“Do I really have no access to transport?”
“Can I really not afford to buy a car?”
The questions have to be asked, is the stated goal the real goal? Are the barriers actual barriers and what other barriers are there? In this example, the problem at first seems to be:
Goal | Barrier 1 | Barrier 2 |
Take the job | No transport | No money |
This is also a good opportunity to look at the relationships between the key elements of the problem . For example, in the 'Job-Transport-Money' problem, there are strong connections between all the elements.
By looking at all the relationships between the key elements, it appears that the problem is more about how to achieve any one of three things, i.e. job, transport or money, because solving one of these sub-problems will, in turn, solve the others.
This example shows how useful it is to have a representation of a problem.
Visual and verbal representations include:
Chain diagrams are powerful and simple ways of representing problems using a combination of diagrams and words. The elements of the problem are set out in words, usually placed in boxes, and positioned in different places on a sheet of paper, using lines to represent the relationship between them.
Chain Diagrams are the simplest type, where all the elements are presented in an ordered list, each element being connected only with the elements immediately before and after it. Chain diagrams usually represent a sequence of events needed for a solution. A simple example of a chain diagram illustrates the job-transport-money example as as follows:
TAKE JOB |
Flow charts allow for inclusion of branches, folds, loops, decision points and many other relationships between the elements. In practice, flow charts can be quite complicated and there are many conventions as to how they are drawn but, generally, simple diagrams are easier to understand and aid in 'seeing' the problem more readily.
Tree diagrams and their close relative, the Decision Tree , are ways of representing situations where there are a number of choices or different possible events to be considered. These types of diagram are particularly useful for considering all the possible consequences of solutions.
Remember that the aim of a visualisation is to make the problem clearer. Over-complicated diagrams will just confuse and make the problem harder to understand.
Listing the elements of a problem can also help to represent priorities, order and sequences in the problem. Goals can be listed in order of importance and barriers in order of difficulty. Separate lists could be made of related goals or barriers. The barriers could be listed in the order in which they need to be solved, or elements of the problem classified in a number of different ways. There are many possibilities, but the aim is to provide a clearer picture of the problem.
1. Get money |
A visual representation and a working definition together makes it far easier to describe a problem to others. Many problems will be far more complex than the example used here.
Continue to: Investigating Ideas and Possible Solutions
See also: Social Problem Solving Project Management Risk Management
Updated: Jan 24, 2023
prob·lem-solv·ing noun -the process of finding solutions to difficult or complex issues. It sounds so simple, doesn’t it? But in reality problem-solving is hard. It's almost always more complex than it seems. That's why problem-solving can be so frustrating sometimes. You can feel like you’re spinning your wheels, arguing in circles, or just failing to find answers that actually work. And when you've got a group working on a problem, it can get even muddier …differences of opinions, viewpoints colored by different backgrounds, history, life experiences, you name it. We’re all looking at life and work from different angles, and that often means disagreement. Sometimes sharp disagreement. That human element, figuring out how to take ourselves out of the equation and make solid, fact-based decisions , is precisely why there’s been so much written on problem-solving. Which creates its own set of problems. Whose method is best? How can you possibly sift through them all? Are we to have one person complete the entire problem-solving process by themselves or rely on a larger team to find answers to our most vexing challenges in the workplace ? Today, we’re going to make sense of it all. We’ll take a close look at nine top problem-solving methods. Then we’ll grab the best elements of all of them to give you a process that will have your team solving problems faster, with better results , and maybe with less sharp disagreement. Ready to dive in? Let’s go!
While there are loads of methods to choose from, we are going to focus on nine of the more common ones. You can use some of these problem-solving techniques reactively to solve a known issue or proactively to find more efficient or effective ways of performing tasks. If you want to explore other methods, check out this resource here . A helpful bit of advice here is to reassure people that you aren’t here to identify the person that caused the problem . You’re working to surface the issue, solve it and make sure it doesn’t happen again, regardless of the person working on the process. It can’t be understated how important it is to continually reassure people of this so that you get unfiltered access to information. Without this, people will often hide things to protect themselves . After all, nobody wants to look bad, do they? With that said, let’s get started...
Alex Osborn coined the term “Creative Problem Solving” in the 1940s with this simple four-step process:
Clarify : Explore the vision, gather data, and formulate questions.
Ideate : This stage should use brainstorming to generate divergent thinking and ideas rather than the random ideas normally associated with brainstorming.
Develop : Formulate solutions as part of an overall plan.
Implement : Put the plan into practice and communicate it to all parties.
Source: http://www.davidcooperrider.com/ai-process/ This method seeks, first and foremost, to identify the strengths in people and organizations and play to that “positive core” rather than focus our energies on improving weaknesses . It starts with an “affirmative topic,” followed by the “positive core (strengths).” Then this method delves into the following stages:
Discovery (fact-finding)
Dream (visioning the future)
Design (strategic purpose)
Destiny (continuous improvement)
3. “FIVE WHYS” METHOD
This method simply suggests that we ask “Why” at least five times during our review of the problem and in search of a fix. This helps us dig deeper to find the the true reason for the problem, or the root cause. Now, this doesn’t mean we just keeping asking the same question five times. Once we get an answer to our first “why”, we ask why to that answer until we get to five “whys”.
Using the “five whys” is part of the “Analyze” phase of Six Sigma but can be used with or without the full Six Sigma process.
Review this simple Wikipedia example of the 5 Whys in action:
The vehicle will not start. (the problem)
Why? - The battery is dead. (First why)
Why? - The alternator is not functioning. (Second why)
Why? - The alternator belt has broken. (Third why)
Why? - The alternator belt was well beyond its useful service life and not replaced. (Fourth why)
Why? - The vehicle was not maintained according to the recommended service schedule. (Fifth why, a root cause)
While many people have at least heard of Lean or Six Sigma, do we know what it is? Like many problem-solving processes, it has five main steps to follow.
Define : Clearly laying out the problem and soliciting feedback from those who are customers of the process is necessary to starting off on the right foot.
Measure : Quantifying the current state of the problem is a key to measuring how well the fix performed once it was implemented.
Analyze : Finding out the root cause of the problem (see number 5 “Root Cause Analysis” below) is one of the hardest and least explored steps of Six Sigma.
Improve : Crafting, executing, and testing the solution for measureable improvement is key. What doesn’t get implemented and measured really won’t make a difference.
Control : Sustaining the fix through a monitoring plan will ensure things continue to stay on track rather than being a short-lived solution.
Compared to other methods, you’ll more often find this technique in a reactive problem-solving mode, but it is helpful nonetheless. Put simply, it requires a persistent approach to finding the highest-level cause, since most reasons you’ll uncover for a problem don’t tell the whole story.
Most of the time, there are many factors that contributed to an issue. The main reason is often shrouded in either intentional or unintentional secrecy. Taking the time to drill down to the root of the issue is key to truly solving the problem.
6. DEMING-SHEWHART CYCLE: PLAN-DO-CHECK-ACT (PDCA)
Named for W. Edwards Deming and Walter A. Shewhart, this model follows a four-step process:
Plan: Establish goals and objectives at the outset to gain agreement. It’s best to start on a small scale in order to test results and get a quick win.
Do: This step is all about the implementation and execution of the solution.
Check: Study and compare actual to expected results. Chart this data to identify trends.
Act/Adjust: If the check phase showed different results, then adjust accordingly. If worse than expected, then try another fix. If the same or better than expected, then use that as the new baseline for future improvements.
