical to cultivate a mindset that views challenges as stepping stones to innovation and expertise. This fundamentally involves a commitment to constant learning and adaptability.Developing a Problem-Solving MindsetNurture a constructive perspective on problem-solving. Recognize that each problem presents a unique chance to refine your skills and push your cognitive boundaries.Embrace Critical ThinkingIncorporating critical thinking into everyday life is essential. This means not taking things at face value but instead questioning underlying assumptions, analyzing information objectively, and assessing evidence before reaching conclusions.Stimulate CreativityCreativity is the cornerstone of innovative problem-solving. Engage in exercises that push the boundaries of conventional thinking. Dedicate time to activities like brainstorming sessions, where wild ideas are not just permitted but encouraged.Learn from Problem-Solving ExpertsThere's much to be learned from observing those who excel at solving problems. Whether you find these individuals in your workplace, online forums, or through professional networks, consider the tactics they employ and extract adaptable strategies for your use.Utilize Structured FrameworksAdopting structured problem-solving frameworks can be immensely beneficial. Whether it's conducting a SWOT analysis to assess strengths, weaknesses, opportunities, and threats, or employing root cause analysis to dive deeper into the genesis of a problem, these frameworks provide clarity and direction.Reflect on Historical ChallengesLook back at previous situations where you've had to solve problems. Reflect on what worked, what didn't, and the lessons learned. This reflection enables you to build on past successes and avoid repeating mistakes.Pursue Continuous LearningExpanding knowledge and skills through ongoing education underpins improvement in any domain, including problem-solving. Taking courses, such as those offered by IIENSTITU, can provide both foundational knowledge and advanced techniques in problem-solving.Exercise Your Brain with GamesBrain exercises like puzzles and strategic games are not just entertainment—they're workouts for your mind. By regularly engaging with them, you improve critical cognitive skills that transfer to problem-solving.Solicit and Utilize FeedbackSoliciting feedback from peers or mentors on your problem-solving approach can provide fresh insights. Constructive feedback can reveal blind spots and refine your strategies.Commit to Consistent PracticeProblem-solving proficiency comes with persistent practice. By repeatedly exposing yourself to problems—large and small—and working diligently toward solutions, you'll refine your approach and grow more adept with each challenge.In essence, elevating your problem-solving skills is a journey that intertwines cognitive development with hands-on experience. By embracing a positive, growth-focused mindset and leveraging a blend of strategic thinking, creativity, and educational resources, you can significantly enhance your ability to tackle problems effectively.

What are the six steps of the practical problem-solving process?

Identifying the Problem The practical problem-solving process commences with identifying the problem. This step involves understanding the issue in depth and distinguishing it from symptoms, assumptions, or opinions. Establishing Objectives Next, objectives or desired outcomes are defined. Clear objectives provide a valuable direction and help to formulate solutions. Objectives should always be specific, measurable, achievable, relevant and time-bound. Investigating and Analyzing the Problem A thorough investigation follows the establishment of objectives. This encompasses gathering all relevant data and verifying its accuracy. Analyzing this information can then unearth root causes and contributing factors. Generating Solutions The fourth step in the process calls for generating potential solutions to the analyzed problem. This stage encourages creative thinking and involves brainstorming a range of options with no immediate judgment passed on their viability. Evaluating and Presenting Solutions Each solution must then be critically evaluated against the objectives, feasibility, and potential impact. The viable solutions are further refined and presented in a coherent, persuasive manner to decision-makers or stakeholders. Implementing the Solution The chosen solution is finally implemented in the last step. This crucial phase requires meticulous planning, defining roles and responsibilities, and executing the plan while monitoring progress. Continuous learning from this phase aids in future problem-solving endeavors. In conclusion, the six steps in the practical problem-solving process offer a structured approach to tackling issues. Each step plays a significant role to ensure the solution is effective, reasonable, and beneficial for all.

The practical problem-solving process is a systematic approach to recognizing, dissecting, and overcoming challenges in a range of contexts. IIENSTITU advocates an effective strategy that encompasses six integral steps. This process serves as an intellectual toolkit for individuals and organizations alike, promoting thoughtful resolution and strategic thinking when confronted by problems.1. Identifying the Problem:To embark on the problem-solving journey, one must first precisely pinpoint the problem. The aim is to differentiate the actual issue from potential distraction elements such as symptoms or assumptions that may cloud the core matter. A detailed problem statement should capture the essence of the issue, its scope, and impact.2. Establishing Objectives:The second step revolves around constructing clear and actionable objectives. What does an ideal situation look like post-resolution? Setting SMART (Specific, Measurable, Achievable, Relevant, and Time-bound) objectives can significantly enhance the focus and direction of the problem-solving process.3. Investigating and Analyzing the Problem:With objectives in hand, the next stage involves an exhaustive investigation, which means collecting pertinent information, facts, and data. Analysis then proceeds to delve deeper, identifying patterns, root causes, and the breadth of the problem's influence. This is the diagnostic phase, where the problem is dissected to understand its intricacies fully.4. Generating Solutions:Generating potential solutions is the creative part of the process. Here, brainstorming and ideation techniques come into play, encouraging the expression of every idea without immediate critique. This is where quantity trumps quality, with the goal of accruing a wide array of potential solutions for further evaluation.5. Evaluating and Presenting Solutions:The multitude of possible solutions generated in the previous step are now scrutinized. Each solution undergoes rigorous examination to ensure alignment with established objectives, feasibility in terms of resources, and overall impact. Subsequently, the most promising solutions are polished and neatly packaged for presentation to those responsible for decision-making or to stakeholders for their buy-in.6. Implementing the Solution:The final step is the execution phase, where the selected solution is put into action. Proper planning, defining roles and responsibilities, and the delegation of tasks are essential. A critical part of this phase also involves setting up mechanisms for monitoring progress and allowing room for iterative adjustments if needed. This ensures that the implemented solution is effectively resolving the problem and that lessons learned are captured for future problem-solving situations.Thus, through the six steps of the practical problem-solving process, one can methodically approach and conquer problems with confidence and precision. The outcome is not just a solution to an immediate problem but a refined skillset that is perpetually honed, enriching one's arsenal of strategic thinking and decision-making capabilities.

What are the 7 steps to problem-solving skills?

Understanding the Seven Steps of Problem-Solving Identifying the Problem The initial step in problem-solving involves determining the actual problem. The step entails understanding what you're attempting to resolve and why it should be addressed. Understanding the Problem The understanding process involves obtaining a clear picture of the problem. This step necessitates data gathering, noting who it affects, identifying root causes, and defining consequences. Generating Possible Solutions The third step involves brainstorming potential solutions. This process should be inclusive and creative to capture a wide range of solutions. Analyzing Potential Solutions Next, sift through the suggested solutions and examine them in terms of feasibility and impact. It's essential to consider both the advantages and drawbacks of each option. Choosing the Best Solution After analyzing potential solutions, select the one you believe most effective. This decision typically requires a delicate balance of practicability, impact, and resources available. Implementing the Solution Once you choose the best solution, it's time for implementation. Put your chosen solution into action, ensuring you've defined roles and responsibilities, and you've got a plan to monitor the progress. Reviewing the Outcome Finally, evaluate the results after implementing the solution. This review confirms whether the solution worked or if the problem remains. You may need to revisit previous steps and explore other solutions if the issue persists. In summary, the seven steps to problem-solving skills include identifying the problem, understanding the problem, generating possible solutions, analyzing these solutions, choosing the best solution, implementing the chosen solution, and reviewing the outcome. These steps, when utilized appropriately, can enhance one's ability to solve issues effectively, leading to more successful, efficient, and satisfactory outcomes.

Effective problem-solving is a critical soft skill in both personal and professional realms, and mastering the process can lead to significantly better outcomes. Let's delve into the seven steps to polish these much-needed skills.1. Identifying the Problem: The cornerstone of problem-solving is accurately identifying the problem. This isn't necessarily straightforward as problems can be complex or ill-defined. A keen eye for detail and a clear head are key. It's crucial to differentiate between the symptoms of a problem and the problem itself, ensuring efforts are focused on the root cause rather than just the effects.2. Understanding the Problem: Once the problem has been identified, it's imperative to understand its intricacies fully. This requires a deep dive into the context and implications. Gathering as much information as possible and asking probing questions lead to a comprehensive understanding. This step may also involve breaking the problem down into smaller, more manageable parts.3. Generating Possible Solutions: Creativity takes center stage here. Exploring a broad array of potential solutions without judgement encourages out-of-the-box thinking. Listing these solutions provides a visual aid to the problem-solving process and encourages further refinement and combination of ideas.4. Analyzing Potential Solutions: With possible solutions laid out, each must be weighed for its pros and cons. This may involve a cost-benefit analysis, considering resources, time, and potential outcomes. The aim is to determine which solutions are realistic and offer the most advantageous results. It's a step that requires objectivity and the ability to anticipate the implications of each solution.5. Choosing the Best Solution: Decision-making skills come to the fore as one must now choose the solution that stands out among the rest. This decision is based on the analysis and should consider long-term as well as short-term impacts. It may also require input from others if the problem has wider ramifications.6. Implementing the Solution: Implementation necessitates attention to detail, careful planning, and often, teamwork. Communication is paramount as those involved need to understand their roles and responsibilities. Tracking the progress and adjusting the plan as necessary are also important components of this step.7. Reviewing the Outcome: After implementation, it's time to reflect. Has the solution worked? What have been the outcomes, and have they solved the problem to satisfaction? If not, a reassessment may be in order, possibly returning to previous steps for further adjustment.Each step in this process is critical to arriving at the best possible solution. It's a skill set that's honed over time and experience. IIENSTITU, an educational platform, understands the importance of such skills in today's complex world and provides courses that include problem-solving as part of their curriculum. Developing problem-solving abilities fosters innovation, improves relationships, and leads to better decision-making, all of which are invaluable in both professional and personal life.

How can I develop my capacity to adapt and respond effectively in unpredictable problem-solving situations?

Understanding the Situation To develop your ability to adapt in unpredictable problem-solving situations, first, understand the situation comprehensibly. Recognize factors, elements, and potential outcomes. Comprehend the context and relevance of the problem in bigger picture. Strengthening Senses Observation Refining your observational skills can significantly enhance adaptive capability. Paying sharp attention to nuances, hidden details, and subtle changes often provide cues to navigate through uncertainties. Stimulating Creative Thinking Encourage creative thinking for finding innovative solutions. Creativity expedites problem-solving by driving you to think outside the box, observe from different perspectives and inspect unorthodox solution methods. Training with Simulated Scenarios Simulated training can remarkably improve your adaptive abilities. Facing a variety of hypothetical situations can enrich both cognitive flexibility and problem-solving skills in dynamic conditions. Encouraging Learning from Failures Embrace setbacks as avenues for learning. Failures often offer valuable insights into what doesn't work, thus enhancing our ability to adapt and respond effectively. Emphasizing Emotional Intelligence Developing emotional intelligence aids in managing stress during unpredictable situations. It helps to maintain a positive attitude, stay focused, and make balanced decisions amidst adversities. Maintaining Self-Belief Have faith in your abilities. Self-belief is instrumental in tackling unknown territories as it fuels perseverance, resilience, and courage to face any problem. Promoting Continuous Learning Promote a culture of continuous learning. Mastery over new skills and knowledge enhances adaptation ability. Stay versatile to adjust with evolving scenarios and to incorporate newfound learnings readily. In essence, enhancing adaptation in unforeseen problem-solving situations requires understanding the situation, strengthening observational skills, fostering creativity, getting trained in simulated environments, learning from failures, honing emotional intelligence, believing in oneself, and encouraging constant learning. By strengthening these areas, one could face challenges head-on and navigate through unpredictable situations confidently.

