problem solving model 4 steps

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The easy 4 step problem-solving process (+ examples)

This is the 4 step problem-solving process that I taught to my students for math problems, but it works for academic and social problems as well.

Every problem may be different, but effective problem solving asks the same four questions and follows the same method.

• What’s the problem? If you don’t know exactly what the problem is, you can’t come up with possible solutions. Something is wrong. What are we going to do about this? This is the foundation and the motivation.
• What do you need to know? This is the most important part of the problem. If you don’t know exactly what the problem is, you can’t come up with possible solutions.
• What do you already know? You already know something related to the problem that will help you solve the problem. It’s not always obvious (especially in the real world), but you know (or can research) something that will help.
• What’s the relationship between the two? Here is where the heavy brainstorming happens. This is where your skills and abilities come into play. The previous steps set you up to find many potential solutions to your problem, regardless of its type.

When I used to tutor kids in math and physics , I would drill this problem-solving process into their heads. This methodology works for any problem, regardless of its complexity or difficulty. In fact, if you look at the various advances in society, you’ll see they all follow some variation of this problem-solving technique.

“The gap between understanding and misunderstanding can best be bridged by thought!” ― Ernest Agyemang Yeboah

Generally speaking, if you can’t solve the problem then your issue is step 3 or step 4; you either don’t know enough or you’re missing the connection.

Good problem solvers always believe step 3 is the issue. In this case, it’s a simple matter of learning more. Less skilled problem solvers believe step 4 is the root cause of their difficulties. In this instance, they simply believe they have limited problem-solving skills.

This is a fixed versus growth mindset and it makes a huge difference in the effort you put forth and the belief you have in yourself to make use of this step-by-step process. These two mindsets make a big difference in your learning because, at its core, learning is problem-solving.

Let’s dig deeper into the 4 steps. In this way, you can better see how to apply them to your learning journey.

Step 1: What’s the problem?

The ability to recognize a specific problem is extremely valuable.

Most people only focus on finding solutions. While a “solutions-oriented” mindset is a good thing, sometimes it pays to focus on the problem. When you focus on the problem, you often make it easier to find a viable solution to it.

When you know the exact nature of the problem, you shorten the time frame needed to find a solution. This reminds me of a story I was once told.

When does the problem-solving process start?

The process starts after you’ve identified the exact nature of the problem.

Homeowners love a well-kept lawn but hate mowing the grass.

Many companies and inventors raced to figure out a more time-efficient way to mow the lawn. Some even tried to design robots that would do the mowing. They all were chasing the solution, but only one inventor took the time to understand the root cause of the problem.

Most people figured that the problem was the labor required to maintain a lawn. The actual problem was just the opposite: maintaining a lawn was labor-intensive. The rearrangement seems trivial, but it reveals the true desire: a well-maintained lawn.

The best solution? Remove maintenance from the equation. A lawn made of artificial grass solved the problem . Hence, an application of Astroturf was discovered.

This way, the law always looked its best. Taking a few moments to apply critical thinking identified the true nature of the problem and yielded a powerful solution.

An example of choosing the right problem to work the problem-solving process on

One thing I’ve learned from tutoring high school students in math : they hate word problems.

This is because they make the student figure out the problem. Finding the solution to a math problem is already stressful. Forcing the student to also figure out what problem needs solving is another level of hell.

Word problems are not always clear about what needs to be solved. They also have the annoying habit of adding extraneous information. An ordinary math problem does not do this. For example, compare the following two problems:

What’s the height of h?

A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?

The first is a simple problem. The second is a complex problem. The end goal in both is the same.

The questions require the same knowledge (trigonometric functions), but the second is more difficult for students. Why? The second problem does not make it clear what the exact problem is. Before mathematics can even begin, you must know the problem, or else you risk solving the wrong one.

If you understand the problem, finding the solution is much easier. Understanding this, ironically, is the biggest problem for people.

Problem-solving is a universal language

Speaking of people, this method also helps settle disagreements.

When we disagree, we rarely take the time to figure out the exact issue. This happens for many reasons, but it always results in a misunderstanding. When each party is clear with their intentions, they can generate the best response.

Education systems fail when they don’t consider the problem they’re supposed to solve. Foreign language education in America is one of the best examples.