7. 8D PROBLEM-SOLVING
While this is named “8D” for eight disciplines, there are actually nine , because the first is listed as step zero. Each of the disciplines represents a phase of this process. Its aim is to implement a quick fix in the short term while working on a more permanent solution with no recurring issues.
Prepare and Plan : Collecting initial information from the team and preparing your approach to the process is a necessary first step.
Form a Team : Select a cross-functional team of people, one leader to run meetings and the process, and one champion/sponsor who will be the final decision-maker.
Describe the Problem : Using inductive and deductive reasoning approaches, lay out the precise issue to be corrected.
Interim Containment Action : Determine if an interim solution needs to be implemented or if it can wait until the final fix is firmed up. If necessary, the interim action is usually removed once the permanent solution is ready for implementation.
Root Cause Analysis and Escape Point : Finding the root of the issue and where in the process it could’ve been found but was not will help identify where and why the issue happened.
Permanent Corrective Action : Incorporating key criteria into the solution, including requirements and wants, will help ensure buy-in from the team and your champion.
Implement and Validate the Permanent Corrective Action : Measuring results from the fix implemented validates it or sends the team back to the drawing board to identity a more robust solution.
Prevent Recurrence : Updating work procedure documents and regular communication about the changes are important to keep old habits in check.
Closure and Team Celebration : Taking time to praise the team for their efforts in resolving the problem acknowledges the part each person played and offers a way to move forward.
The US Army has been solving problems for more than a couple of centuries , so why not take a look at the problem-solving process they’ve refined over many years? They recommend this five step process:
Identify the Problem : Take time to understand the situation and define a scope and limitations before moving forward.
Gather Information : Uncover facts, assumptions, and opinions about the problem, and challenge them to get to the truth.
Develop Screening and Evaluation Criteria :
Five screening items should be questioned. Is it feasible, acceptable, distinguishable, and complete?
Evaluation criteria should have these 5 elements: short title, definition, unit of measure, benchmark, and formula.
Generate, Analyze, and Compare Possible Solutions : Most fixes are analyzed, but do you compare yours to one another as a final vetting method?
Choose a Solution and Implement : Put the fix into practice and follow up to ensure it is being followed consistently and having the desired effect.
Tim Hurson introduced this model in 2007 with his book, Think Better. It consists of the following six actions.
Ask "What is going on?" : Define the impact of the problem and the aim of its solution.
Ask "What is success?" : Spell out the expected outcome, what should not be in fix, values to be considered, and how things will be evaluated.
Ask "What is the question?" : Tailor questions to the problem type. Valuable resources can be wasted asking questions that aren’t truly relevant to the issue.
Generate answers : Prioritize answers that are the most relevant to solutions, without excluding any suggestion to present to the decision-makers.
Forge the solution : Refine the raw list of prioritized fixes, looking for ways to combine them for a more powerful solution or eliminate fixes that don’t fit the evaluation criteria.
Align resources: Identify resources, team, and stakeholders needed to implement and maintain the solution.
Now that we’ve reviewed a number of problem-solving methods, we’ve compiled the various steps into a straightforward, yet in-depth, s tep-by-step process to use the best of all methods.
1. DIG DEEP: IDENTIFY, DEFINE, AND CLARIFY THE ISSUE
“Elementary, my dear Watson,” you might say.
This is true, but we often forget the fundamentals before trying to solve a problem. So take some time to gain understanding of critical stakeholder’s viewpoints to clarify the problem and cement consensus behind what the issue really is.
Sometimes it feels like you’re on the same page, but minor misunderstandings mean you’re not really in full agreement.. It’s better to take the time to drill down on an issue before you get too far into solving a problem that may not be the exact problem . Which leads us to…
This part of the process involves identifying these three items :
What happened?
Why did it happen?
What process do we need to employ to significantly reduce the chances of it happening again ?
You’ll usually need to sort through a series of situations to find the primary cause. So be careful not to stop at the first cause you uncover . Dig further into the situation to expose the root of the issue. We don’t want to install a solution that only fixes a surface-level issue and not the root. T here are typically three types of causes :
Physical: Perhaps a part failed due to poor design or manufacturing.
Human error: A person either did something wrong or didn’t do what needed to be done.
Organizational: This one is mostly about a system, process, or policy that contributed to the error .
When searching for the root cause, it is important to ensure people that you aren’t there to assign blame to a person but rather identify the problem so a fix can prevent future issues.
3. PRODUCE A VARIETY OF SOLUTION OPTIONS
So far, you’ve approached the problem as a data scientist, searching for clues to the real issue. Now, it’s important to keep your eyes and ears open, in case you run across a fix suggested by one of those involved in the process failure. Because they are closest to the problem, they will often have an idea of how to fix things. In other cases, they may be too close, and unable to see how the process could change.
The bottom line is to solicit solution ideas from a variety of sources , both close to and far away from the process you’re trying to improve.
You just never know where the top fix might come from!
4. FULLY EVALUATE AND SELECT PLANNED FIX(ES)
Evaluating solutions to a defined problem can be tricky since each one will have cost, political, or other factors associated with it. Running each fix through a filter of cost and impact is a vital step toward identifying a solid solution and hopefully settling on the one with the highest impact and low or acceptable cost.
Categorizing each solution in one of these four categoriescan help teams sift through them:
High Cost/Low Impact: Implement these last, if at all, since t hey are expensive and won’t move the needle much .
Low Cost/Low Impact: These are cheap, but you won’t get much impact.
High Cost/High Impact: These can be used but should be second to the next category.
Low Cost/High Impact: Getting a solid “bang for your buck” is what these fixes are all about. Start with these first .
5. DOCUMENT THE FINAL SOLUTION AND WHAT SUCCESS LOOKS LIKE
Formalize a document that all interested parties (front-line staff, supervisors, leadership, etc.) agree to follow. This will go a long way towards making sure everyone fully understands what the new process looks like, as well as what success will look like .
While it might seem tedious, try to be overly descriptive in the explanation of the solution and how success will be achieved. This is usually necessary to gain full buy-in and commitment to continually following the solution. We often assume certain things that others may not know unless we are more explicit with our communications.
6. SUCCESSFULLY SELL AND EXECUTE THE FIX
Arriving at this stage in the process only to forget to consistently apply the solution would be a waste of time, yet many organizations fall down in the execution phase . Part of making sure that doesn’t happen is to communicate the fix and ask for questions multiple times until all parties have a solid grasp on what is now required of them.
One often-overlooked element of this is the politics involved in gaining approval for your solution. Knowing and anticipating objections of those in senior or key leadership positions is central to gaining buy-in before fix implementation.
7. RINSE AND REPEAT: EVALUATE, MONITOR, AND FOLLOW UP
Next, doing check-ins with the new process will ensure that the solution is working (or identity if further reforms are necessary) . You’ll also see if the measure of predefined success has been attained (or is making progress in that regard).
Without regularly monitoring the fix, you can only gauge the success or failure of the solution by speculation and hearsay. And without hard data to review, most people will tell their own version of the story.
8. COLLABORATIVE CONTINGENCIES, ITERATION, AND COURSE CORRECTION
Going into any problem-solving process, we should take note that we will not be done once the solution is implemented (or even if it seems to be working better at the moment). Any part of any process will always be subject to the need for future iterations and course corrections . To think otherwise would be either foolish or naive.
There might need to be slight, moderate, or wholesale changes to the solution previously implemented as new information is gained, new technologies are discovered, etc.
Want to test your problem-solving skills?
Take a look at these twenty case study scenario exercises to see how well you can come up with solutions to these problems.
Still have a desire to discover more about solving problems?
Check out these 14 articles and books...