Facilitating Effective Adaptation in Unpredictable Problem-Solving SituationsTo bolster one's ability to adapt and respond effectively in unpredictable problem-solving scenarios, it is imperative to cultivate a deep understanding of the situation at hand. This means dissecting the problem, recognizing its components, including possible risks and opportunities, as well as grasping its significance within a larger context.Enhancing Observational AcuityA sharpened sense of observation plays a pivotal role in adaptive abilities. By keeping a keen eye on subtleties and being alert to changes in the environment, one is often able to pick up critical signals that can guide decision-making in uncertain situations.Stoking the Flames of CreativityNurturing creative thought is essential for devising unique and innovative solutions to complex problems. Creative problem-solving pushes boundaries, prompting individuals to consider diverse perspectives and explore solutions beyond conventional thinking.Experience Through SimulationEngaging in simulated scenarios is a powerful way to boost adaptability. Tailored simulations expose individuals to a plethora of hypothetical challenges, fostering cognitive agility and bolstering the skill set needed to tackle real-world unpredictable problems.Learning from MisstepsRather than seeing setbacks as purely negative, it is crucial to recognize them as formative experiences. Failures illuminate the pitfalls in our strategies, refining our understanding of what to avoid and increasing our adaptive capacity for future endeavors.Emotional Intelligence as a PillarA high degree of emotional intelligence can be a deciding factor in managing the pressure that comes with unpredictable situations. It empowers individuals to keep composed, maintain clarity of thought, and make balanced judgments even when faced with the unknown.The Power of Self-BeliefFaith in one's abilities is the bedrock of venturing into uncharted territory. Self-confidence is crucial as it propels persistence, facilitates recovery from setbacks, and instills the bravery required to confront novel challenges.A Commitment to Lifelong LearningUpholding a commitment to continual self-improvement ensures that one's adaptive skill set keeps pace with an ever-changing world. Perpetual learning is vital for staying relevant and capable of assimilating new knowledge and rapidly applying it when confronted with unprecedented situations.In summation, elevating adaptability in the face of unforeseen problem-solving challenges hinges on a multi-faceted approach: deep comprehension of issues, refined observational prowess, encouragement of inventive thinking, practical experience via simulations, wisdom gained from failures, well-developed emotional intelligence, unwavering self-belief, and a relentless pursuit of personal growth. By fostering these qualities, individuals are well-equipped to handle the unpredictable with confidence and dexterity.

In what ways can upskilling in interdisciplinary knowledge contribute to enhancing practical problem-solving skills?

Enhanced Understanding through Interdisciplinary Knowledge Upskilling in interdisciplinary knowledge can foster enhanced understanding of varied domains. Being skilled in different study areas provides a unique amalgam of insights. It ruptures the traditional silos of knowledge, triggering innovative thinking. Boosting Problem-Solving Ability This innovative thinking in turn empowers the practical problem-solving skills. Decision-making models that include more than one discipline heighten the potential for comprehensive solutions. The blended expertise helps in deconstructing complex problems into manageable parts. Boosting Innovation Interdisciplinary knowledge escalates innovation. It equips individuals with diverse perspectives, fueling creativity. Fresh, innovative solutions often emerge from this amalgamation of varying viewpoints. As result, problem solving extends beyond the routine approaches. Facilitating Collaboration Interdisciplinary skills facilitate collaboration. Working as a team means encountering various perspectives. Adequate knowledge about diverse fields aids communication and understanding among team members. Improved collaboration results in effective problem-solving. Broadened Horizon Interdisciplinary skills foster a broader horizon, intensifying curiosity. They equip individuals to explore unfamiliar territories and face new challenges with confidence. This eagerness to explore further magnifies problem-solving capacities. In short, upskilling in interdisciplinary knowledge acts as a catalyzer, enhancing practical problem-solving skills. It not only instills innovative, comprehensive, and collaborative approaches, but also broadens horizons, boosting problem-solving capabilities. Hence, acquiring interdisciplinary knowledge and skills is crucial in today's complex and interconnected world.

Enhancing practical problem-solving skills through upskilling in interdisciplinary knowledge is a multifaceted process that benefits individuals in numerous ways:Cross-Pollination of IdeasInterdisciplinary knowledge allows for the cross-pollination of ideas between distinct areas of study. For instance, principles of design thinking can be applied to scientific research, or insights from psychology can enhance approaches in business strategy. This cross-disciplinary approach leads to a synthesis of ideas that can solve problems more creatively and effectively.Improved Analytical SkillsLearning across disciplines sharpens analytical skills, as it exposes individuals to various methods of analysis and models of thought. For example, a professional with a background in both technology and social sciences may view data privacy challenges from both a technical and societal perspective, enabling them to develop holistic strategies that address technical vulnerabilities while considering ethical implications.Enhanced AdaptabilityThe breadth of knowledge gained from interdisciplinary study enhances adaptability, an essential skill in a rapidly changing world. An employee who is up to date with trends in both economics and environmental studies, for example, may be better prepared to navigate and contribute to a company’s sustainability initiatives in a fluctuating economy.Promotion of Systems ThinkingUnderstanding the interconnectedness of systems is one of the major advantages of interdisciplinary knowledge. Individuals learn to identify and understand the complex interplay between various elements within a system, enabling them to foresee potential challenges and opportunities, as well as devise integrated solutions that consider multiple factors.Developing a Global MindsetInterdisciplinary knowledge often includes global or cultural studies, encouraging a broader awareness of the world. This global mindset is critical in today’s interconnected economy. It fosters greater cultural sensitivity, which is paramount when solving problems that span different geographic regions and demographics.Cognitive FlexibilityLearning different disciplines expands one's cognitive flexibility—the ability to switch between different modes of thought depending on the context. Cognitive flexibility is directly linked to problem-solving skills, as it enables individuals to approach problems from fresh angles and adapt to new situations with ease.Addressing 21st-Century ChallengesThe complex challenges of the 21st century, such as climate change, public health crises, and technological disruptions, cannot be adequately tackled by isolated disciplines. Interdisciplinary knowledge allows individuals to understand the multifaceted nature of these issues and develop comprehensive approaches to address them.Fostering Innovation in Education and TrainingEducational institutions such as IIENSTITU recognize the importance of interdisciplinary knowledge and offer programs designed to equip students with a comprehensive skill set. Such institutions are at the forefront of fostering innovation in education and training by blending learning across different fields and thus moulding well-rounded problem-solvers who are valuable in any professional context.In conclusion, upskilling in interdisciplinary knowledge is more than just accumulating information from various fields. It is about building a versatile, robust, and innovative approach to problem-solving that leverages the strengths of multiple disciplines. As the global landscape continues to evolve and present new complexities, interdisciplinary proficiency will become even more critical in devising effective solutions to both everyday and global-scale challenges.

How can I incorporate effective feedback and reflection techniques to continuously refine my problem-solving capabilities?

Importance of Feedback Integrating effective feedback is paramount to refining problem-solving skills. Feedback offers clear evidence of your thought processes and indicates areas for improvement. Encourage feedback from peers, mentors, and teachers. Established channels of open and honest communication can act as a support system to guide your growth. Reflection Techniques Reflection, on the other hand, lets you critically examine your problem-solving procedure. Use reflective journals to jot down your experiences, noting what went well, what didn't, and potential areas of improvement. Analyze these experiences and identify the strategies that worked best. Adopting Experimentation Experimentation encourages a trial-and-error approach. It promotes risk-taking and resilience in the face of unsuccessful attempts. Learn from these failures and use them as stepping-stones to devise new, innovative strategies. Leveraging Collaborative Problem Solving Collaborative problem-solving introduces new perspectives. Explain your problem-solving approach to others and grasp their suggestions. Diverse viewpoints can spark creativity and faster solution finding. Include these insights in your problem-solving toolkit. Continuous Learning Continuous learning is crucial for constant refinement of skills. Embarking on lifelong learning equips you with new techniques that can supplement your existing problem-solving chops. Enrolling in online courses or attending workshops can provide deeper insights. In sum, effectively incorporating feedback and reflection techniques can sharpen your problem-solving abilities. Experimentation and collaboration serve to further enhance these skills. Continuous learning is ultimately the key to stay updated with evolving best practices and strategies.

Incorporating feedback and reflection into your problem-solving routine is a dynamic way to enhance your capabilities and achieve better outcomes. By seeking feedback and participating in thoughtful reflection, you create a continuous loop of improvement that can refine your problem-solving skills over time.Feedback is a critical component of the learning process that provides you with insights into your performance. When solving problems, actively solicit feedback from colleagues, mentors, or industry peers who can offer a different perspective on your approach. Constructive criticism can shine a light on aspects of your process that may be overlooked from your vantage point. This outside view can point out the strengths and weaknesses in your strategy, leading to more effective problem-solving methods.Equally important is reflection, a personal and introspective process that allows you to contemplate on your problem-solving journey. By maintaining a reflective practice, such as writing in a journal or diary, you give yourself the opportunity to consider your experiences in depth. Deliberately look back at the problems you have tackled, assessing what strategies succeeded and where you encountered obstacles. Reflect on the choices you made and consider alternative strategies that could have led to a different outcome. This internal feedback mechanism is crucial for personal growth and hones your ability to approach problems with a fresh perspective.Experimentation is another key practice in refining problem-solving skills. Adopt a mindset that embraces trial and error, understanding that not all solutions will be successful on the first attempt. This resilience in the face of failure fosters creativity, as you learn to pivot and explore different angles until you find the most viable solution.Collaboration further enriches your problem-solving toolbox. By engaging with others, you leverage the collective intelligence of a group, gaining access to a wider range of experiences and knowledge. Share your thought process with your team or peers, be open to their input, and integrate their insights into your problem-solving strategy.Lastly, the dedication to continuous learning keeps you informed on new methodologies and technologies that can refine your problem-solving skills. Ongoing education, like enrolling in online courses provided by platforms such as IIENSTITU, or attending industry-relevant workshops, ensures that you remain well-versed in the latest trends and strategies within your field.Ultimately, the combination of seeking feedback, practicing reflection, engaging in experimentation, collaborating with others, and committing to continuous learning creates a powerful framework for improving your problem-solving capabilities. By integrating these approaches, you develop a robust skill set that is adaptable, innovative, and resilient to the complexities of any problem-solving situation.

SHe is a graduate of Akdeniz University, Department of Business Administration. She graduated from the university with a faculty degree. It has contributed to its environment with its social responsibility project. She writes articles about business and its fields.

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HBR On Leadership podcast series

Do You Understand the Problem You’re Trying to Solve?

To solve tough problems at work, first ask these questions.

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Problem solving skills are invaluable in any job. But all too often, we jump to find solutions to a problem without taking time to really understand the dilemma we face, according to Thomas Wedell-Wedellsborg , an expert in innovation and the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

In this episode, you’ll learn how to reframe tough problems by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for just one root cause can be misleading.

Key episode topics include: leadership, decision making and problem solving, power and influence, business management.

HBR On Leadership curates the best case studies and conversations with the world’s top business and management experts, to help you unlock the best in those around you. New episodes every week.

  • Listen to the original HBR IdeaCast episode: The Secret to Better Problem Solving (2016)
  • Find more episodes of HBR IdeaCast
  • Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org .

HANNAH BATES: Welcome to HBR on Leadership , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock the best in those around you.

Problem solving skills are invaluable in any job. But even the most experienced among us can fall into the trap of solving the wrong problem.

Thomas Wedell-Wedellsborg says that all too often, we jump to find solutions to a problem – without taking time to really understand what we’re facing.

He’s an expert in innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

  In this episode, you’ll learn how to reframe tough problems, by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for one root cause can be misleading. And you’ll learn how to use experimentation and rapid prototyping as problem-solving tools.

This episode originally aired on HBR IdeaCast in December 2016. Here it is.

SARAH GREEN CARMICHAEL: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Sarah Green Carmichael.

Problem solving is popular. People put it on their resumes. Managers believe they excel at it. Companies count it as a key proficiency. We solve customers’ problems.

The problem is we often solve the wrong problems. Albert Einstein and Peter Drucker alike have discussed the difficulty of effective diagnosis. There are great frameworks for getting teams to attack true problems, but they’re often hard to do daily and on the fly. That’s where our guest comes in.

Thomas Wedell-Wedellsborg is a consultant who helps companies and managers reframe their problems so they can come up with an effective solution faster. He asks the question “Are You Solving The Right Problems?” in the January-February 2017 issue of Harvard Business Review. Thomas, thank you so much for coming on the HBR IdeaCast .

THOMAS WEDELL-WEDELLSBORG: Thanks for inviting me.

SARAH GREEN CARMICHAEL: So, I thought maybe we could start by talking about the problem of talking about problem reframing. What is that exactly?

THOMAS WEDELL-WEDELLSBORG: Basically, when people face a problem, they tend to jump into solution mode to rapidly, and very often that means that they don’t really understand, necessarily, the problem they’re trying to solve. And so, reframing is really a– at heart, it’s a method that helps you avoid that by taking a second to go in and ask two questions, basically saying, first of all, wait. What is the problem we’re trying to solve? And then crucially asking, is there a different way to think about what the problem actually is?

SARAH GREEN CARMICHAEL: So, I feel like so often when this comes up in meetings, you know, someone says that, and maybe they throw out the Einstein quote about you spend an hour of problem solving, you spend 55 minutes to find the problem. And then everyone else in the room kind of gets irritated. So, maybe just give us an example of maybe how this would work in practice in a way that would not, sort of, set people’s teeth on edge, like oh, here Sarah goes again, reframing the whole problem instead of just solving it.