The problem is that students can’t speak the target language. It seems obvious that the solution is to have students spend most of their time speaking. Unfortunately, language classes spend a ridiculous amount of time learning grammar rules and memorizing vocabulary.

The problem is not that the students don’t know the imperfect past tense verb conjugations in Spanish. The problem is that they can’t use the language to accomplish anything. Every year, kids graduate from American high schools without the ability to speak another language, despite studying one for 4 years.

Well begun is half done

Before you begin to learn something, be sure that you understand the exact nature of the problem. This will make clear what you need to know and what you can discard. When you know the exact problem you’re tasked with solving, you save precious time and energy. Doing this increases the likelihood that you’ll succeed.

Step 2: What do you need to know?

All problems are the result of insufficient knowledge. To solve the problem, you must identify what you need to know. You must understand the cause of the problem. If you get this wrong, you won’t arrive at the correct solution.

Either you’ll solve what you thought was the problem, only to find out this wasn’t the real issue and now you’ve still got trouble or you won’t and you still have trouble. Either way, the problem persists.

If you solve a different problem than the correct one, you’ll get a solution that you can’t use. The only thing that wastes more time than an unsolved problem is solving the wrong one.

Imagine that your car won’t start. You replace the alternator, the starter, and the ignition switch. The car still doesn’t start. You’ve explored all the main solutions, so now you consider some different solutions.

Now you replace the engine, but you still can’t get it to start. Your replacements and repairs solved other problems, but not the main one: the car won’t start.

Then it turns out that all you needed was gas.

This example is a little extreme, but I hope it makes the point. For something more relatable, let’s return to the problem with language learning.

You need basic communication to navigate a foreign country you’re visiting; let’s say Mexico. When you enroll in a Spanish course, they teach you a bunch of unimportant words and phrases. You stick with it, believing it will eventually click.

When you land, you can tell everyone your name and ask for the location of the bathroom. This does not help when you need to ask for directions or tell the driver which airport terminal to drop you off at.

Finding the solution to chess problems works the same way

The book “The Amateur Mind” by IM Jeremy Silman improved my chess by teaching me how to analyze the board.

It’s only with a proper analysis of imbalances that you can make the best move. Though you may not always choose the correct line of play, the book teaches you how to recognize what you need to know . It teaches you how to identify the problem—before you create an action plan to solve it.

The problem-solving method always starts with identifying the problem or asking “What do you need to know?”. It’s only after you brainstorm this that you can move on to the next step.

Learn the method I used to earn a physics degree, learn Spanish, and win a national boxing title

• I was a terrible math student in high school who wrote off mathematics. I eventually overcame my difficulties and went on to earn a B.A. Physics with a minor in math
• I pieced together the best works on the internet to teach myself Spanish as an adult
• *I didn’t start boxing until the very old age of 22, yet I went on to win a national championship, get a high-paying amateur sponsorship, and get signed by Roc Nation Sports as a profession.

I’ve used this method to progress in mentally and physically demanding domains.

While the specifics may differ, I believe that the general methods for learning are the same in all domains.

This free e-book breaks down the most important techniques I’ve used for learning.

Step 3: What do you already know?

The only way to know if you lack knowledge is by gaining some in the first place. All advances and solutions arise from the accumulation and implementation of prior information. You must first consider what it is that you already know in the context of the problem at hand.

Isaac Newton once said, “If I have seen further, it is by standing on the shoulders of giants.” This is Newton’s way of explaining that his advancements in physics and mathematics would be impossible if it were not for previous discoveries.

Mathematics is a great place to see this idea at work. Consider the following problem:

What is the domain and range of y=(x^2)+6?

This simple algebra problem relies on you knowing a few things already. You must know:

• The definition of “domain” and “range”
• That you can never square any real number and get a negative

Once you know those things, this becomes easy to solve. This is also how we learn languages.

An example of the problem-solving process with a foreign language

Anyone interested in serious foreign language study (as opposed to a “crash course” or “survival course”) should learn the infinitive form of verbs in their target language. You can’t make progress without them because they’re the root of all conjugations. It’s only once you have a grasp of the infinitives that you can completely express yourself. Consider the problem-solving steps applied in the following example.

I know that I want to say “I don’t eat eggs” to my Mexican waiter. That’s the problem.