1. THE LEAN SIX SIGMA POCKET TOOLBOOK: A QUICK REFERENCE GUIDE TO NEARLY 100 TOOLS FOR IMPROVING QUALITY AND SPEED
This book is like a Bible for Lean Six Sigma , all in a pocket-sized package.
2. SOME SAGE PROBLEM SOLVING ADVICE
The American Society for Quality has a short article on how it’s important to focus on the problem before searching for a solution.
3. THE SECRET TO BETTER PROBLEM SOLVING: HARVARD BUSINESS REVIEW
Wondering if you are solving the right problems? Check out this Harvard Business Review article.
Looking for a fun and easy problem-solving book that was written by a McKinsey consultant? Take a look!
5. THE BASICS OF CREATIVE PROBLEM SOLVING – CPS
If you want a deeper dive into the seven steps of Creative Problem Solving , see this article.
6. APPRECIATIVE INQUIRY : A POSITIVE REVOLUTION IN CHANGE
Appreciative Inquiry has been proven effective in organizations ranging from Roadway Express and British Airways to the United Nations and the United States Navy. Review this book to join the positive revolution.
7. PROBLEM SOLVING: NINE CASE STUDIES AND LESSONS LEARNED
The Seattle Police Department has put together nine case studies that you can practice solving . While they are about police work, they have practical application in the sleuthing of work-related problems.
8. ROOT CAUSE ANALYSIS : THE CORE OF PROBLEM SOLVING AND CORRECTIVE ACTION
Need a resource to delve further into Root Cause Analysis? Look no further than this book for answers to your most vexing questions .
9. SOLVING BUSINESS PROBLEMS : THE CASE OF POOR FRANK
This solid case study illustrates the complexities of solving problems in business.
10. THE 8-DISCIPLINES PROBLEM SOLVING METHODOLOGY
Learn all about the “8Ds” with this concise primer.
11. THE PROBLEM-SOLVING PROCESS THAT PREVENTS GROUPTHINK HBR
Need to reduce groupthink in your organization’s problem-solving process ? Check out this article from the Harvard Business Review.
12. THINK BETTER : AN INNOVATOR'S GUIDE TO PRODUCTIVE THINKING
Tim Hurson details his own Productive Thinking Model at great length in this book from the author.
13. 5 STEPS TO SOLVING THE PROBLEMS WITH YOUR PROBLEM SOLVING INC MAGAZINE
This simple five-step process will help you break down the problem, analyze it, prioritize solutions, and sell them internally.
14. CRITICAL THINKING : A BEGINNER'S GUIDE TO CRITICAL THINKING, BETTER DECISION MAKING, AND PROBLEM SOLVING!
There's a lot to take in here, but following some of these methods are sure to improve your problem-solving process. However, if you really want to take problem-solving to the next level, InitiativeOne can come alongside your team to help you solve problems much faster than you ever have before.
There are several parts to this leadership transformation process provided by InitiativeOne, including a personal profile assessment, cognitive learning, group sessions with real-world challenges, personal discovery, and a toolkit to empower leaders to perform at their best.
There are really only two things stopping good teams from being great. One is how they make decisions and two is how they solve problems. Contact us today to grow your team’s leadership performance by making decisions and solving problems more swiftly than ever before!
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Definition:
Problem Solving is the process of identifying, analyzing, and finding effective solutions to complex issues or challenges.
Key Steps in Problem Solving:
Skills and Qualities for Effective Problem Solving:
August 17, 2023 by MindManager Blog
Whether you run a business, manage a team, or work in an industry where change is the norm, it may feel like something is always going wrong. Thankfully, becoming proficient in the problem solving process can alleviate a great deal of the stress that business issues can create.
Understanding the right way to solve problems not only takes the guesswork out of how to deal with difficult, unexpected, or complex situations, it can lead to more effective long-term solutions.
In this article, we’ll walk you through the 5 steps of problem solving, and help you explore a few examples of problem solving scenarios where you can see the problem solving process in action before putting it to work.
When something isn’t working, it’s important to understand what’s at the root of the problem so you can fix it and prevent it from happening again. That’s why resolving difficult or complex issues works best when you apply proven business problem solving tools and techniques – from soft skills, to software.
The problem solving process typically includes:
While skills like active listening, collaboration, and leadership play an important role in problem solving, tools like visual mapping software make it easier to define and share problem solving objectives, play out various solutions, and even put the best fit to work.
Before you can take your first step toward solving a problem, you need to have a clear idea of what the issue is and the outcome you want to achieve by resolving it.
For example, if your company currently manufactures 50 widgets a day, but you’ve started processing orders for 75 widgets a day, you could simply say you have a production deficit.
However, the problem solving process will prove far more valuable if you define the start and end point by clarifying that production is running short by 25 widgets a day, and you need to increase daily production by 50%.
Once you know where you’re at and where you need to end up, these five steps will take you from Point A to Point B:
In practice, you might not hit a home-run with every solution you execute. But the beauty of a repeatable process like problem solving is that you can carry out steps 4 and 5 again by drawing from the brainstorm options you documented during step 2.
The best way to get a sense of how the problem solving process works before you try it for yourself is to work through some simple scenarios.
Here are three examples of how you can apply business problem solving techniques to common workplace challenges.
Building on our original manufacturing example, you determine that your company is consistently short producing 25 widgets a day and needs to increase daily production by 50%.
Since you’d like to gather data and input from both your manufacturing and sales order departments, you schedule a brainstorming session to discover the root cause of the shortage.
After examining four key production areas – machines, materials, methods, and management – you determine the cause of the problem: the material used to manufacture your widgets can only be fed into your equipment once the machinery warms up to a specific temperature for the day.
Your team comes up with three possible solutions.
After weighing the expense of the first two solutions, and conducting some online research, you decide that switching to a comparable but less expensive material that can be worked at a lower temperature is your best option.
You implement your plan, monitor your widget quality and output over the following week, and declare your solution a success when daily production increases by 100%.
Business training is booming and you’ve had to onboard new staff over the past month. Now you learn that several clients have expressed concern about the quality of your recent training sessions.
After speaking with both clients and staff, you discover there are actually two distinct factors contributing to your quality problem:
You could look for a new conference room or re-schedule upcoming training sessions until after your new equipment arrives. But your team collaboratively determines that the best way to mitigate both issues at once is by temporarily renting the high-quality sound and visual system they need.
Using benchmarks that include several weeks of feedback from session attendees, and random session spot-checks you conduct personally, you conclude the solution has worked.
You’ve invested heavily in product marketing, but still can’t meet your sales goals. Specifically, you missed your revenue target by 30% last year and would like to meet that same target this year.
After collecting and examining reams of information from your sales and accounting departments, you sit down with your marketing team to figure out what’s hindering your success in the marketplace.
Determining that your product isn’t competitively priced, you map out two viable solutions.
Since you’re in a hurry for results, you decide to immediately reduce the price of your product and market it accordingly.
When revenue figures for the following quarter show sales have declined even further – and marketing surveys show potential customers are doubting the quality of your product – you revert back to your original pricing, revisit your problem solving process, and implement the market analysis solution instead.
With the valuable information you gain, you finally arrive at just the right product price for your target market and sales begin to pick up. Although you miss your revenue target again this year, you meet it by the second quarter of the following year.
Kickstart your collaborative brainstorming sessions and try MindManager for free today !
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Psychology Spot
All About Psychology
Problem solving is a complex psychological process through which we try to find the best way to overcome an obstacle or face a challenge. Unfortunately, this process is not always linear, but can follow tortuous paths, plunging us into a situation of psychological anguish when we believe that there is no possible solution.