THOMAS WEDELL-WEDELLSBORG: I mean, you’re bringing up something that’s, I think is crucial, which is to create legitimacy for the method. So, one of the reasons why I put out the article is to give people a tool to say actually, this thing is still important, and we need to do it. But I think the really critical thing in order to make this work in a meeting is actually to learn how to do it fast, because if you have the idea that you need to spend 30 minutes in a meeting delving deeply into the problem, I mean, that’s going to be uphill for most problems. So, the critical thing here is really to try to make it a practice you can implement very, very rapidly.

There’s an example that I would suggest memorizing. This is the example that I use to explain very rapidly what it is. And it’s basically, I call it the slow elevator problem. You imagine that you are the owner of an office building, and that your tenants are complaining that the elevator’s slow.

Now, if you take that problem framing for granted, you’re going to start thinking creatively around how do we make the elevator faster. Do we install a new motor? Do we have to buy a new lift somewhere?

The thing is, though, if you ask people who actually work with facilities management, well, they’re going to have a different solution for you, which is put up a mirror next to the elevator. That’s what happens is, of course, that people go oh, I’m busy. I’m busy. I’m– oh, a mirror. Oh, that’s beautiful.

And then they forget time. What’s interesting about that example is that the idea with a mirror is actually a solution to a different problem than the one you first proposed. And so, the whole idea here is once you get good at using reframing, you can quickly identify other aspects of the problem that might be much better to try to solve than the original one you found. It’s not necessarily that the first one is wrong. It’s just that there might be better problems out there to attack that we can, means we can do things much faster, cheaper, or better.

SARAH GREEN CARMICHAEL: So, in that example, I can understand how A, it’s probably expensive to make the elevator faster, so it’s much cheaper just to put up a mirror. And B, maybe the real problem people are actually feeling, even though they’re not articulating it right, is like, I hate waiting for the elevator. But if you let them sort of fix their hair or check their teeth, they’re suddenly distracted and don’t notice.

But if you have, this is sort of a pedestrian example, but say you have a roommate or a spouse who doesn’t clean up the kitchen. Facing that problem and not having your elegant solution already there to highlight the contrast between the perceived problem and the real problem, how would you take a problem like that and attack it using this method so that you can see what some of the other options might be?

THOMAS WEDELL-WEDELLSBORG: Right. So, I mean, let’s say it’s you who have that problem. I would go in and say, first of all, what would you say the problem is? Like, if you were to describe your view of the problem, what would that be?

SARAH GREEN CARMICHAEL: I hate cleaning the kitchen, and I want someone else to clean it up.

THOMAS WEDELL-WEDELLSBORG: OK. So, my first observation, you know, that somebody else might not necessarily be your spouse. So, already there, there’s an inbuilt assumption in your question around oh, it has to be my husband who does the cleaning. So, it might actually be worth, already there to say, is that really the only problem you have? That you hate cleaning the kitchen, and you want to avoid it? Or might there be something around, as well, getting a better relationship in terms of how you solve problems in general or establishing a better way to handle small problems when dealing with your spouse?

SARAH GREEN CARMICHAEL: Or maybe, now that I’m thinking that, maybe the problem is that you just can’t find the stuff in the kitchen when you need to find it.

THOMAS WEDELL-WEDELLSBORG: Right, and so that’s an example of a reframing, that actually why is it a problem that the kitchen is not clean? Is it only because you hate the act of cleaning, or does it actually mean that it just takes you a lot longer and gets a lot messier to actually use the kitchen, which is a different problem. The way you describe this problem now, is there anything that’s missing from that description?

SARAH GREEN CARMICHAEL: That is a really good question.

THOMAS WEDELL-WEDELLSBORG: Other, basically asking other factors that we are not talking about right now, and I say those because people tend to, when given a problem, they tend to delve deeper into the detail. What often is missing is actually an element outside of the initial description of the problem that might be really relevant to what’s going on. Like, why does the kitchen get messy in the first place? Is it something about the way you use it or your cooking habits? Is it because the neighbor’s kids, kind of, use it all the time?

There might, very often, there might be issues that you’re not really thinking about when you first describe the problem that actually has a big effect on it.

SARAH GREEN CARMICHAEL: I think at this point it would be helpful to maybe get another business example, and I’m wondering if you could tell us the story of the dog adoption problem.

THOMAS WEDELL-WEDELLSBORG: Yeah. This is a big problem in the US. If you work in the shelter industry, basically because dogs are so popular, more than 3 million dogs every year enter a shelter, and currently only about half of those actually find a new home and get adopted. And so, this is a problem that has persisted. It’s been, like, a structural problem for decades in this space. In the last three years, where people found new ways to address it.

So a woman called Lori Weise who runs a rescue organization in South LA, and she actually went in and challenged the very idea of what we were trying to do. She said, no, no. The problem we’re trying to solve is not about how to get more people to adopt dogs. It is about keeping the dogs with their first family so they never enter the shelter system in the first place.

In 2013, she started what’s called a Shelter Intervention Program that basically works like this. If a family comes and wants to hand over their dog, these are called owner surrenders. It’s about 30% of all dogs that come into a shelter. All they would do is go up and ask, if you could, would you like to keep your animal? And if they said yes, they would try to fix whatever helped them fix the problem, but that made them turn over this.

And sometimes that might be that they moved into a new building. The landlord required a deposit, and they simply didn’t have the money to put down a deposit. Or the dog might need a $10 rabies shot, but they didn’t know how to get access to a vet.

And so, by instigating that program, just in the first year, she took her, basically the amount of dollars they spent per animal they helped went from something like $85 down to around $60. Just an immediate impact, and her program now is being rolled out, is being supported by the ASPCA, which is one of the big animal welfare stations, and it’s being rolled out to various other places.

And I think what really struck me with that example was this was not dependent on having the internet. This was not, oh, we needed to have everybody mobile before we could come up with this. This, conceivably, we could have done 20 years ago. Only, it only happened when somebody, like in this case Lori, went in and actually rethought what the problem they were trying to solve was in the first place.

SARAH GREEN CARMICHAEL: So, what I also think is so interesting about that example is that when you talk about it, it doesn’t sound like the kind of thing that would have been thought of through other kinds of problem solving methods. There wasn’t necessarily an After Action Review or a 5 Whys exercise or a Six Sigma type intervention. I don’t want to throw those other methods under the bus, but how can you get such powerful results with such a very simple way of thinking about something?

THOMAS WEDELL-WEDELLSBORG: That was something that struck me as well. This, in a way, reframing and the idea of the problem diagnosis is important is something we’ve known for a long, long time. And we’ve actually have built some tools to help out. If you worked with us professionally, you are familiar with, like, Six Sigma, TRIZ, and so on. You mentioned 5 Whys. A root cause analysis is another one that a lot of people are familiar with.

Those are our good tools, and they’re definitely better than nothing. But what I notice when I work with the companies applying those was those tools tend to make you dig deeper into the first understanding of the problem we have. If it’s the elevator example, people start asking, well, is that the cable strength, or is the capacity of the elevator? That they kind of get caught by the details.

That, in a way, is a bad way to work on problems because it really assumes that there’s like a, you can almost hear it, a root cause. That you have to dig down and find the one true problem, and everything else was just symptoms. That’s a bad way to think about problems because problems tend to be multicausal.

There tend to be lots of causes or levers you can potentially press to address a problem. And if you think there’s only one, if that’s the right problem, that’s actually a dangerous way. And so I think that’s why, that this is a method I’ve worked with over the last five years, trying to basically refine how to make people better at this, and the key tends to be this thing about shifting out and saying, is there a totally different way of thinking about the problem versus getting too caught up in the mechanistic details of what happens.

SARAH GREEN CARMICHAEL: What about experimentation? Because that’s another method that’s become really popular with the rise of Lean Startup and lots of other innovation methodologies. Why wouldn’t it have worked to, say, experiment with many different types of fixing the dog adoption problem, and then just pick the one that works the best?

THOMAS WEDELL-WEDELLSBORG: You could say in the dog space, that’s what’s been going on. I mean, there is, in this industry and a lot of, it’s largely volunteer driven. People have experimented, and they found different ways of trying to cope. And that has definitely made the problem better. So, I wouldn’t say that experimentation is bad, quite the contrary. Rapid prototyping, quickly putting something out into the world and learning from it, that’s a fantastic way to learn more and to move forward.

My point is, though, that I feel we’ve come to rely too much on that. There’s like, if you look at the start up space, the wisdom is now just to put something quickly into the market, and then if it doesn’t work, pivot and just do more stuff. What reframing really is, I think of it as the cognitive counterpoint to prototyping. So, this is really a way of seeing very quickly, like not just working on the solution, but also working on our understanding of the problem and trying to see is there a different way to think about that.

If you only stick with experimentation, again, you tend to sometimes stay too much in the same space trying minute variations of something instead of taking a step back and saying, wait a minute. What is this telling us about what the real issue is?

SARAH GREEN CARMICHAEL: So, to go back to something that we touched on earlier, when we were talking about the completely hypothetical example of a spouse who does not clean the kitchen–

THOMAS WEDELL-WEDELLSBORG: Completely, completely hypothetical.

SARAH GREEN CARMICHAEL: Yes. For the record, my husband is a great kitchen cleaner.

You started asking me some questions that I could see immediately were helping me rethink that problem. Is that kind of the key, just having a checklist of questions to ask yourself? How do you really start to put this into practice?

THOMAS WEDELL-WEDELLSBORG: I think there are two steps in that. The first one is just to make yourself better at the method. Yes, you should kind of work with a checklist. In the article, I kind of outlined seven practices that you can use to do this.

But importantly, I would say you have to consider that as, basically, a set of training wheels. I think there’s a big, big danger in getting caught in a checklist. This is something I work with.

My co-author Paddy Miller, it’s one of his insights. That if you start giving people a checklist for things like this, they start following it. And that’s actually a problem, because what you really want them to do is start challenging their thinking.

So the way to handle this is to get some practice using it. Do use the checklist initially, but then try to step away from it and try to see if you can organically make– it’s almost a habit of mind. When you run into a colleague in the hallway and she has a problem and you have five minutes, like, delving in and just starting asking some of those questions and using your intuition to say, wait, how is she talking about this problem? And is there a question or two I can ask her about the problem that can help her rethink it?

SARAH GREEN CARMICHAEL: Well, that is also just a very different approach, because I think in that situation, most of us can’t go 30 seconds without jumping in and offering solutions.

THOMAS WEDELL-WEDELLSBORG: Very true. The drive toward solutions is very strong. And to be clear, I mean, there’s nothing wrong with that if the solutions work. So, many problems are just solved by oh, you know, oh, here’s the way to do that. Great.

But this is really a powerful method for those problems where either it’s something we’ve been banging our heads against tons of times without making progress, or when you need to come up with a really creative solution. When you’re facing a competitor with a much bigger budget, and you know, if you solve the same problem later, you’re not going to win. So, that basic idea of taking that approach to problems can often help you move forward in a different way than just like, oh, I have a solution.

I would say there’s also, there’s some interesting psychological stuff going on, right? Where you may have tried this, but if somebody tries to serve up a solution to a problem I have, I’m often resistant towards them. Kind if like, no, no, no, no, no, no. That solution is not going to work in my world. Whereas if you get them to discuss and analyze what the problem really is, you might actually dig something up.

Let’s go back to the kitchen example. One powerful question is just to say, what’s your own part in creating this problem? It’s very often, like, people, they describe problems as if it’s something that’s inflicted upon them from the external world, and they are innocent bystanders in that.

SARAH GREEN CARMICHAEL: Right, or crazy customers with unreasonable demands.

THOMAS WEDELL-WEDELLSBORG: Exactly, right. I don’t think I’ve ever met an agency or consultancy that didn’t, like, gossip about their customers. Oh, my god, they’re horrible. That, you know, classic thing, why don’t they want to take more risk? Well, risk is bad.

It’s their business that’s on the line, not the consultancy’s, right? So, absolutely, that’s one of the things when you step into a different mindset and kind of, wait. Oh yeah, maybe I actually am part of creating this problem in a sense, as well. That tends to open some new doors for you to move forward, in a way, with stuff that you may have been struggling with for years.

SARAH GREEN CARMICHAEL: So, we’ve surfaced a couple of questions that are useful. I’m curious to know, what are some of the other questions that you find yourself asking in these situations, given that you have made this sort of mental habit that you do? What are the questions that people seem to find really useful?

THOMAS WEDELL-WEDELLSBORG: One easy one is just to ask if there are any positive exceptions to the problem. So, was there day where your kitchen was actually spotlessly clean? And then asking, what was different about that day? Like, what happened there that didn’t happen the other days? That can very often point people towards a factor that they hadn’t considered previously.