I don’t know how to say that, but last night I told my date “No bebo alcohol” (“I don’t drink alcohol”). I also know the infinitive for “eat” in Spanish (comer). This is what I already know.

Now I can execute the final step of problem-solving.

Step 4: What’s the relationship between the two?

I see the connection. I can use all of my problem-solving strategies and methods to solve my particular problem.

I know the infinitive for the Spanish word “drink” is “beber” . Last night, I changed it to “bebo” to express a similar idea. I should be able to do the same thing to the word for “eat”.

“No como huevos” is a pretty accurate guess.

In the math example, the same process occurs. You don’t know the answer to “What is the domain and range of y=(x^2)+6?” You only know what “domain” and “range” mean and that negatives aren’t possible when you square a real number.

A domain of all real numbers and a range of all numbers equal to and greater than six is the answer.

This is relating what you don’t know to what you already do know. The solutions appear simple, but walking through them is an excellent demonstration of the process of problem-solving.

In most cases, the solution won’t be this simple, but the process or finding it is the same. This may seem trivial, but this is a model for thinking that has served the greatest minds in history.

A recap of the 4 steps of the simple problem-solving process

• What’s the problem? There’s something wrong. There’s something amiss.
• What do you need to know? This is how to fix what’s wrong.
• What do you already know? You already know something useful that will help you find an effective solution.
• What’s the relationship between the previous two? When you use what you know to help figure out what you don’t know, there is no problem that won’t yield.

Learning is simply problem-solving. You’ll learn faster if you view it this way.

What was once complicated will become simple.

What was once convoluted will become clear.

Ed Latimore

I’m a writer, competitive chess player, Army veteran, physicist, and former professional heavyweight boxer. My work focuses on self-development, realizing your potential, and sobriety—speaking from personal experience, having overcome both poverty and addiction.

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Easy Problem Solving Using the 4-step Method

June 7, 2017  by  Jennifer Haury Category:  Guest Author ,  Management

At a recent hospital town forum, hospital leaders are outlining the changes coming when a lone, brave nurse raises her hand and says, “We just can’t take any more changes. They are layered on top of each other and each one is rolled out in a different way. We are exhausted and it’s overloading us all.”  

 “Flavor of the Month” Fatigue

Change fatigue. You hear about it in every industry, from government sectors to software design to manufacturing to healthcare and more. When policy and leadership changes and process improvement overlap it’s no surprise when people complain about “flavor of the month,” and resist it just so they can keep some routine to their days.

In a time where change is required just to keep up with the shifting environment, one way to ease fatigue is to standardize HOW we change. If we use a best practice for solving problems, we can ensure that the right people are involved and problems are solved permanently, not temporarily. Better yet, HOW we change can become the habit and routine we long for.

The 4-step Problem Solving Method

The model we’ve used with clients is based on the A3 problem-solving methodology used by many “lean” production-based companies. In addition to being simpler, our 4-step method is visual, which helps remind the user what goes into each box.

The steps are as follows

• Develop a Problem Statement
• Determine Root Causes
• Rank Root Causes in Order of Importance
• Create an Action Plan

Step 1: Develop a Problem Statement

Developing a good problem statement always seems a lot easier than it generally turns out to be.  For example, this statement: “We don’t have enough staff,” frequently shows up as a problem statement. However, it suggests the solution—“GET MORE STAFF” — and fails to address the real problem that more staff might solve, such as answering phones in a timely manner.

The trick is to develop a problem statement that does not suggest a solution.  Avoiding the following words/phrases: “lack of,” “no,” “not enough,” or “too much” is key. When I start to fall into the trap of suggesting a solution, I ask: “So what problem does that cause?” This usually helps to get to a more effective problem statement.

Once you’ve developed a problem statement, you’ll need to define your target goal, measure your actual condition, then determine the gap. If we ran a restaurant and our problem was: “Customers complaining about burnt toast during morning shift,” the target goal might be: “Toast golden brown 100% of morning shift.”

Focus on a tangible, achievable target goal then measure how often that target is occurring. If our actual condition is: “Toast golden brown 50% of the time,” then our gap is: “Burnt toast 50% of the time.” That gap is now a refined problem to take to Step 2.