On the other hand, knowing the phases of problem solving will save us a lot of headaches. Providing a coherent structure to the situation that concerns us, and having a common thread that guides us along the way, will help us to put some order in the mental chaos that problems usually generate.
Experience can be a plus or, on the contrary, become an impediment to solving problems. Psychologists from the universities of Hong Kong and Princeton examined how we implement problem-solving strategies by asking a group of people to solve a series of problems with matches.
Participants were presented with a series of linked squares. Each square in the matrix was made up of separate pieces, and people had to remove a certain number of matches while keeping a specified number of squares intact. The interesting thing about these types of problems is that they generally have more than one solution, different strategies can be used and these must change according to the configuration of the matrix, just as it usually happens with life problems.
These researchers found that participants went through two major stages in problem solving. At first they let themselves be carried away by the perceptual characteristics of the problem and began to explore different strategies, some successful and others not.
In a second moment they used the accumulated experience to narrow their options of strategies, focusing on those that were more successful. The problem is that the more the participants trusted their strategic knowledge, the more difficulties they had in solving problems that demanded the application of novel strategies. In practice, they suffered from a kind of functional fixation.
These series of experiments show us that to solve a problem we must keep an open mind because along the way circumstances are likely to change and we need the mental flexibility necessary to change our problem-solving strategies.
1. Identify the problem
It may seem like a truism, but the truth is that identifying the real problem is not as easy as it seems, especially when it comes to a situation that affects us emotionally. In fact, when the problem is too scary or we sense that we do not have the psychological tools to solve it, we usually put into practice defense mechanisms such as displacement that allow us to erase the problematic situation from our conscious mind.
Instead, being able to identify the problem is the first step in finding a solution. Many times that means stopping looking outside for the culprits and searching within, wondering why a situation is particularly bothering or hindering us.
2. Understand the problem
Many times the problem brings with it the seed of the solution. So one of the steps in solving a problem is making sure we understand it. It is not enough to identify the problem, we need to define it. For this we need to analyze it from different perspectives.
For example, if we are trying to carry out a professional project that does not finish taking off, we have to clarify the reasons. Do we need more training? Are we in an overly competitive sector? Do we have enough resources? We need to understand the source of the problem.
Organizing the information available is another crucial step in the problem-solving process. We have to ask ourselves both, what we know about the problem and everything we do not know. Ultimately, the accuracy of the solution will largely depend on the amount of information available.
3. Assume a psychological distance
Most of the major problems in life have the potential to generate an emotional tsunami. However, many times that affective involvement obfuscates and prevents us from thinking clearly. That is why on many occasions one of the most important but least known phases for solving problems consists of moving away from what concerns us. To assume a psychological distance , we can take a few days away from the problematic environment or try to stop thinking about what worries us for a while.
During that time the unconscious mind will continue to work and is likely to generate creative and perfectly valid insights that lead to the solution of the problem. That distance to allow us to overcome the functional fixations that prevent us from thinking outside the box, giving way to a mental restructuring that will allow us to see the problem from another perspective.
4. Find solutions and develop strategies
Each problem is different, so it will require a specific solution. A solution cannot always be reached by insight, so it will be necessary to think of possible alternatives to solve the problem. Synectics , for example, is a problem-solving method that uses creativity to find original solutions.
The next step is to develop a strategy, since solutions that do not materialize in concrete steps are very difficult to implement. Therefore, we must ask ourselves how we are going to implement our solution. In this phase of problem solving it is important to be honest with ourselves and “land” that strategy taking into account our resources and real availability. It is useless to develop a great strategy if we cannot apply it later.
5. Evaluation of progress
Very few problems are solved overnight. These are generally complex situations that we must patiently “unwind” over time. Therefore, another of the phases to solve a problem consists of monitoring the results that we are achieving. This way we make sure that we are on the right track and we are not wasting energy and time uselessly.
In this last stage of problem solving it is important to be able to adapt our expectations. It is difficult for a professional project to take off in the blink of an eye, so we must focus on the small steps that indicate that the solution is paying off. To do this, it is important to sit down and reflect on the impact of the solution from time to time.
We must also bear in mind that circumstances often change, so we may need to make adjustments to our initial solution. This requires great mental flexibility to change course when we realize that the strategy is not as effective as we would like.
Fedor, A. et. Al. (2015) Problem solving stages in the five square problem. Front. Psychol ; 6: 1050.
Louis Lee, N. Y. & Johnson-Laird, P. N. (2013) Strategic changes in problem solving. Journal of Cognitive Psychology ; 25: 165–173.
Gillen, G. (2009) Managing Executive Function Impairments to Optimize Function. Cognitive and Perceptual Rehabilitation ; 245-283.
I am a psychologist and I spent several years writing articles for scientific journals specialized in Health and Psychology. I want to help you create great experiences. Learn more about me .
10/07/2024 By Jennifer Delgado
09/07/2024 By Jennifer Delgado
In Psychology, you get to read about a ton of therapies. It’s mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches.
Yet, you can’t deny the kernel of truth that’s there in all of them. All therapies, despite being different, have one thing in common- they all aim to solve people’s problems. They all aim to equip people with problem-solving strategies to help them deal with their life problems.
Problem-solving is really at the core of everything we do. Throughout our lives, we’re constantly trying to solve one problem or another. When we can’t, all sorts of psychological problems take hold. Getting good at solving problems is a fundamental life skill.
What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists.
To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are:
The problem itself can either be well-defined or ill-defined. A well-defined problem is one where you can clearly see where you are (A), where you want to go (B), and what you need to do to get there (engaging the right operators).
For example, feeling hungry and wanting to eat can be seen as a problem, albeit a simple one for many. Your initial state is hunger (A) and your final state is satisfaction or no hunger (B). Going to the kitchen and finding something to eat is using the right operator.
In contrast, ill-defined or complex problems are those where one or more of the three problem solving stages aren’t clear. For example, if your goal is to bring about world peace, what is it exactly that you want to do?
It’s been rightly said that a problem well-defined is a problem half-solved. Whenever you face an ill-defined problem, the first thing you need to do is get clear about all the three stages.
Often, people will have a decent idea of where they are (A) and where they want to be (B). What they usually get stuck on is finding the right operators.
When people first attempt to solve a problem, i.e. when they first engage their operators, they often have an initial theory of solving the problem. As I mentioned in my article on overcoming challenges for complex problems, this initial theory is often wrong.
But, at the time, it’s usually the result of the best information the individual can gather about the problem. When this initial theory fails, the problem-solver gets more data, and he refines the theory. Eventually, he finds an actual theory i.e. a theory that works. This finally allows him to engage the right operators to move from A to B.
These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are:
When you follow a step-by-step procedure to solve a problem or reach a goal, you’re using an algorithm. If you follow the steps exactly, you’re guaranteed to find the solution. The drawback of this strategy is that it can get cumbersome and time-consuming for large problems.
Say I hand you a 200-page book and ask you to read out to me what’s written on page 100. If you start from page 1 and keep turning the pages, you’ll eventually reach page 100. There’s no question about it. But the process is time-consuming. So instead you use what’s called a heuristic.
Heuristics are rules of thumb that people use to simplify problems. They’re often based on memories from past experiences. They cut down the number of steps needed to solve a problem, but they don’t always guarantee a solution. Heuristics save us time and effort if they work.
You know that page 100 lies in the middle of the book. Instead of starting from page one, you try to open the book in the middle. Of course, you may not hit page 100, but you can get really close with just a couple of tries.