THOMAS WEDELL-WEDELLSBORG: S,o that is your solution. Take-out from [INAUDIBLE]. That might have other problems.

Another good question, and this is a little bit more high level. It’s actually more making an observation about labeling how that person thinks about the problem. And what I mean with that is, we have problem categories in our head. So, if I say, let’s say that you describe a problem to me and say, well, we have a really great product and are, it’s much better than our previous product, but people aren’t buying it. I think we need to put more marketing dollars into this.

Now you can go in and say, that’s interesting. This sounds like you’re thinking of this as a communications problem. Is there a different way of thinking about that? Because you can almost tell how, when the second you say communications, there are some ideas about how do you solve a communications problem. Typically with more communication.

And what you might do is go in and suggest, well, have you considered that it might be, say, an incentive problem? Are there incentives on behalf of the purchasing manager at your clients that are obstructing you? Might there be incentive issues with your own sales force that makes them want to sell the old product instead of the new one?

So literally, just identifying what type of problem does this person think about, and is there different potential way of thinking about it? Might it be an emotional problem, a timing problem, an expectations management problem? Thinking about what label of what type of problem that person is kind of thinking as it of.

SARAH GREEN CARMICHAEL: That’s really interesting, too, because I think so many of us get requests for advice that we’re really not qualified to give. So, maybe the next time that happens, instead of muddying my way through, I will just ask some of those questions that we talked about instead.

THOMAS WEDELL-WEDELLSBORG: That sounds like a good idea.

SARAH GREEN CARMICHAEL: So, Thomas, this has really helped me reframe the way I think about a couple of problems in my own life, and I’m just wondering. I know you do this professionally, but is there a problem in your life that thinking this way has helped you solve?

THOMAS WEDELL-WEDELLSBORG: I’ve, of course, I’ve been swallowing my own medicine on this, too, and I think I have, well, maybe two different examples, and in one case somebody else did the reframing for me. But in one case, when I was younger, I often kind of struggled a little bit. I mean, this is my teenage years, kind of hanging out with my parents. I thought they were pretty annoying people. That’s not really fair, because they’re quite wonderful, but that’s what life is when you’re a teenager.

And one of the things that struck me, suddenly, and this was kind of the positive exception was, there was actually an evening where we really had a good time, and there wasn’t a conflict. And the core thing was, I wasn’t just seeing them in their old house where I grew up. It was, actually, we were at a restaurant. And it suddenly struck me that so much of the sometimes, kind of, a little bit, you love them but they’re annoying kind of dynamic, is tied to the place, is tied to the setting you are in.

And of course, if– you know, I live abroad now, if I visit my parents and I stay in my old bedroom, you know, my mother comes in and wants to wake me up in the morning. Stuff like that, right? And it just struck me so, so clearly that it’s– when I change this setting, if I go out and have dinner with them at a different place, that the dynamic, just that dynamic disappears.

SARAH GREEN CARMICHAEL: Well, Thomas, this has been really, really helpful. Thank you for talking with me today.


HANNAH BATES: That was Thomas Wedell-Wedellsborg in conversation with Sarah Green Carmichael on the HBR IdeaCast. He’s an expert in problem solving and innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

We’ll be back next Wednesday with another hand-picked conversation about leadership from the Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

We’re a production of Harvard Business Review. If you want more podcasts, articles, case studies, books, and videos like this, find it all at HBR dot org.

This episode was produced by Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Music by Coma Media. Special thanks to Maureen Hoch, Adi Ignatius, Karen Player, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener.

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Kinicki, Organizational Behavior 3e  develops students' problem-solving skills through a unique, consistent, integrated 3-step Problem-Solving Approach that lets them immediately put research-based knowledge into practice in their personal and professional lives.  Organizational Behavior 3e  explicitly addresses OB implications for students' core career readiness skills, showing how OB provides them with the higher-level soft skills employers seek, such as problem solving, critical thinking, leadership and decision making. The understanding and application of OB theories and concepts provides tremendous value to students' lives today and throughout their careers.


1. Making OB Work for Me

2. Values and Attitudes

3. Individual Differences and Emotions 

4. Social Perception and Managing Diversity

5. Foundations of Employee Motivation 

6. Performance Management

7. Positive Organizational Behavior


8. Groups and Teams

9. Communication in the Digital Age

10. Managing Conflict and Negotiation

11. Decision Making and Creativity

12. Power, Influence, and Politics 

13. Leadership Effectiveness


14. Organizational Culture, Socialization, and Mentoring

15. Organizational Design, Effectiveness, and Innovation

16. Managing Change and Stress

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Comprehensive Interview Guide: 60+ Professions Explored in Detail

26 Good Examples of Problem Solving (Interview Answers)

By Biron Clark

Published: November 15, 2023

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 will be more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical in your approach.

But how do they measure this?

They’re going to ask you interview questions about these problem solving skills, and they might also look for examples of problem solving on your resume and cover letter. So coming up, I’m going to share a list of examples of problem solving, whether you’re an experienced job seeker or recent graduate.

Then I’ll share sample interview answers to, “Give an example of a time you used logic to solve a problem?”

Problem-Solving Defined

It is the ability to identify the 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 also involves critical thinking, communication, listening, creativity, research, data gathering, risk assessment, continuous learning, decision-making, and other soft and technical skills.

Solving problems not only prevent losses or damages but also boosts self-confidence and reputation when you successfully execute it. The spotlight shines on you when people see you handle issues with ease and savvy despite the challenges. Your ability and potential to be a future leader that can take on more significant roles and tackle bigger setbacks shine through. Problem-solving is a skill you can master by learning from others and acquiring wisdom from their and your own experiences. 

It takes a village to come up with solutions, but a good problem solver can steer the team towards the best choice and implement it to achieve the desired result.

Watch: 26 Good Examples of Problem Solving

Examples of problem solving scenarios 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

You can share all of the examples above when you’re asked questions about problem solving in your interview. As you can see, even if you have no professional work experience, it’s possible to think back to problems and unexpected challenges that you faced in your studies and discuss how you solved them.

Interview Answers to “Give an Example of an Occasion When You Used Logic to Solve 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,” since you’re likely to hear this interview question in all sorts of industries.

Example Answer 1:

At my current job, I recently solved a problem where a client was upset about our software pricing. They had misunderstood the sales representative who explained pricing originally, and when their package renewed for its second month, they called to complain about the invoice. I apologized for the confusion and then spoke to our billing team to see what type of solution we could come up with. We decided that the best course of action was to offer a long-term pricing package that would provide a discount. This not only solved the problem but got the customer to agree to a longer-term contract, which means we’ll keep their business for at least one year now, and they’re happy with the pricing. I feel I got the best possible outcome and the way I chose to solve the problem was effective.

Example Answer 2:

In my last job, I had to do quite a bit of problem solving related to our shift scheduling. We had four people quit within a week and the department was severely understaffed. I coordinated a ramp-up of our hiring efforts, I got approval from the department head to offer bonuses for overtime work, and then I found eight employees who were willing to do overtime this month. I think the key problem solving skills here were taking initiative, communicating clearly, and reacting quickly to solve this problem before it became an even bigger issue.

Example Answer 3:

In my current marketing role, my manager asked me to come up with a solution to our declining social media engagement. I assessed our current strategy and recent results, analyzed what some of our top competitors were doing, and then came up with an exact blueprint we could follow this year to emulate our best competitors but also stand out and develop a unique voice as a brand. I feel this is a good example of using logic to solve a problem because it was based on analysis and observation of competitors, rather than guessing or quickly reacting to the situation without reliable data. I always use logic and data to solve problems when possible. The project turned out to be a success and we increased our social media engagement by an average of 82% by the end of the year.

Answering Questions About Problem Solving with the STAR Method

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 mention problem solving as a necessary skill), I recommend using the STAR method to tell your story.

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. So before jumping in and talking about the problem that needed solving, make sure to describe the general situation. What job/company were you working at? When was this? Then, you can describe the task at hand and the problem that needed solving. 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 a positive result you got.

Whether you’re answering interview questions about problem solving or writing a cover letter, you should only choose examples where you got a positive result and successfully solved the issue.

Example answer:

Situation : We had an irate client who was a social media influencer and had impossible delivery time demands we could not meet. She spoke negatively about us in her vlog and asked her followers to boycott our products. (Task : To develop an official statement to explain our company’s side, clarify the issue, and prevent it from getting out of hand). Action : I drafted a statement that balanced empathy, understanding, and utmost customer service with facts, logic, and fairness. It was direct, simple, succinct, and phrased to highlight our brand values while addressing the issue in a logical yet sensitive way.   We also tapped our influencer partners to subtly and indirectly share their positive experiences with our brand so we could counter the negative content being shared online.  Result : We got the results we worked for through proper communication and a positive and strategic campaign. The irate client agreed to have a dialogue with us. She apologized to us, and we reaffirmed our commitment to delivering quality service to all. We assured her that she can reach out to us anytime regarding her purchases and that we’d gladly accommodate her requests whenever possible. She also retracted her negative statements in her vlog and urged her followers to keep supporting our brand.

What Are Good Outcomes of Problem Solving?

Whenever you answer interview questions about problem solving or share examples of problem solving in a cover letter, you want to be sure you’re sharing a positive outcome.

Below are good outcomes of problem solving:

  • Saving the company time or money
  • Making the company money
  • Pleasing/keeping a customer
  • Obtaining new customers
  • Solving a safety issue
  • Solving a staffing/scheduling issue
  • Solving a logistical issue
  • Solving a company hiring issue
  • Solving a technical/software issue
  • Making a process more efficient and faster for the company
  • Creating a new business process to make the company more profitable
  • Improving the company’s brand/image/reputation
  • Getting the company positive reviews from customers/clients

Every employer wants to make more money, save money, and save time. If you can assess your problem solving experience and think about how you’ve helped past employers in those three areas, then that’s a great start. That’s where I recommend you begin looking for stories of times you had to solve problems.

Tips to Improve Your Problem Solving Skills

Throughout your career, you’re going to get hired for better jobs and earn more money if you can show employers that you’re a problem solver. 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.

Next, 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 get better at researching and analyzing a situation, but also how you can get better at communicating, deciding 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.

If you practice the tips above, you’ll be ready to share detailed, impressive stories and problem solving examples that will make hiring managers want to offer you the job. Every employer appreciates a problem solver, whether solving problems is a requirement listed on the job description or not. And you never know which hiring manager or interviewer will ask you about a time you solved a problem, so you should always be ready to discuss this when applying for a job.

Related interview questions & answers:

  • How do you handle stress?
  • How do you handle conflict?
  • Tell me about a time when you failed

Biron Clark

About the Author

Read more articles by Biron Clark

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About the author

Angelo Kinicki

Dr. Angelo Kinicki is an award winning professor, author, and consultant. He is a Professor of Management and is the recipient of the Weatherup/Overby Chair in Leadership at Arizona State University, (http://wpcarey.asu.edu/directory/stafffaculty.cfm). He also is a Dean's Council of 100 Distinguished Scholar at the W. P. Carey School of Business. He joined the faculty in 1982, the year he received his doctorate in business administration from Kent State University. His primary research interests include leadership, organizational culture, organizational change and multilevel issues associated with organizational effectiveness. Angelo has published over 90 articles in a variety of academic journals and is co-author of seven textbooks (21 including revisions) that are used by hundreds of universities around the world. Several of his books have been translated into multiple languages.

Angelo is a busy international consultant and is a principal at Kinicki and Associates. Inc.,(http://kinicki.com/) a management consulting firm that works with top management teams to create organizational change aimed at increasing organizational effectiveness and profitability. He has worked with many Fortune 500 firms as well as numerous entrepreneurial organizations in diverse industries. His expertise includes facilitating strategic/operational planning sessions, diagnosing the causes of organizational and work-unit problems, conducting organizational culture interventions, implementing performance management systems, designing and implementing performance appraisal systems, developing and administering surveys to assess employee attitudes, and leading management/executive education programs. He developed a 3600 leadership feedback instrument called the Performance Management Leadership Survey (PMLS) that is used by companies throughout the United States and Europe.

Angelo also is the recipient of several teaching awards from Arizona State University, including the John W. Teets Outstanding Graduate Teacher Award (2009-2010), the Outstanding Teaching Award--MBA and Master's Program (2007-2008), the John W. Teets Outstanding Graduate Teacher Award (2004-2005), the Graduate Teaching Excellence Award (1998-1999), the Continuing Education Teaching Excellence Award (1991-1992), and the Undergraduate Teaching Excellence Award (1987-1988).