If you open page 90, for instance, you can then algorithmically move from 90 to 100. Thus, you can use a combination of heuristics and algorithms to solve the problem. In real life, we often solve problems like this.
When police are looking for suspects in an investigation, they try to narrow down the problem similarly. Knowing the suspect is 6 feet tall isn’t enough, as there could be thousands of people out there with that height.
Knowing the suspect is 6 feet tall, male, wears glasses, and has blond hair narrows down the problem significantly.
When you have an initial theory to solve a problem, you try it out. If you fail, you refine or change your theory and try again. This is the trial-and-error process of solving problems. Behavioral and cognitive trial and error often go hand in hand, but for many problems, we start with behavioural trial and error until we’re forced to think.
Say you’re in a maze, trying to find your way out. You try one route without giving it much thought and you find it leads to nowhere. Then you try another route and fail again. This is behavioural trial and error because you aren’t putting any thought into your trials. You’re just throwing things at the wall to see what sticks.
This isn’t an ideal strategy but can be useful in situations where it’s impossible to get any information about the problem without doing some trials.
Then, when you have enough information about the problem, you shuffle that information in your mind to find a solution. This is cognitive trial and error or analytical thinking. Behavioral trial and error can take a lot of time, so using cognitive trial and error as much as possible is advisable. You got to sharpen your axe before you cut the tree.
When solving complex problems, people get frustrated after having tried several operators that didn’t work. They abandon their problem and go on with their routine activities. Suddenly, they get a flash of insight that makes them confident they can now solve the problem.
I’ve done an entire article on the underlying mechanics of insight . Long story short, when you take a step back from your problem, it helps you see things in a new light. You make use of associations that were previously unavailable to you.
You get more puzzle pieces to work with and this increases the odds of you finding a path from A to B, i.e. finding operators that work.
No matter what problem-solving strategy you employ, it’s all about finding out what works. Your actual theory tells you what operators will take you from A to B. Complex problems don’t reveal their actual theories easily solely because they are complex.
Therefore, the first step to solving a complex problem is getting as clear as you can about what you’re trying to accomplish- collecting as much information as you can about the problem.
This gives you enough raw materials to formulate an initial theory. We want our initial theory to be as close to an actual theory as possible. This saves time and resources.
Solving a complex problem can mean investing a lot of resources. Therefore, it is recommended you verify your initial theory if you can. I call this pilot problem-solving.
Before businesses invest in making a product, they sometimes distribute free versions to a small sample of potential customers to ensure their target audience will be receptive to the product.
Before making a series of TV episodes, TV show producers often release pilot episodes to figure out whether the show can take off.
Before conducting a large study, researchers do a pilot study to survey a small sample of the population to determine if the study is worth carrying out.
The same ‘testing the waters’ approach needs to be applied to solving any complex problem you might be facing. Is your problem worth investing a lot of resources in? In management, we’re constantly taught about Return On Investment (ROI). The ROI should justify the investment.
If the answer is yes, go ahead and formulate your initial theory based on extensive research. Find a way to verify your initial theory. You need this reassurance that you’re going in the right direction, especially for complex problems that take a long time to solve.
Problem solving boils down to getting your causal thinking right. Finding solutions is all about finding out what works, i.e. finding operators that take you from A to B. To succeed, you need to be confident in your initial theory (If I do X and Y, they’ll lead me to B). You need to be sure that doing X and Y will lead you to B- doing X and Y will cause B.
All obstacles to problem-solving or goal-accomplishing are rooted in faulty causal thinking leading to not engaging the right operators. When your causal thinking is on point, you’ll have no problem engaging the right operators.
As you can imagine, for complex problems, getting our causal thinking right isn’t easy. That’s why we need to formulate an initial theory and refine it over time.
I like to think of problem-solving as the ability to project the present into the past or into the future. When you’re solving problems, you’re basically looking at your present situation and asking yourself two questions:
“What caused this?” (Projecting present into the past)
“What will this cause?” (Projecting present into the future)
The first question is more relevant to problem-solving and the second to goal-accomplishing.
If you find yourself in a mess , you need to answer the “What caused this?” question correctly. For the operators you’re currently engaging to reach your goal, ask yourself, “What will this cause?” If you think they cannot cause B, it’s time to refine your initial theory.
Hi, I’m Hanan Parvez (MA Psychology). I’ve published over 500 articles and authored one book. My work has been featured in Forbes , Business Insider , Reader’s Digest , and Entrepreneur .
Problem solving is a critical skill for success in business – in fact it’s often what you are hired and paid to do. This article explains the five problem solving steps and provides strategies on how to execute each one.
Before we talk about the stages of problem solving, it’s important to have a definition of what it is. Let’s look at the two roots of problem solving — problems and solutions.
Problem – a state of desire for reaching a definite goal from a present condition [1] Solution – the management of a problem in a way that successfully meets the goals set for treating it
[1] Problem solving on Wikipedia
One important call-out is the importance of having a goal. As defined above, the solution may not completely solve problem, but it does meet the goals you establish for treating it–you may not be able to completely resolve the problem (end world hunger), but you can have a goal to help it (reduce the number of starving children by 10%).
With that understanding of problem solving, let’s talk about the steps that can get you there. The five problem solving steps are shown in the chart below:
However this chart as is a little misleading. Not all problems follow these steps linearly, especially for very challenging problems. Instead, you’ll likely move back and forth between the steps as you continue to work on the problem, as shown below:
Let’s explore of these steps in more detail, understanding what it is and the inputs and outputs of each phase.
aka What are you trying to solve? In addition to getting clear on what the problem is, defining the problem also establishes a goal for what you want to achieve.
Input: something is wrong or something could be improved. Output: a clear definition of the opportunity and a goal for fixing it.
aka What are some ways to solve the problem? The goal is to create a list of possible solutions to choose from. The harder the problem, the more solutions you may need.
Input: a goal; research of the problem and possible solutions; imagination. Output: pick-list of possible solutions that would achieve the stated goal.
aka What are you going to do? The ideal solution is effective (it will meet the goal), efficient (is affordable), and has the fewest side effects (limited consequences from implementation).
Input: pick-list of possible solutions; decision-making criteria. Output: decision of what solution you will implement.
aka What are you doing? The implementation of a solution requires planning and execution. It’s often iterative, where the focus should be on short implementation cycles with testing and feedback, not trying to get it “perfect” the first time.
Input: decision; planning; hard work. Output: resolution to the problem.
aka What did you do? To know you successfully solved the problem, it’s important to review what worked, what didn’t and what impact the solution had. It also helps you improve long-term problem solving skills and keeps you from re-inventing the wheel.
Input: resolutions; results of the implementation. Output: insights; case-studies; bullets on your resume.
Once you understand the five steps of problem solving, you can build your skill level in each one. Often we’re naturally good at a couple of the phases and not as naturally good at others. Some people are great at generating ideas but struggle implementing them. Other people have great execution skills but can’t make decisions on which solutions to use. Knowing the different problem solving steps allows you to work on your weak areas, or team-up with someone who’s strengths complement yours.
Want to improve your problem solving skills? Want to perfect the art of problem solving? Check out our training programs or try these 20 problem solving activities to improve creativity .
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very helpful and informative training
Thank you for the information
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I’m writing my 7th edition of Effective Security Management. I would like to use your circular graphic illustration in a new chapter on problem solving. You’re welcome to phone me at — with attribution.