Angelo is an award winning researcher. He has received several research awards, including a best research paper award from the Organizational Behavior (OB) division of the Academy of Management, the All Time Best Reviewer Award (June 1996 - June 1999) and the Excellent Reviewer Award (1997-1998) from the Academy of Management Journal. Angelo also was selected to serve on the editorial review boards for the Academy of Management Journal, Personnel Psychology, the Journal of Management, and the Journal of Vocational Behavior. Professionally, Angelo has been an active member of the Academy of Management, including service as a representative at large for the Organizational Behavior (OB) division, member of the Best Paper Award committee for both the OB and Human Resources (HR) divisions, chair of the committee to select the best publication in the Academy of Management Journal, and program committee reviewer for the OB and HR divisions.

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The 7 step method for Practical Problem Solving skills & the 10 most common mistakes to avoid

Updated: Sep 13, 2023

A 7 step process for Practical Problem Solving

Why do you need a Practical Problem Solving method?

Practical Problem Solving models are often shared online BUT the pitfalls are rarely well explained. In this blog we’ll be drawing on our own painful experience gained over 25 years, working across the world with hundreds of companies to illuminate those pitfalls. Here are the top 10 pitfalls as a list, scroll down for tips on how to avoid each.

Too big a problem

Looking in the wrong place

Brainstorming alone

Having a loose focus

Getting hung up on your fishbone

Switching between brain sides

Being rooted to the spot

Changing too much at once

Spending money too early

Not having a Plan to Check against

The Practical Problem Solving (PPS) model we learned and successfully applied from working with Toyota group, has 7 steps. We’ll show you each of those steps and the most common pitfall at each step.

We’ll even “open the kimono” and tell you about our personal biggest practical problem solving failure - more of that later. At the end we’ll share 3 secrets to help you to turbo charge your Practical Problem Solving

The initial question, as ever, has to be “Why do we need a method for Problem Solving?”

There are three main reasons

1) Containment

We’re generally okay at containment when a problem happens, at mopping up

2) Short-term countermeasure

We're not bad at coming up with a short-term countermeasure (solution) but

3) Recurrence Prevention

Most manufacturers aren't particularly strong on recurrence prevention - they don't get to the root cause

A common problem is people jumping to conclusions based on previous experiences, leading to the wrong conclusions because something is different to last time.

A Practical Problem Solving method

So, here's the Practical Problem Solving method, showing the 7 steps.

An image of a 7 step Practical Problem Solving method

You can see that it's a funnel shape reflecting the fact that we're going from a large area, vaguely grasped and explained, down to a really focused problem that we've solved.

The 7 steps to our Practical Problem Solving method

The seven steps are:

1) “Grasp the current condition”

Understand what's going on and find your tight focus point

2) “Locate process causing the problem”

That's the process where it's caused not where it's found in in your physical process

3) “Investigate”

Using two tools often here, and for the next couple of steps - 5 why and fishbone

4) “Identify the probable causes”

Where we narrow down from our fishbone into what we think are the most likely causes – one, two or three of them and have a look at each in depth

5) “Identify the root cause”

What we as a team believe, through go-look-see observation and experimentation, is the root cause

6) “Countermeasure”

Try solutions, one at a time

7) “Confirm”

Using our PDCA cycle to make sure that we've got rid of the problem

Note the two things on the right of the funnel to look at. Firstly, it’s very important to protect the customer early and stop bad material or other problems flowing out to them. Secondly, you’ll see halfway down, after you've done a bit of investigation that you're ready to set a target: A “What?” by “How much?” by “When?”

A Problem Solving example: Fizzy drink canning factory

At Sempai we use a fizzy drink canning factory example as a Problem Solving example, along with our training materials, to help our clients start-to-finish through this process on their own shopfloor. Get in touch if you’d like us to help you this way. I’ll reference the fizzy drink can below.

An image of a Practical Problem Solving example

10 Pitfalls in the 7 step Practical Problem Solving method

Let’s go back to the funnel model to look at the Problem Solving pitfalls

Step 1) - “Grasp the current condition” - Pitfall

The key pitfall here is NOT having a tight focus, having too broad a problem to try to solve. This is where our fizzy drink cans come in. On the picture below, having done some Data Analysis and using 80/20 thinking , if we just go after ‘dents’ our focus is too broad as there are actually 3 types of dents - 30 of one type, 8 of a second and 4 of a third. We’d pick the defect with 30 instances as it’s the highest (occasionally there are defects that have a lower frequency but cost more per defect).

An image of a dented can as a Practical Problem Solving example in manufacturing

Problem Solving is hard enough to do without trying to mix up and unpick a heap of variables affecting 3 different problems. If you try and do them all at once, you won't manage it. Picking 1 of the 3 to solve is good “Problem Framing”.

Step 2) - “Locate process causing the problem” - Pitfall

Critically, here you're not looking for the process where you FOUND the problem. It's where you identify that it's being CREATED. There's a very big difference between treating a symptom and a cause. Be careful that you’re not looking in the wrong spot.

Step 3) - “Investigate” - Pitfalls

This is often the area of biggest weakness, apart from Problem Framing in Step 1 above. When it comes to problem solving there are two major tools - Fishbone (aka Ishikawa diagram) and the 5 Whys. There are others, these are just the most common and useful.

The Fishbone and 5 Whys can be used together or they can be used independently. You don't always have to use both, but I'll come back to that later.

The first pitfall, in the Investigate step, is to brainstorm alone if you use a fishbone. Doing this, you only get one narrow set of ideas and experience. Involving other functions, like Maintenance for breakdowns, or Quality engineers for defects brings in other experts. Never, ever, forget to include the most important expert of all – your Operator. They know the process better than anyone as they live with it for 40 hours a week.

The second pitfall on this step is to remember is that you need a tight scope, a very tight problem well described. Not “dents” but a type of “dent” on a certain flavour of fizzy drink (if it’s made down a different line to the others!)

Step 4) - “Identify the probable causes” - Pitfalls

If you’ve used a Fishbone, you’ll then have maybe 20-40 post-it notes with possible causes on. You now go back over all of your post-it notes to identify the most probable causes. Don't get hung up trying to work out, scientifically, which are the right ones to pursue. Just agree as a team and pick the top two or three you believe. Then pursue them one at a time.

Also, don't try to critique AS YOU brainstorm as switching from one side of your brain (creative) to the other (analytical) gets the worst of both worlds. It’s mentally jarring and ideas won’t flow. Finish the brainstorm first, then critique the ideas respectfully.

Step 5) - “Identify the root cause” - Pitfall

Here you take your “probable causes” one a time and pursue the 5 whys – checking at each why stage whether what you’re suggesting is true. The pitfall here is simply staying in a training room or being rooted to the spot in the factory where you’re doing the Problem Solving. You can’t do either Step 4 or 5 in a training room or without looking at the process close up. Go-look-see and confirm on the shop floor.

Step 6) - “Countermeasure” - Pitfall

It’s really important to countermeasure (put a fix in place) for one thing at a time, otherwise you don't know which change got you the result - it's just a mix of variables. Don’t spend money too early, try solutions with old or scrapped materials, capital is scarce, thinking is free.

Step 7) - “Confirm” - Pitfall

Confirm is where we use our Plan Do Check Act (PDCA) cycle to see if our countermeasure has worked. To know if it has, you need something to compare against. So, at Plan stage, quantify the result you expect. For example, say after Step 4 “Investigate” that you have enough information to set a target. If you set that target at “20% reduction in dents in orange cans vertically across the bottom rim” and you only achieve 5% after countermeasure, you know that you’ve missed something.

Knowing when your Practical Problem Solving has worked!

There are two ways to check whether your countermeasures work:

You can recreate the problem at will

If you can turn it on and off you’ve sorted it

Data Analysis

When you do your daily or weekly Data Analysis, this specific problem doesn't occur again or is greatly reduced.

3 secrets to turbocharge your practical problem solving

We promised earlier to tell you about our biggest ever failure. That was 20 years ago when being trained by a Japanese sensei. We locked a team, for two days, in a room with a vaguely defined problem and created the world's biggest fishbone.

A fishbone that we guessed and speculated about and didn't go to the shop floor enough, to grasp and confirm. That combination of a bad focus and too many guesses meant it was a waste of time.

As promised, here’s a bonus of 3 secrets to turbocharge your practical problem solving:

Secret 1: Speed

If you can get to a problem fast it's like a fresh crime scene for a detective. It's warm, there's a body, there's a smoking gun and blood on the floor. It's easy to crack. If you get there late it's like a cold case

Secret 2: You don't always need a Fishbone

Some people love a fishbone but, to a man with a hammer, everything looks like a nail. We only use it in certain circumstances; like if we can't recreate a defect or it looks as though there are multiple variables involved, or if there's a benefit to getting a team around it.

Secret 3: Avoid problems altogether!

This is the closest we’ll get to a silver bullet. Train your people to be able to spot abnormality early, get your shop floor organised through your 5s and standardised work, so that you can react when things start to go wrong, rather than when there's a problem.

Number 3) is so powerful we've built a module dedicated to avoiding problems in SempaiGuide, our digital lean toolkit for manufacturers. Check out the demo here .

That’s the major pitfalls covered. One last piece of advice is to follow the steps, use data and verify on the gemba at every stage. Otherwise, you’re just guessing. To accompany this article, we’ve created this video on our YouTube channel

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  • Published: 10 April 2024

A hybrid particle swarm optimization algorithm for solving engineering problem

  • Jinwei Qiao 1 , 2 ,
  • Guangyuan Wang 1 , 2 ,
  • Zhi Yang 1 , 2 ,
  • Xiaochuan Luo 3 ,
  • Jun Chen 1 , 2 ,
  • Kan Li 4 &
  • Pengbo Liu 1 , 2  

Scientific Reports volume  14 , Article number:  8357 ( 2024 ) Cite this article

Metrics details

  • Computational science
  • Mechanical engineering

To overcome the disadvantages of premature convergence and easy trapping into local optimum solutions, this paper proposes an improved particle swarm optimization algorithm (named NDWPSO algorithm) based on multiple hybrid strategies. Firstly, the elite opposition-based learning method is utilized to initialize the particle position matrix. Secondly, the dynamic inertial weight parameters are given to improve the global search speed in the early iterative phase. Thirdly, a new local optimal jump-out strategy is proposed to overcome the "premature" problem. Finally, the algorithm applies the spiral shrinkage search strategy from the whale optimization algorithm (WOA) and the Differential Evolution (DE) mutation strategy in the later iteration to accelerate the convergence speed. The NDWPSO is further compared with other 8 well-known nature-inspired algorithms (3 PSO variants and 5 other intelligent algorithms) on 23 benchmark test functions and three practical engineering problems. Simulation results prove that the NDWPSO algorithm obtains better results for all 49 sets of data than the other 3 PSO variants. Compared with 5 other intelligent algorithms, the NDWPSO obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( \({f}_{1}-{f}_{13}\) ) with 3 kinds of dimensional spaces (Dim = 30,50,100) and 80% of the best optimal solutions for 10 fixed-multimodal benchmark functions. Also, the best design solutions are obtained by NDWPSO for all 3 classical practical engineering problems.


In the ever-changing society, new optimization problems arise every moment, and they are distributed in various fields, such as automation control 1 , statistical physics 2 , security prevention and temperature prediction 3 , artificial intelligence 4 , and telecommunication technology 5 . Faced with a constant stream of practical engineering optimization problems, traditional solution methods gradually lose their efficiency and convenience, making it more and more expensive to solve the problems. Therefore, researchers have developed many metaheuristic algorithms and successfully applied them to the solution of optimization problems. Among them, Particle swarm optimization (PSO) algorithm 6 is one of the most widely used swarm intelligence algorithms.

However, the basic PSO has a simple operating principle and solves problems with high efficiency and good computational performance, but it suffers from the disadvantages of easily trapping in local optima and premature convergence. To improve the overall performance of the particle swarm algorithm, an improved particle swarm optimization algorithm is proposed by the multiple hybrid strategy in this paper. The improved PSO incorporates the search ideas of other intelligent algorithms (DE, WOA), so the improved algorithm proposed in this paper is named NDWPSO. The main improvement schemes are divided into the following 4 points: Firstly, a strategy of elite opposition-based learning is introduced into the particle population position initialization. A high-quality initialization matrix of population position can improve the convergence speed of the algorithm. Secondly, a dynamic weight methodology is adopted for the acceleration coefficients by combining the iterative map and linearly transformed method. This method utilizes the chaotic nature of the mapping function, the fast convergence capability of the dynamic weighting scheme, and the time-varying property of the acceleration coefficients. Thus, the global search and local search of the algorithm are balanced and the global search speed of the population is improved. Thirdly, a determination mechanism is set up to detect whether the algorithm falls into a local optimum. When the algorithm is “premature”, the population resets 40% of the position information to overcome the local optimum. Finally, the spiral shrinking mechanism combined with the DE/best/2 position mutation is used in the later iteration, which further improves the solution accuracy.

The structure of the paper is given as follows: Sect. “ Particle swarm optimization (PSO) ” describes the principle of the particle swarm algorithm. Section “ Improved particle swarm optimization algorithm ” shows the detailed improvement strategy and a comparison experiment of inertia weight is set up for the proposed NDWPSO. Section “ Experiment and discussion ” includes the experimental and result discussion sections on the performance of the improved algorithm. Section “ Conclusions and future works ” summarizes the main findings of this study.

Literature review

This section reviews some metaheuristic algorithms and other improved PSO algorithms. A simple discussion about recently proposed research studies is given.

Metaheuristic algorithms

A series of metaheuristic algorithms have been proposed in recent years by using various innovative approaches. For instance, Lin et al. 7 proposed a novel artificial bee colony algorithm (ABCLGII) in 2018 and compared ABCLGII with other outstanding ABC variants on 52 frequently used test functions. Abed-alguni et al. 8 proposed an exploratory cuckoo search (ECS) algorithm in 2021 and carried out several experiments to investigate the performance of ECS by 14 benchmark functions. Brajević 9 presented a novel shuffle-based artificial bee colony (SB-ABC) algorithm for solving integer programming and minimax problems in 2021. The experiments are tested on 7 integer programming problems and 10 minimax problems. In 2022, Khan et al. 10 proposed a non-deterministic meta-heuristic algorithm called Non-linear Activated Beetle Antennae Search (NABAS) for a non-convex tax-aware portfolio selection problem. Brajević et al. 11 proposed a hybridization of the sine cosine algorithm (HSCA) in 2022 to solve 15 complex structural and mechanical engineering design optimization problems. Abed-Alguni et al. 12 proposed an improved Salp Swarm Algorithm (ISSA) in 2022 for single-objective continuous optimization problems. A set of 14 standard benchmark functions was used to evaluate the performance of ISSA. In 2023, Nadimi et al. 13 proposed a binary starling murmuration optimization (BSMO) to select the effective features from different important diseases. In the same year, Nadimi et al. 14 systematically reviewed the last 5 years' developments of WOA and made a critical analysis of those WOA variants. In 2024, Fatahi et al. 15 proposed an Improved Binary Quantum-based Avian Navigation Optimizer Algorithm (IBQANA) for the Feature Subset Selection problem in the medical area. Experimental evaluation on 12 medical datasets demonstrates that IBQANA outperforms 7 established algorithms. Abed-alguni et al. 16 proposed an Improved Binary DJaya Algorithm (IBJA) to solve the Feature Selection problem in 2024. The IBJA’s performance was compared against 4 ML classifiers and 10 efficient optimization algorithms.

Improved PSO algorithms

Many researchers have constantly proposed some improved PSO algorithms to solve engineering problems in different fields. For instance, Yeh 17 proposed an improved particle swarm algorithm, which combines a new self-boundary search and a bivariate update mechanism, to solve the reliability redundancy allocation problem (RRAP) problem. Solomon et al. 18 designed a collaborative multi-group particle swarm algorithm with high parallelism that was used to test the adaptability of Graphics Processing Units (GPUs) in distributed computing environments. Mukhopadhyay and Banerjee 19 proposed a chaotic multi-group particle swarm optimization (CMS-PSO) to estimate the unknown parameters of an autonomous chaotic laser system. Duan et al. 20 designed an improved particle swarm algorithm with nonlinear adjustment of inertia weights to improve the coupling accuracy between laser diodes and single-mode fibers. Sun et al. 21 proposed a particle swarm optimization algorithm combined with non-Gaussian stochastic distribution for the optimal design of wind turbine blades. Based on a multiple swarm scheme, Liu et al. 22 proposed an improved particle swarm optimization algorithm to predict the temperatures of steel billets for the reheating furnace. In 2022, Gad 23 analyzed the existing 2140 papers on Swarm Intelligence between 2017 and 2019 and pointed out that the PSO algorithm still needs further research. In general, the improved methods can be classified into four categories:

Adjusting the distribution of algorithm parameters. Feng et al. 24 used a nonlinear adaptive method on inertia weights to balance local and global search and introduced asynchronously varying acceleration coefficients.

Changing the updating formula of the particle swarm position. Both papers 25 and 26 used chaotic mapping functions to update the inertia weight parameters and combined them with a dynamic weighting strategy to update the particle swarm positions. This improved approach enables the particle swarm algorithm to be equipped with fast convergence of performance.

The initialization of the swarm. Alsaidy and Abbood proposed 27 a hybrid task scheduling algorithm that replaced the random initialization of the meta-heuristic algorithm with the heuristic algorithms MCT-PSO and LJFP-PSO.

Combining with other intelligent algorithms: Liu et al. 28 introduced the differential evolution (DE) algorithm into PSO to increase the particle swarm as diversity and reduce the probability of the population falling into local optimum.

Particle swarm optimization (PSO)

The particle swarm optimization algorithm is a population intelligence algorithm for solving continuous and discrete optimization problems. It originated from the social behavior of individuals in bird and fish flocks 6 . The core of the PSO algorithm is that an individual particle identifies potential solutions by flight in a defined constraint space adjusts its exploration direction to approach the global optimal solution based on the shared information among the group, and finally solves the optimization problem. Each particle \(i\) includes two attributes: velocity vector \({V}_{i}=\left[{v}_{i1},{v}_{i2},{v}_{i3},{...,v}_{ij},{...,v}_{iD},\right]\) and position vector \({X}_{i}=[{x}_{i1},{x}_{i2},{x}_{i3},...,{x}_{ij},...,{x}_{iD}]\) . The velocity vector is used to modify the motion path of the swarm; the position vector represents a potential solution for the optimization problem. Here, \(j=\mathrm{1,2},\dots ,D\) , \(D\) represents the dimension of the constraint space. The equations for updating the velocity and position of the particle swarm are shown in Eqs. ( 1 ) and ( 2 ).

Here \({Pbest}_{i}^{k}\) represents the previous optimal position of the particle \(i\) , and \({Gbest}\) is the optimal position discovered by the whole population. \(i=\mathrm{1,2},\dots ,n\) , \(n\) denotes the size of the particle swarm. \({c}_{1}\) and \({c}_{2}\) are the acceleration constants, which are used to adjust the search step of the particle 29 . \({r}_{1}\) and \({r}_{2}\) are two random uniform values distributed in the range \([\mathrm{0,1}]\) , which are used to improve the randomness of the particle search. \(\omega\) inertia weight parameter, which is used to adjust the scale of the search range of the particle swarm 30 . The basic PSO sets the inertia weight parameter as a time-varying parameter to balance global exploration and local seeking. The updated equation of the inertia weight parameter is given as follows:

where \({\omega }_{max}\) and \({\omega }_{min}\) represent the upper and lower limits of the range of inertia weight parameter. \(k\) and \(Mk\) are the current iteration and maximum iteration.

Improved particle swarm optimization algorithm

According to the no free lunch theory 31 , it is known that no algorithm can solve every practical problem with high quality and efficiency for increasingly complex and diverse optimization problems. In this section, several improvement strategies are proposed to improve the search efficiency and overcome this shortcoming of the basic PSO algorithm.

Improvement strategies

The optimization strategies of the improved PSO algorithm are shown as follows:

The inertia weight parameter is updated by an improved chaotic variables method instead of a linear decreasing strategy. Chaotic mapping performs the whole search at a higher speed and is more resistant to falling into local optimal than the probability-dependent random search 32 . However, the population may result in that particles can easily fly out of the global optimum boundary. To ensure that the population can converge to the global optimum, an improved Iterative mapping is adopted and shown as follows:

Here \({\omega }_{k}\) is the inertia weight parameter in the iteration \(k\) , \(b\) is the control parameter in the range \([\mathrm{0,1}]\) .

The acceleration coefficients are updated by the linear transformation. \({c}_{1}\) and \({c}_{2}\) represent the influential coefficients of the particles by their own and population information, respectively. To improve the search performance of the population, \({c}_{1}\) and \({c}_{2}\) are changed from fixed values to time-varying parameter parameters, that are updated by linear transformation with the number of iterations:

where \({c}_{max}\) and \({c}_{min}\) are the maximum and minimum values of acceleration coefficients, respectively.

The initialization scheme is determined by elite opposition-based learning . The high-quality initial population will accelerate the solution speed of the algorithm and improve the accuracy of the optimal solution. Thus, the elite backward learning strategy 33 is introduced to generate the position matrix of the initial population. Suppose the elite individual of the population is \({X}=[{x}_{1},{x}_{2},{x}_{3},...,{x}_{j},...,{x}_{D}]\) , and the elite opposition-based solution of \(X\) is \({X}_{o}=[{x}_{{\text{o}}1},{x}_{{\text{o}}2},{x}_{{\text{o}}3},...,{x}_{oj},...,{x}_{oD}]\) . The formula for the elite opposition-based solution is as follows:

where \({k}_{r}\) is the random value in the range \((\mathrm{0,1})\) . \({ux}_{oij}\) and \({lx}_{oij}\) are dynamic boundaries of the elite opposition-based solution in \(j\) dimensional variables. The advantage of dynamic boundary is to reduce the exploration space of particles, which is beneficial to the convergence of the algorithm. When the elite opposition-based solution is out of bounds, the out-of-bounds processing is performed. The equation is given as follows:

After calculating the fitness function values of the elite solution and the elite opposition-based solution, respectively, \(n\) high quality solutions were selected to form a new initial population position matrix.

The position updating Eq. ( 2 ) is modified based on the strategy of dynamic weight. To improve the speed of the global search of the population, the strategy of dynamic weight from the artificial bee colony algorithm 34 is introduced to enhance the computational performance. The new position updating equation is shown as follows:

Here \(\rho\) is the random value in the range \((\mathrm{0,1})\) . \(\psi\) represents the acceleration coefficient and \({\omega }{\prime}\) is the dynamic weight coefficient. The updated equations of the above parameters are as follows:

where \(f(i)\) denotes the fitness function value of individual particle \(i\) and u is the average of the population fitness function values in the current iteration. The Eqs. ( 11 , 12 ) are introduced into the position updating equation. And they can attract the particle towards positions of the best-so-far solution in the search space.

New local optimal jump-out strategy is added for escaping from the local optimal. When the value of the fitness function for the population optimal particles does not change in M iterations, the algorithm determines that the population falls into a local optimal. The scheme in which the population jumps out of the local optimum is to reset the position information of the 40% of individuals within the population, in other words, to randomly generate the position vector in the search space. M is set to 5% of the maximum number of iterations.

New spiral update search strategy is added after the local optimal jump-out strategy. Since the whale optimization algorithm (WOA) was good at exploring the local search space 35 , the spiral update search strategy in the WOA 36 is introduced to update the position of the particles after the swarm jumps out of local optimal. The equation for the spiral update is as follows:

Here \(D=\left|{x}_{i}\left(k\right)-Gbest\right|\) denotes the distance between the particle itself and the global optimal solution so far. \(B\) is the constant that defines the shape of the logarithmic spiral. \(l\) is the random value in \([-\mathrm{1,1}]\) . \(l\) represents the distance between the newly generated particle and the global optimal position, \(l=-1\) means the closest distance, while \(l=1\) means the farthest distance, and the meaning of this parameter can be directly observed by Fig.  1 .

figure 1

Spiral updating position.

The DE/best/2 mutation strategy is introduced to form the mutant particle. 4 individuals in the population are randomly selected that differ from the current particle, then the vector difference between them is rescaled, and the difference vector is combined with the global optimal position to form the mutant particle. The equation for mutation of particle position is shown as follows:

where \({x}^{*}\) is the mutated particle, \(F\) is the scale factor of mutation, \({r}_{1}\) , \({r}_{2}\) , \({r}_{3}\) , \({r}_{4}\) are random integer values in \((0,n]\) and not equal to \(i\) , respectively. Specific particles are selected for mutation with the screening conditions as follows:

where \(Cr\) represents the probability of mutation, \(rand\left(\mathrm{0,1}\right)\) is a random number in \(\left(\mathrm{0,1}\right)\) , and \({i}_{rand}\) is a random integer value in \((0,n]\) .

The improved PSO incorporates the search ideas of other intelligent algorithms (DE, WOA), so the improved algorithm proposed in this paper is named NDWPSO. The pseudo-code for the NDWPSO algorithm is given as follows:

figure a

The main procedure of NDWPSO.