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i love your presentation. It’s very clear. I think I would use it in teaching my class problem solving procedures. Thank you
It is well defined steps, thank you.
these step can you email them to me so I can print them out these steps are very helpful
I like the content of this article, it is really helpful. I would like to know much on how PAID process (i.e. Problem statement, Analyze the problem, Identify likely causes, and Define the actual causes) works in Problem Solving.
very useful information on problem solving process.Thank you for the update.
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It makes sense that a business would want to have an effective problem solving strategy. Things could get bad if they can’t find solutions! I think one of the most important things about problem solving is communication.
Well in our school teacher teach us –
1) problem ldentification 2) structuring the problem 3) looking for possible solutions 4) lmplementation 5) monitoring or seeking feedback 6) decision making
Pleace write about it …
I teach Professional communication (Speech) and I find the 5 steps to problem solving as described here the best method. Your teacher actually uses 4 steps. The Feedback and decision making are follow up to the actual implementation and solving of the problem.
i know the steps of doing some guideline for problem solving
steps are very useful to solve my problem
The steps given are very effective. Thank you for the wonderful presentation of the cycle/steps/procedure and their connections.
I like the steps for problem solving
It is very useful for solving difficult problem i would reccomend it to a friend
this is very interesting because once u have learned you will always differentiate the right from the wrong.
I like the contents of the problem solving steps. informative.
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On this page we discuss "What is problem polving?" under three headings: introduction, four stages of problem solving, and the scientific approach.
Naturally enough, problem solving is about solving problems. And we’ll restrict ourselves to thinking about mathematical problems here even though problem solving in school has a wider goal. When you think about it, the whole aim of education is to equip students to solve problems.
But problem solving also contributes to mathematics itself. Mathematics consists of skills and processes. The skills are things that we are all familiar with. These include the basic arithmetical processes and the algorithms that go with them. They include algebra in all its levels as well as sophisticated areas such as the calculus. This is the side of the subject that is largely represented in the Strands of Number and Algebra, Geometry and Measurement and Statistics.
On the other hand, the processes of mathematics are the ways of using the skills creatively in new situations. Mathematical processes include problem solving, logic and reasoning, and communicating ideas. These are the parts of mathematics that enable us to use the skills in a wide variety of situations.
It is worth starting by distinguishing between the three words "method", "answer" and "solution". By "method" we mean the means used to get an answer. This will generally involve one or more Problem Solving Strategies . On the other hand, we use "answer" to mean a number, quantity or some other entity that the problem is asking for. Finally, a "solution" is the whole process of solving a problem, including the method of obtaining an answer and the answer itself.
method + answer = solution
But how do we do Problem Solving? There are four basic steps. Pólya enunciated these in 1945 but all of them were known and used well before then. Pólya’s four stages of problem solving are listed below.
1. Understand and explore the problem 2. Find a strategy 3. Use the strategy to solve the problem 4. Look back and reflect on the solution.
Although we have listed the four stages in order, for difficult problems it may not be possible to simply move through them consecutively to produce an answer. It is frequently the case that students move backwards and forwards between and across the steps.
You can't solve a problem unless you can first understand it. This requires not only knowing what you have to find but also the key pieces of information that need to be put together to obtain the answer.
Students will often not be able to absorb all the important information of a problem in one go. It will almost always be necessary to read a problem several times, both at the start and while working on it. With younger students it is worth repeating the problem and then asking them to put the question in their own words. Older students might use a highlighter to mark the important parts of the problem.
Finding a strategy tends to suggest that it is a simple matter to think of an appropriate strategy. However, for many problems students may find it necessary to play around with the information before they are able to think of a strategy that might produce a solution. This exploratory phase will also help them to understand the problem better and may make them aware of some piece of information that they had neglected after the first reading.
Having explored the problem and decided on a strategy, the third step, solve the problem , can be attempted. Hopefully now the problem will be solved and an answer obtained. During this phase it is important for the students to keep a track of what they are doing. This is useful to show others what they have done and it is also helpful in finding errors should the right answer not be found.
At this point many students, especially mathematically able ones, will stop. But it is worth getting them into the habit of looking back over what they have done. There are several good reasons for this. First of all it is good practice for them to check their working and make sure that they have not made any errors. Second, it is vital to make sure that the answer they obtained is in fact the answer to the problem. Third, in looking back and thinking a little more about the problem, students are often able to see another way of solving the problem. This new solution may be a nicer solution than the original and may give more insight into what is really going on. Finally, students may be able to generalise or extend the problem.
Generalising a problem means creating a problem that has the original problem as a special case. So a problem about three pigs may be changed into one which has any number of pigs.
In Problem 4 of What is a Problem? , there is a problem on towers. The last part of that problem asks how many towers can be built for any particular height. The answer to this problem will contain the answer to the previous three questions. There we were asked for the number of towers of height one, two and three. If we have some sort of formula, or expression, for any height, then we can substitute into that formula to get the answer for height three, for instance. So the "any" height formula is a generalisation of the height three case. It contains the height three case as a special example.
Extending a problem is a related idea. Here though, we are looking at a new problem that is somehow related to the first one. For instance, a problem that involves addition might be looked at to see if it makes any sense with multiplication. A rather nice problem is to take any whole number and divide it by two if it’s even and multiply it by three and add one if it’s odd. Keep repeating this manipulation. Is the answer you get eventually 1? We’ll do an example. Let’s start with 34. Then we get
34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
We certainly got to 1 then. Now it turns out that no one in the world knows if you will always get to 1 this way, no matter where you start. That’s something for you to worry about. But where does the extension come in? Well we can extend this problem, by just changing the 3 to 5. So this time instead of dividing by 2 if the number is even and multiplying it by three and adding one if it’s odd, try dividing by 2 if the number is even and multiplying it by 5 and adding one if it’s odd. This new problem doesn’t contain the first one as a special case, so it’s not a generalisation. It is an extension though – it’s a problem that is closely related to the original.
It is by this method of generalisation and extension that mathematics makes great strides forward. Up until Pythagoras’ time, many right-angled triangles were known. For instance, it was known that a triangle with sides 3, 4 and 5 was a right-angled triangle. Similarly people knew that triangles with sides 5, 12 and 13, and 7, 24 and 25 were right angled. Pythagoras’ generalisation was to show that EVERY triangle with sides a, b, c was a right-angled triangle if and only if a 2 + b 2 = c 2 .
This brings us to an aspect of problem solving that we haven’t mentioned so far. That is justification (or proof). Your students may often be able to guess what the answer to a problem is but their solution is not complete until they can justify their answer.
Now in some problems it is hard to find a justification. Indeed you may believe that it is not something that any of the class can do. So you may be happy that the students can find an answer. However, bear in mind that this justification is what sets mathematics apart from every other discipline. Consequently the justification step is an important one that shouldn’t be missed too often.
Another way of looking at the Problem Solving process is what might be called the scientific approach. We show this in the diagram below.
Here the problem is given and initially the idea is to experiment with it or explore it in order to get some feeling as to how to proceed. After a while it is hoped that the solver is able to make a conjecture or guess what the answer might be. If the conjecture is true it might be possible to prove or justify it. In that case the looking back process sets in and an effort is made to generalise or extend the problem. In this case you have essentially chosen a new problem and so the whole process starts over again.
Sometimes, however, the conjecture is wrong and so a counter-example is found. This is an example that contradicts the conjecture. In that case another conjecture is sought and you have to look for a proof or another counterexample.
Some problems are too hard so it is necessary to give up. Now you may give up so that you can take a rest, in which case it is a ‘for now’ giving up. Actually this is a good problem solving strategy. Often when you give up for a while your subconscious takes over and comes up with a good idea that you can follow. On the other hand, some problems are so hard that you eventually have to give up ‘for ever’. There have been many difficult problems throughout history that mathematicians have had to give up on.