Comparing the distribution of inertia weight parameters

There are several improved PSO algorithms (such as CDWPSO 25 , and SDWPSO 26 ) that adopt the dynamic weighted particle position update strategy as their improvement strategy. The updated equations of the CDWPSO and the SDWPSO algorithm for the inertia weight parameters are given as follows:

where \({\text{A}}\) is a value in \((\mathrm{0,1}]\) . \({r}_{max}\) and \({r}_{min}\) are the upper and lower limits of the fluctuation range of the inertia weight parameters, \(k\) is the current number of algorithm iterations, and \(Mk\) denotes the maximum number of iterations.

Considering that the update method of inertia weight parameters by our proposed NDWPSO is comparable to the CDWPSO, and SDWPSO, a comparison experiment for the distribution of inertia weight parameters is set up in this section. The maximum number of iterations in the experiment is \(Mk=500\) . The distributions of CDWPSO, SDWPSO, and NDWPSO inertia weights are shown sequentially in Fig.  2 .

figure 2

The inertial weight distribution of CDWPSO, SDWPSO, and NDWPSO.

In Fig.  2 , the inertia weight value of CDWPSO is a random value in (0,1]. It may make individual particles fly out of the range in the late iteration of the algorithm. Similarly, the inertia weight value of SDWPSO is a value that tends to zero infinitely, so that the swarm no longer can fly in the search space, making the algorithm extremely easy to fall into the local optimal value. On the other hand, the distribution of the inertia weights of the NDWPSO forms a gentle slope by two curves. Thus, the swarm can faster lock the global optimum range in the early iterations and locate the global optimal more precisely in the late iterations. The reason is that the inertia weight values between two adjacent iterations are inversely proportional to each other. Besides, the time-varying part of the inertial weight within NDWPSO is designed to reduce the chaos characteristic of the parameters. The inertia weight value of NDWPSO avoids the disadvantages of the above two schemes, so its design is more reasonable.

Experiment and discussion

In this section, three experiments are set up to evaluate the performance of NDWPSO: (1) the experiment of 23 classical functions 37 between NDWPSO and three particle swarm algorithms (PSO 6 , CDWPSO 25 , SDWPSO 26 ); (2) the experiment of benchmark test functions between NDWPSO and other intelligent algorithms (Whale Optimization Algorithm (WOA) 36 , Harris Hawk Algorithm (HHO) 38 , Gray Wolf Optimization Algorithm (GWO) 39 , Archimedes Algorithm (AOA) 40 , Equilibrium Optimizer (EO) 41 and Differential Evolution (DE) 42 ); (3) the experiment for solving three real engineering problems (welded beam design 43 , pressure vessel design 44 , and three-bar truss design 38 ). All experiments are run on a computer with Intel i5-11400F GPU, 2.60 GHz, 16 GB RAM, and the code is written with MATLAB R2017b.

The benchmark test functions are 23 classical functions, which consist of indefinite unimodal (F1–F7), indefinite dimensional multimodal functions (F8–F13), and fixed-dimensional multimodal functions (F14–F23). The unimodal benchmark function is used to evaluate the global search performance of different algorithms, while the multimodal benchmark function reflects the ability of the algorithm to escape from the local optimal. The mathematical equations of the benchmark functions are shown and found as Supplementary Tables S1 – S3 online.

Experiments on benchmark functions between NDWPSO, and other PSO variants

The purpose of the experiment is to show the performance advantages of the NDWPSO algorithm. Here, the dimensions and corresponding population sizes of 13 benchmark functions (7 unimodal and 6 multimodal) are set to (30, 40), (50, 70), and (100, 130). The population size of 10 fixed multimodal functions is set to 40. Each algorithm is repeated 30 times independently, and the maximum number of iterations is 200. The performance of the algorithm is measured by the mean and the standard deviation (SD) of the results for different benchmark functions. The parameters of the NDWPSO are set as: \({[{\omega }_{min},\omega }_{max}]=[\mathrm{0.4,0.9}]\) , \(\left[{c}_{max},{c}_{min}\right]=\left[\mathrm{2.5,1.5}\right],{V}_{max}=0.1,b={e}^{-50}, M=0.05\times Mk, B=1,F=0.7, Cr=0.9.\) And, \(A={\omega }_{max}\) for CDWPSO; \({[r}_{max},{r}_{min}]=[\mathrm{4,0}]\) for SDWPSO.

Besides, the experimental data are retained to two decimal places, but some experimental data will increase the number of retained data to pursue more accuracy in comparison. The best results in each group of experiments will be displayed in bold font. The experimental data is set to 0 if the value is below 10 –323 . The experimental parameter settings in this paper are different from the references (PSO 6 , CDWPSO 25 , SDWPSO 26 , so the final experimental data differ from the ones within the reference.

As shown in Tables 1 and 2 , the NDWPSO algorithm obtains better results for all 49 sets of data than other PSO variants, which include not only 13 indefinite-dimensional benchmark functions and 10 fixed-multimodal benchmark functions. Remarkably, the SDWPSO algorithm obtains the same accuracy of calculation as NDWPSO for both unimodal functions f 1 –f 4 and multimodal functions f 9 –f 11 . The solution accuracy of NDWPSO is higher than that of other PSO variants for fixed-multimodal benchmark functions f 14 -f 23 . The conclusion can be drawn that the NDWPSO has excellent global search capability, local search capability, and the capability for escaping the local optimal.

In addition, the convergence curves of the 23 benchmark functions are shown in Figs. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 . The NDWPSO algorithm has a faster convergence speed in the early stage of the search for processing functions f1-f6, f8-f14, f16, f17, and finds the global optimal solution with a smaller number of iterations. In the remaining benchmark function experiments, the NDWPSO algorithm shows no outstanding performance for convergence speed in the early iterations. There are two reasons of no outstanding performance in the early iterations. On one hand, the fixed-multimodal benchmark function has many disturbances and local optimal solutions in the whole search space. on the other hand, the initialization scheme based on elite opposition-based learning is still stochastic, which leads to the initial position far from the global optimal solution. The inertia weight based on chaotic mapping and the strategy of spiral updating can significantly improve the convergence speed and computational accuracy of the algorithm in the late search stage. Finally, the NDWPSO algorithm can find better solutions than other algorithms in the middle and late stages of the search.

figure 3

Evolution curve of NDWPSO and other PSO algorithms for f1 (Dim = 30,50,100).

figure 4

Evolution curve of NDWPSO and other PSO algorithms for f2 (Dim = 30,50,100).

figure 5

Evolution curve of NDWPSO and other PSO algorithms for f3 (Dim = 30,50,100).

figure 6

Evolution curve of NDWPSO and other PSO algorithms for f4 (Dim = 30,50,100).

figure 7

Evolution curve of NDWPSO and other PSO algorithms for f5 (Dim = 30,50,100).

figure 8

Evolution curve of NDWPSO and other PSO algorithms for f6 (Dim = 30,50,100).

figure 9

Evolution curve of NDWPSO and other PSO algorithms for f7 (Dim = 30,50,100).

figure 10

Evolution curve of NDWPSO and other PSO algorithms for f8 (Dim = 30,50,100).

figure 11

Evolution curve of NDWPSO and other PSO algorithms for f9 (Dim = 30,50,100).

figure 12

Evolution curve of NDWPSO and other PSO algorithms for f10 (Dim = 30,50,100).

figure 13

Evolution curve of NDWPSO and other PSO algorithms for f11(Dim = 30,50,100).

figure 14

Evolution curve of NDWPSO and other PSO algorithms for f12 (Dim = 30,50,100).

figure 15

Evolution curve of NDWPSO and other PSO algorithms for f13 (Dim = 30,50,100).

figure 16

Evolution curve of NDWPSO and other PSO algorithms for f14, f15, f16.

figure 17

Evolution curve of NDWPSO and other PSO algorithms for f17, f18, f19.

figure 18

Evolution curve of NDWPSO and other PSO algorithms for f20, f21, f22.

figure 19

Evolution curve of NDWPSO and other PSO algorithms for f23.

To evaluate the performance of different PSO algorithms, a statistical test is conducted. Due to the stochastic nature of the meta-heuristics, it is not enough to compare algorithms based on only the mean and standard deviation values. The optimization results cannot be assumed to obey the normal distribution; thus, it is necessary to judge whether the results of the algorithms differ from each other in a statistically significant way. Here, the Wilcoxon non-parametric statistical test 45 is used to obtain a parameter called p -value to verify whether two sets of solutions are different to a statistically significant extent or not. Generally, it is considered that p  ≤ 0.5 can be considered as a statistically significant superiority of the results. The p -values calculated in Wilcoxon’s rank-sum test comparing NDWPSO and other PSO algorithms are listed in Table  3 for all benchmark functions. The p -values in Table  3 additionally present the superiority of the NDWPSO because all of the p -values are much smaller than 0.5.

In general, the NDWPSO has the fastest convergence rate when finding the global optimum from Figs. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 , and thus we can conclude that the NDWPSO is superior to the other PSO variants during the process of optimization.

Comparison experiments between NDWPSO and other intelligent algorithms

Experiments are conducted to compare NDWPSO with several other intelligent algorithms (WOA, HHO, GWO, AOA, EO and DE). The experimental object is 23 benchmark functions, and the experimental parameters of the NDWPSO algorithm are set the same as in Experiment 4.1. The maximum number of iterations of the experiment is increased to 2000 to fully demonstrate the performance of each algorithm. Each algorithm is repeated 30 times individually. The parameters of the relevant intelligent algorithms in the experiments are set as shown in Table 4 . To ensure the fairness of the algorithm comparison, all parameters are concerning the original parameters in the relevant algorithm literature. The experimental results are shown in Tables 5 , 6 , 7 and 8 and Figs. 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 and 36 .

figure 20

Evolution curve of NDWPSO and other algorithms for f1 (Dim = 30,50,100).

figure 21

Evolution curve of NDWPSO and other algorithms for f2 (Dim = 30,50,100).

figure 22

Evolution curve of NDWPSO and other algorithms for f3(Dim = 30,50,100).

figure 23

Evolution curve of NDWPSO and other algorithms for f4 (Dim = 30,50,100).

figure 24

Evolution curve of NDWPSO and other algorithms for f5 (Dim = 30,50,100).

figure 25

Evolution curve of NDWPSO and other algorithms for f6 (Dim = 30,50,100).

figure 26

Evolution curve of NDWPSO and other algorithms for f7 (Dim = 30,50,100).

figure 27

Evolution curve of NDWPSO and other algorithms for f8 (Dim = 30,50,100).

figure 28

Evolution curve of NDWPSO and other algorithms for f9(Dim = 30,50,100).

figure 29

Evolution curve of NDWPSO and other algorithms for f10 (Dim = 30,50,100).

figure 30

Evolution curve of NDWPSO and other algorithms for f11 (Dim = 30,50,100).

figure 31

Evolution curve of NDWPSO and other algorithms for f12 (Dim = 30,50,100).

figure 32

Evolution curve of NDWPSO and other algorithms for f13 (Dim = 30,50,100).

figure 33

Evolution curve of NDWPSO and other algorithms for f14, f15, f16.

figure 34

Evolution curve of NDWPSO and other algorithms for f17, f18, f19.

figure 35

Evolution curve of NDWPSO and other algorithms for f20, f21, f22.

figure 36

Evolution curve of NDWPSO and other algorithms for f23.

The experimental data of NDWPSO and other intelligent algorithms for handling 30, 50, and 100-dimensional benchmark functions ( \({f}_{1}-{f}_{13}\) ) are recorded in Tables 8 , 9 and 10 , respectively. The comparison data of fixed-multimodal benchmark tests ( \({f}_{14}-{f}_{23}\) ) are recorded in Table 11 . According to the data in Tables 5 , 6 and 7 , the NDWPSO algorithm obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( \({f}_{1}-{f}_{13}\) ) in the search space of three dimensions (Dim = 30, 50, 100), respectively. In Table 8 , the NDWPSO algorithm obtains 80% of the optimal solutions in 10 fixed-multimodal benchmark functions.

The convergence curves of each algorithm are shown in Figs. 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 and 36 . The NDWPSO algorithm demonstrates two convergence behaviors when calculating the benchmark functions in 30, 50, and 100-dimensional search spaces. The first behavior is the fast convergence of NDWPSO with a small number of iterations at the beginning of the search. The reason is that the Iterative-mapping strategy and the position update scheme of dynamic weighting are used in the NDWPSO algorithm. This scheme can quickly target the region in the search space where the global optimum is located, and then precisely lock the optimal solution. When NDWPSO processes the functions \({f}_{1}-{f}_{4}\) , and \({f}_{9}-{f}_{11}\) , the behavior can be reflected in the convergence trend of their corresponding curves. The second behavior is that NDWPSO gradually improves the convergence accuracy and rapidly approaches the global optimal in the middle and late stages of the iteration. The NDWPSO algorithm fails to converge quickly in the early iterations, which is possible to prevent the swarm from falling into a local optimal. The behavior can be demonstrated by the convergence trend of the curves when NDWPSO handles the functions \({f}_{6}\) , \({f}_{12}\) , and \({f}_{13}\) , and it also shows that the NDWPSO algorithm has an excellent ability of local search.