Stumped five ways to hone your problem-solving skills.
Respect the worth of other people's insights
Problems continuously arise in organizational life, making problem-solving an essential skill for leaders. Leaders who are good at tackling conundrums are likely to be more effective at overcoming obstacles and guiding their teams to achieve their goals. So, what’s the secret to better problem-solving skills?
“Too often, people fail because they haven’t correctly defined what the problem is,” says David Ross, an international strategist, founder of consultancy Phoenix Strategic Management and author of Confronting the Storm: Regenerating Leadership and Hope in the Age of Uncertainty .
Ross explains that as teams grapple with “wicked” problems – those where there can be several root causes for why a problem exists – there can often be disagreement on the initial assumptions made. As a result, their chances of successfully solving the problem are low.
“Before commencing the process of solving the problem, it is worthwhile identifying who your key stakeholders are and talking to them about the issue,” Ross recommends. “Who could be affected by the issue? What is the problem – and why? How are people affected?”
He argues that if leaders treat people with dignity, respecting the worth of their insights, they are more likely to successfully solve problems.
Best 5% interest savings accounts of 2024, 2. unfocus the mind.
“To solve problems, we need to commit to making time to face a problem in its full complexity, which also requires that we take back control of our thinking,” says Chris Griffiths, an expert on creativity and innovative thinking skills, founder and CEO of software provider OpenGenius, and co-author of The Focus Fix: Finding Clarity, Creativity and Resilience in an Overwhelming World .
To do this, it’s necessary to harness the power of the unfocused mind, according to Griffiths. “It might sound oxymoronic, but just like our devices, our brain needs time to recharge,” he says. “ A plethora of research has shown that daydreaming allows us to make creative connections and see abstract solutions that are not obvious when we’re engaged in direct work.”
To make use of the unfocused mind in problem solving, you must begin by getting to know the problem from all angles. “At this stage, don’t worry about actually solving the problem,” says Griffiths. “You’re simply giving your subconscious mind the information it needs to get creative with when you zone out. From here, pick a monotonous or rhythmic activity that will help you to activate the daydreaming state – that might be a walk, some doodling, or even some chores.”
Do this regularly, argues Griffiths, and you’ll soon find that flashes of inspiration and novel solutions naturally present themselves while you’re ostensibly thinking of other things. He says: “By allowing you to access the fullest creative potential of your own brain, daydreaming acts as a skeleton key for a wide range of problems.”
“Admitting to not knowing the future takes courage,” says Professor Stephen Wyatt, founder and lead consultant at consultancy Corporate Rebirth and author of Antidote to the Crisis of Leadership: Opportunity in Complexity . “Leaders are worried our teams won’t respect us and our boards will lose faith in us, but what doesn’t work is drawing up plans and forecasts and holding yourself or others rigidly to them.”
Wyatt advises leaders to heighten their situational awareness – to look broadly, integrate more perspectives and be able to connect the dots. “We need to be comfortable in making judgment calls as the future is unknown,” he says. “There is no data on it. But equally, very few initiatives cannot be adjusted, refined or reviewed while in motion.”
Leaders need to stay vigilant, according to Wyatt, create the capacity of the enterprise to adapt and maintain the support of stakeholders. “The concept of the infallible leader needs to be updated,” he concludes.
“Organisations, and arguably society more widely, are obsessed with problems and the notion of problems,” says Steve Hearsum, founder of organizational change consultancy Edge + Stretch and author of No Silver Bullet: Bursting the Bubble of the Organisational Quick Fix .
Hearsum argues that this tendency is complicated by the myth of fixability, namely the idea that all problems, however complex, have a solution. “Our need for certainty, to minimize and dampen the anxiety of ‘not knowing,’ leads us to oversimplify and ignore or filter out anything that challenges the idea that there is a solution,” he says.
Leaders need to shift their mindset to cultivate their comfort with not knowing and couple that with being OK with being wrong, sometimes, notes Hearsum. He adds: “That means developing reflexivity to understand your own beliefs and judgments, and what influences these, asking questions and experimenting.”
Leaders must be able to communicate problems in order to find solutions to them. But they should avoid bombarding their teams with complex, technical details since these can overwhelm their people’s cognitive load, says Dr Jessica Barker MBE , author of Hacked: The Secrets Behind Cyber Attacks .
Instead, she recommends that leaders frame their messages in ways that cut through jargon and ensure that their advice is relevant, accessible and actionable. “An essential leadership skill for this is empathy,” Barker explains. “When you’re trying to build a positive culture, it is crucial to understand why people are not practicing the behaviors you want rather than trying to force that behavioral change with fear, uncertainty and doubt.”
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By Teach Educator
Published on: February 4, 2024
7 Steps to Problem-Solving is a systematic process that involves analyzing a situation, generating possible solutions, and implementing the best course of action. While different problem-solving models exist, a common approach often involves the following seven steps:
It’s important to note that these steps are not always linear and may involve iteration. Problem-solving is often an ongoing process, and feedback from the implementation and evaluation stages may lead to adjustments in the chosen solution or the identification of new issues that need to be addressed.
A high school has noticed a decline in student engagement and performance in mathematics classes over the past few years. Students seem disinterested, and there is a noticeable decrease in test scores. The traditional teaching methods are not effectively capturing students’ attention, and there’s a need for innovative solutions to rekindle interest in mathematics.
Identify the problem:.
This problem-solving approach in education involves a systematic process of identifying, analyzing, and addressing issues to enhance the learning experience for students.
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Algorithm for corn crop row recognition during different growth stages based on st-yolov8s network.
2. materials and methods, 2.1. dataset construction, 2.2. model construction, 2.2.1. swin transformer model construction, 2.2.2. st-yolov8s model construction, 2.3. improved supergreen method, 2.4. local–global detection method, 3. results and discussion, 3.1. experimental platform, 3.2. crop row segment detection experiment, 3.3. crop row segment segmentation experiment, 3.4. crop row line detection experiment, 4. conclusions, author contributions, data availability statement, conflicts of interest.
Click here to enlarge figure
Method | Advantage | Disadvantage |
---|---|---|
GNSS | Global coverage and high accuracy | Poor stability and signal susceptibility to environmental influences |
LiDAR | Highly accurate and unaffected by the environment | Higher cost and complexity of operation |
Computer vision | Good autonomy and real time | Sensitivity to environmental factors |
Target | Method | Accuracy | Author |
---|---|---|---|
- | ENet | 84.94% | Yu et al. (2023) |
Rice | Transformer | 92.93% | Li et al. (2023) |
Rice | UNet + MobileNet V2 | 90.8% | He et al. (2022) |
Rice | SSD + MobileNet | 92.8% | Liu et al. (2020) |
Corn | Faster-RCNN + VGG19 | 97.71% | Quan et al. (2019) |
Corn | YOLOv5 | 97.8% | Yang et al. (2023) |
- | GCN + ResNet-101 | 97.5% | Jiang et al. (2020) |
Corn | UNet + ASPP | 90.18% | Diao et al. (2023) |
Rice | YOLOv3 | 91.47% | Zhang et al. (2020) |
Potato | UNet + VGG16 | 97.29% | Yang et al. (2022) |
- | YOLOv4 + MobileNet V3 | 93.6% | Hu et al. (2021) |
- | SegNet | 93.58% | Bah et al. (2019) |
Rice | YOLOv5 + PFocal Loss | - | Wang et al. (2023) |
Category | Number |
---|---|
Seedling stage | 5328 |
Mid-growth stage | 4672 |
Name | Related Configuration |
---|---|
Operating system | Windows 10 (64 bit) |
CPU | Intel(R) Xeon(R) CPU E5-2678 v3 @ 2.50 GHz |
GPU | NVIDIA GeForce RTX 3080 Ti |
Software and environment | PyCharm 2021.3, Python 3.8, Pytorch 1.10 |
Growth Stage | Network | MAP |
---|---|---|
ST-YOLOv5s | 91.13% | |
Seedling stage | ST-YOLOv7 | 85.36% |
ST-YOLOv8s | 93.89% | |
ST-YOLOv5s | 91.78% | |
Mid-growth stage | ST-YOLOv7 | 84.77% |
ST-YOLOv8s | 92.27% |
Evaluation Metrics | Detection Frame Midpoint + Least Squares Method | FAST Corner Point Detection + Least Squares Method | SUSAN Corner Point Detection + Least Squares Method | This Paper |
---|---|---|---|---|
Accuracy W | 79.41% | 86.32% | 90.80% | 96.79% |
Average angle error N | 4.36° | 2.19° | 1.28° | 0.58° |
Average fitting time T | 52.30 ms | 65.00 ms | 80.77 ms | 47.00 ms |
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Diao, Z.; Ma, S.; Zhang, D.; Zhang, J.; Guo, P.; He, Z.; Zhao, S.; Zhang, B. Algorithm for Corn Crop Row Recognition during Different Growth Stages Based on ST-YOLOv8s Network. Agronomy 2024 , 14 , 1466. https://doi.org/10.3390/agronomy14071466
Diao Z, Ma S, Zhang D, Zhang J, Guo P, He Z, Zhao S, Zhang B. Algorithm for Corn Crop Row Recognition during Different Growth Stages Based on ST-YOLOv8s Network. Agronomy . 2024; 14(7):1466. https://doi.org/10.3390/agronomy14071466
Diao, Zhihua, Shushuai Ma, Dongyan Zhang, Jingcheng Zhang, Peiliang Guo, Zhendong He, Suna Zhao, and Baohua Zhang. 2024. "Algorithm for Corn Crop Row Recognition during Different Growth Stages Based on ST-YOLOv8s Network" Agronomy 14, no. 7: 1466. https://doi.org/10.3390/agronomy14071466
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Seek alternatives that may solve the problem ; 3. Evaluate and select an alternative: ... Brainstorming and team problem-solving techniques are both useful tools in this stage of problem solving. Many alternative solutions to the problem should be generated before final evaluation. A common mistake in problem solving is that alternatives are ...
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 ...
Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything ...
3 Basic Steps of Problem Solving. As the name suggests, problem solving starts with a problem and ends with solutions. The step in the middle is the analysis. The level of detail within a problem changes based on the magnitude of an issue, but the basic steps of problem solving remain the same regardless of the type of problem: ...
Step 1 - Define the Problem. The definition of the problem is the first step in effective problem solving. This may appear to be a simple task, but it is actually quite difficult. This is because problems are frequently complex and multi-layered, making it easy to confuse symptoms with the underlying cause.
This step of the problem-solving process is all about thinking outside of the box, challenging old assumptions, and thinking laterally. This stage is the one that tends to cause the most overwhelm in teams because it requires just the right balance of creativity and critical thinking, which tends to cause a lot of friction.
Conclusion. The three stages of problem solving - preparation, production, and judgment - form a cognitive framework that underpins effective decision-making and resolving challenges. Each stage is interconnected and builds upon the previous one, allowing individuals to develop a comprehensive understanding of the problem, explore various ...
Essentially every problem-solving heuristic in mathematics goes back to George Polya's How to Solve It; my approach is no exception. However, this cyclic description might help to keep the process cognitively present. A few months ago, I produced a video describing this the three stages of the problem-solving cycle: Understand, Strategize, and Implement.
Problem-solving is a vital skill for coping with various challenges in life. This webpage explains the different strategies and obstacles that can affect how you solve problems, and offers tips on how to improve your problem-solving skills. Learn how to identify, analyze, and overcome problems with Verywell Mind.
From Why Groups Struggle to Solve Problems Together , Nov 07, 2019. Find new ideas and classic advice on strategy, innovation and leadership, for global leaders from the world's best business and ...
7. Solution evaluation. 1. Problem identification. The first stage of any problem solving process is to identify the problem (s) you need to solve. This often looks like using group discussions and activities to help a group surface and effectively articulate the challenges they're facing and wish to resolve.
Get unlimited access to all our career-boosting content and member benefits with our 7-day free trial. Although problem-solving is something everyone does on a daily basis, many people lack confidence in their ability. Here we look at the basic problem-solving process to help keep you on the right track.
Evaluate the options. Select the best solution. Create an implementation plan. Communicate your solution. Let's look at each step in a little more detail. The first solution you come up with won't always be the best - taking the time to consider your options is an essential problem solving technique. 1.
To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].
This page continues from Problem Solving an Introduction that introduces problem solving as a concept and outlines the stages used to successfully solve problems.. This page covers the first two stages in the problem solving process: Identifying the Problem and Structuring the Problem. Stage One: Identifying the Problem. Before being able to confront a problem its existence needs to be identified.
It starts with an "affirmative topic," followed by the "positive core (strengths).". Then this method delves into the following stages: Discovery (fact-finding) Dream (visioning the future) Design (strategic purpose) Destiny (continuous improvement) 3. "FIVE WHYS" METHOD. The 5 Whys of Problem-Solving Method.
Problem Solving is the process of identifying, analyzing, and finding effective solutions to complex issues or challenges. Key Steps in Problem Solving: Identification of the problem: Recognizing and clearly defining the issue that needs to be resolved. Analysis and research: Gathering relevant information, data, and facts to understand the ...
The problem solving process typically includes: Pinpointing what's broken by gathering data and consulting with team members. Figuring out why it's not working by mapping out and troubleshooting the problem. Deciding on the most effective way to fix it by brainstorming and then implementing a solution. While skills like active listening ...
The Stages of Problem Solving We Can All Apply. 1. Identify the problem. SEE ALSO Ipse dixit, the widespread fallacy of "gratuitous affirmation". It may seem like a truism, but the truth is that identifying the real problem is not as easy as it seems, especially when it comes to a situation that affects us emotionally.
Problem-solving stages. What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists. To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are ...
The implementation of a solution requires planning and execution. It's often iterative, where the focus should be on short implementation cycles with testing and feedback, not trying to get it "perfect" the first time. Input: decision; planning; hard work. Output: resolution to the problem. 5.
Pólya's four stages of problem solving are listed below. Four stages of problem solving . 1. Understand and explore the problem 2. Find a strategy 3. Use the strategy to solve the problem 4. Look back and reflect on the solution. Although we have listed the four stages in order, for difficult problems it may not be possible to simply move ...
"At this stage, don't worry about actually solving the problem," says Griffiths. "You're simply giving your subconscious mind the information it needs to get creative with when you zone out.
Problem-solving is often an ongoing process, and feedback from the implementation and evaluation stages may lead to adjustments in the chosen solution or the identification of new issues that need to be addressed. Problem-Solving Example in Education. Certainly: Let's consider a problem-solving example in the context of education.
Corn crop row recognition during different growth stages is a major difficulty faced by the current development of visual navigation technology for agricultural robots. In order to solve this problem, an algorithm for recognizing corn crop rows during different growth stages is presented based on the ST-YOLOv8s network. Firstly, a dataset of corn crop rows during different growth stages ...