Combining the experimental data with the convergence curves, it is concluded that the NDWPSO algorithm has a faster convergence speed, so the effectiveness and global convergence of the NDWPSO algorithm are more outstanding than other intelligent algorithms.

Experiments on classical engineering problems

Three constrained classical engineering design problems (welded beam design, pressure vessel design 43 , and three-bar truss design 38 ) are used to evaluate the NDWPSO algorithm. The experiments are the NDWPSO algorithm and 5 other intelligent algorithms (WOA 36 , HHO, GWO, AOA, EO 41 ). Each algorithm is provided with the maximum number of iterations and population size ( \({\text{Mk}}=500,\mathrm{ n}=40\) ), and then repeats 30 times, independently. The parameters of the algorithms are set the same as in Table 4 . The experimental results of three engineering design problems are recorded in Tables 9 , 10 and 11 in turn. The result data is the average value of the solved data.

Welded beam design

The target of the welded beam design problem is to find the optimal manufacturing cost for the welded beam with the constraints, as shown in Fig.  37 . The constraints are the thickness of the weld seam ( \({\text{h}}\) ), the length of the clamped bar ( \({\text{l}}\) ), the height of the bar ( \({\text{t}}\) ) and the thickness of the bar ( \({\text{b}}\) ). The mathematical formulation of the optimization problem is given as follows:

figure 37

Welded beam design.

In Table 9 , the NDWPSO, GWO, and EO algorithms obtain the best optimal cost. Besides, the standard deviation (SD) of t NDWPSO is the lowest, which means it has very good results in solving the welded beam design problem.

Pressure vessel design

Kannan and Kramer 43 proposed the pressure vessel design problem as shown in Fig.  38 to minimize the total cost, including the cost of material, forming, and welding. There are four design optimized objects: the thickness of the shell \({T}_{s}\) ; the thickness of the head \({T}_{h}\) ; the inner radius \({\text{R}}\) ; the length of the cylindrical section without considering the head \({\text{L}}\) . The problem includes the objective function and constraints as follows:

figure 38

Pressure vessel design.

The results in Table 10 show that the NDWPSO algorithm obtains the lowest optimal cost with the same constraints and has the lowest standard deviation compared with other algorithms, which again proves the good performance of NDWPSO in terms of solution accuracy.

Three-bar truss design

This structural design problem 44 is one of the most widely-used case studies as shown in Fig.  39 . There are two main design parameters: the area of the bar1 and 3 ( \({A}_{1}={A}_{3}\) ) and area of bar 2 ( \({A}_{2}\) ). The objective is to minimize the weight of the truss. This problem is subject to several constraints as well: stress, deflection, and buckling constraints. The problem is formulated as follows:

figure 39

Three-bar truss design.

From Table 11 , NDWPSO obtains the best design solution in this engineering problem and has the smallest standard deviation of the result data. In summary, the NDWPSO can reveal very competitive results compared to other intelligent algorithms.

Conclusions and future works

An improved algorithm named NDWPSO is proposed to enhance the solving speed and improve the computational accuracy at the same time. The improved NDWPSO algorithm incorporates the search ideas of other intelligent algorithms (DE, WOA). Besides, we also proposed some new hybrid strategies to adjust the distribution of algorithm parameters (such as the inertia weight parameter, the acceleration coefficients, the initialization scheme, the position updating equation, and so on).

23 classical benchmark functions: indefinite unimodal (f1-f7), indefinite multimodal (f8-f13), and fixed-dimensional multimodal(f14-f23) are applied to evaluate the effective line and feasibility of the NDWPSO algorithm. Firstly, NDWPSO is compared with PSO, CDWPSO, and SDWPSO. The simulation results can prove the exploitative, exploratory, and local optima avoidance of NDWPSO. Secondly, the NDWPSO algorithm is compared with 5 other intelligent algorithms (WOA, HHO, GWO, AOA, EO). The NDWPSO algorithm also has better performance than other intelligent algorithms. Finally, 3 classical engineering problems are applied to prove that the NDWPSO algorithm shows superior results compared to other algorithms for the constrained engineering optimization problems.

Although the proposed NDWPSO is superior in many computation aspects, there are still some limitations and further improvements are needed. The NDWPSO performs a limit initialize on each particle by the strategy of “elite opposition-based learning”, it takes more computation time before speed update. Besides, the” local optimal jump-out” strategy also brings some random process. How to reduce the random process and how to improve the limit initialize efficiency are the issues that need to be further discussed. In addition, in future work, researchers will try to apply the NDWPSO algorithm to wider fields to solve more complex and diverse optimization problems.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

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This work was supported by Key R&D plan of Shandong Province, China (2021CXGC010207, 2023CXGC01020); First batch of talent research projects of Qilu University of Technology in 2023 (2023RCKY116); Introduction of urgently needed talent projects in Key Supported Regions of Shandong Province; Key Projects of Natural Science Foundation of Shandong Province (ZR2020ME116); the Innovation Ability Improvement Project for Technology-based Small- and Medium-sized Enterprises of Shandong Province (2022TSGC2051, 2023TSGC0024, 2023TSGC0931); National Key R&D Program of China (2019YFB1705002), LiaoNing Revitalization Talents Program (XLYC2002041) and Young Innovative Talents Introduction & Cultivation Program for Colleges and Universities of Shandong Province (Granted by Department of Education of Shandong Province, Sub-Title: Innovative Research Team of High Performance Integrated Device).

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a practical problem solving


Integrating inquiry and mathematical modeling when teaching a common topic in lower secondary school: an istem approach provisionally accepted.

  • 1 Hong Kong Baptist University, Hong Kong, SAR China

The final, formatted version of the article will be published soon.

The world has been increasingly shaped by Science, Technology, Engineering and Mathematics (STEM). This has resulted in educational systems across the globe implementing STEM education. To reap maximum benefits, researchers are now advocating for the integration of STEM domains. In recent studies, the integration of science and mathematics has become increasingly popular. The domains are much more suitable for integration because of their fields of application and their mutual approach towards problem-solving. However, there is little empirical evidence to drive the development of a practical model for classroom implementation. This study aims to cover that gap through integrating mathematics and science concepts when teaching a common topic to two classes of Form 1 (13-14 years) students. A mathematics and a science teacher went through two cycles of lesson study, integrating and teaching the concept of density. Results show a strong synergy between the BSCS 5E instructional model of inquiry and mathematical modeling; hence the methodological approaches can be used to integrate common topics like density. Further, teacher collaboration, teacher immersion in the iSTEM practices, teacher's knowledge, and skills of the other subject and an in-depth understanding of a problem and its contextualization, are variables that can be capitalized on to enhance the teacher's capacity to implement innovative and integrated STEM programs effectively.

Keywords: iSTEM1, Inquiry2, mathematical modeling3, Integration model4, Science5. Mathematics6, Density7

Received: 26 Jan 2024; Accepted: 10 Apr 2024.

Copyright: © 2024 Manunure and Leung. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Mr. Kevin Manunure, Hong Kong Baptist University, Kowloon, Hong Kong, SAR China

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  8. Problem-Solving Strategies and Obstacles

    Problem-solving involves taking certain steps and using psychological strategies. Learn problem-solving techniques and how to overcome obstacles to solving problems. ... Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code. Soc Personal Psychol Compass. 2021;15(2):e12579. doi ...

  9. What is Problem Solving? Steps, Process & Techniques

    Problem Solving Resources. You can also search articles, case studies, and publications for problem solving resources. Books. Innovative Business Management Using TRIZ. Introduction To 8D Problem Solving: Including Practical Applications and Examples. The Quality Toolbox. Root Cause Analysis: The Core of Problem Solving and Corrective Action ...

  10. Learn Toyota's 8 Step Practical Problem Solving Methodology

    https://gembaacademy.com | The Gemba Academy Practical Problem Solving course explains the exact 8 step problem solving process used by these lean exemplars ...

  11. 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.

  12. The Problem-Solving Process

    The Problem-Solving Process. Problem-solving is an important part of planning and decision-making. The process has much in common with the decision-making process, and in the case of complex decisions, can form part of the process itself. We face and solve problems every day, in a variety of guises and of differing complexity.

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

    The problem-solving process typically includes the following steps: Identify the issue: Recognize the problem that needs to be solved. Analyze the situation: Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present. Generate potential solutions: Brainstorm a list of possible ...

  14. 8 Consistent Behaviors Of Practically Perfect Problem Solvers

    Problem Solving rated significantly higher for women (T-Value 2.432, Sig. 0.015). ... these behaviors teach us some essential requirements for practical problem-solving that we ALL need to improve!

  15. 12 Approaches To Problem-Solving for Every Situation

    Brainstorm options to solve the problem. Select an option. Create an implementation plan. Execute the plan and monitor the results. Evaluate the solution. Read more: Effective Problem Solving Steps in the Workplace. 2. Collaborative. This approach involves including multiple people in the problem-solving process.

  16. How To Solve The Problems? Practical Problem Solving Skills

    Practical Problem Solving Skills. Figure out what kind of problem you're trying to solve. Make sure you understand the problem. This may require reading and re-reading the issue several times and brainstorming possible solutions. Come up with a solution. Try out different methods to see which one works best for you.

  17. Everyday Life Developing Practical Problem Solving Skills ...

    Practical problem-solving skills are necessary for making decisions, managing stress, and staying organized. Here is a guide to developing functional problem-solving skills for everyday life.

  18. Do You Understand the Problem You're Trying to Solve?

    To Solve Your Toughest Problems, Change the Problems You Solve. In this episode, you'll learn how to reframe tough problems by asking questions that reveal all the factors and assumptions that ...

  19. Organizational Behavior: A Practical, Problem-Solving Approach

    Kinicki, Organizational Behavior 3e develops students' problem-solving skills through a unique, consistent, integrated 3-step Problem-Solving Approach that lets them immediately put research-based knowledge into practice in their personal and professional lives. Organizational Behavior 3e explicitly addresses OB implications for students' core career readiness skills, showing how OB provides ...

  20. Organizational Behavior: A Practical, Problem-Solving Approach

    Do you want to learn how to apply organizational behavior concepts and theories to real-world situations? Organizational Behavior: A Practical, Problem-Solving Approach is a comprehensive and engaging ebook that covers the latest research and best practices in this fascinating field. You will discover how to enhance your personal effectiveness, team performance, and organizational outcomes ...

  21. 26 Good Examples of Problem Solving (Interview Answers)

    Examples of Problem Solving Scenarios 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 ...

  22. A Practical Guide for Policy Analysis: The Eightfold Path to More

    " A Practical Guide for Policy Analysis is the essential text to introduce health policy students to the practice of policy analysis. The authors offer a persuasive argument for why defining the problem is the fundamental yet challenging first step of policy analysis; this lesson is critical for health policy, where issue rhetoric abounds.

  23. Organizational Behavior: A Practical, Problem-Solving Approach

    Kinicki, Organizational Behavior 3e develops students' problem-solving skills through a unique, consistent, integrated 3-step Problem-Solving Approach that lets them immediately put research-based knowledge into practice in their personal and professional lives.

  24. Enhancing Spatial Problem-Solving Through Data-Driven Methods: A

    Enhancing Spatial Problem-Solving Through Data-Driven Methods: A Practical Approach Utilizing Immersive Technologies and Multimodal Physical Tracking. Author: Henner Bendig. Faculty for Information and Communication / Usability Lab, Flensburg University of Applied Sciences, Germany.

  25. The 7 step method for Practical Problem Solving skills & the 10 most

    Step 3) - "Investigate" - Pitfalls. This is often the area of biggest weakness, apart from Problem Framing in Step 1 above. When it comes to problem solving there are two major tools - Fishbone (aka Ishikawa diagram) and the 5 Whys. There are others, these are just the most common and useful.

  26. A hybrid particle swarm optimization algorithm for solving ...

    According to the no free lunch theory 31, it is known that no algorithm can solve every practical problem with high quality and efficiency for increasingly complex and diverse optimization ...

  27. Frontiers

    The domains are much more suitable for integration because of their fields of application and their mutual approach towards problem-solving. However, there is little empirical evidence to drive the development of a practical model for classroom implementation.

  28. Congress wants border 'solutions' but ignores these practical fixes

    Problem-solving should be a higher priority than exaggerating border problems and demanding undefined "solutions." Ed Kissam is a trustee of the Werner-Kohnstamm Family Giving Fund.