Step 2:  Determine Root Causes

In Step 2, we want to understand the root causes. For example, if the gap is burnt toast 50% of the time, what are all the possible reasons why?

This is when you brainstorm. It could be an inattentive cook or a broken pop-up mechanism. Cooks could be using different methods to time the toasting process or some breads toast more quickly.  During brainstorming, you’ll want to include everyone in the process since observing these interactions might also shed light on why the problem is occurring.

Once we have an idea of why, we then use the 5-why process to arrive at a root cause.  Ask “Why?” five times or until it no longer makes sense to ask. Root causes can be tricky.  For example, if the pop up mechanism is broken you could just buy a new toaster, right? But if you asked WHY it broke, you may learn cooks are pressing down too hard on the pop up mechanism, causing it to break. In this case, the problem would just reoccur if you bought a new toaster.

When you find you are fixing reoccurring problems that indicates you haven’t solved for the root cause. Through the 5-why process, you can get to the root cause and fix the problem permanently.

Step 3: Rank Root Causes

Once you know what’s causing the problem (and there may be multiple root causes), it’s time to move to Step 3 to understand which causes, if solved for, would close your gap. Here you rank the root causes in order of importance by looking at which causes would have the greatest impact in closing the gap.

There may be times when you don’t want to go after your largest root cause (perhaps because it requires others to change what they are doing, will take longer, or is dependent on other things getting fixed, etc). Sometimes you’ll find it’s better to start with a solution that has a smaller impact but can be done quickly.

Step 4: Create an Action Plan

In Step 4 you create your action plan — who is going to do what and by when. Documenting all of this and making it visible helps to communicate the plan to others and helps hold them accountable during implementation.

This is where your countermeasures or experiments to fix the problem are detailed. Will we train our chefs on how to use a new “pop-up mechanism” free toaster? Will we dedicate one toaster for white bread and one for wheat?  

Make sure to measure your results after you’ve implemented your plan to see if your target is met. If not, that’s okay; just go through the steps again until the problem is resolved.

Final Thoughts

Using the 4-step method has been an easy way for teams to change how they solve problems. One team I was working with started challenging their “solution jumps” and found this method was a better way to avoid assumptions which led to never really solving their problems.  It was easy to use in a conference room and helped them make their thinking visual so everyone could be involved and engaged in solving the problems their team faced. 

Do you have a problem-solving method that you use at your worksite?  Let us know in the comments below. 

MRSC is a private nonprofit organization serving local governments in Washington State. Eligible government agencies in Washington State may use our free, one-on-one Ask MRSC service to get answers to legal, policy, or financial questions.

About Jennifer Haury

Jennifer Haury is the CEO of All Angles Consulting, LLC and guest authored this post for MRSC.

Jennifer has over 28 years learning in the healthcare industry (17 in leadership positions or consulting in performance improvement and organizational anthropology) and is a Lean Six Sigma Black Belt.

She is a trusted, experienced leader with a keen interest in performance improvement and organizational anthropology. Jennifer is particularly concerned with the sustainability of continuous improvement programs and the cultural values and beliefs that translate into behaviors that either get in our own way or help us succeed in transforming our work.

The views expressed in guest columns represent the opinions of the author and do not necessarily reflect those of MRSC.

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An Overview of 4-Step Problem Solving

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

What is problem solving, definition and importance.

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

Problem-Solving Steps

The problem-solving process typically includes the following steps:

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

Defining the Problem

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

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

Generating Solutions

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

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

Evaluating and Selecting Solutions

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

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

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

Implementing and Monitoring the Solution

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

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

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

Problem-Solving Techniques

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

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

Brainstorming

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

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

When brainstorming, remember to:

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

Root Cause Analysis

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

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

SWOT Analysis

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

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

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

Mind Mapping

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

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

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

Examples of Problem Solving in Various Contexts

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

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

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

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

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

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

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

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 they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

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

40 problem-solving techniques and processes

All teams and organizations encounter challenges. Approaching those challenges without a structured problem solving process can end up making things worse.

Proven problem solving techniques such as those outlined below can guide your group through a process of identifying problems and challenges , ideating on possible solutions , and then evaluating and implementing the most suitable .

In this post, you'll find problem-solving tools you can use to develop effective solutions. You'll also find some tips for facilitating the problem solving process and solving complex problems.

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What is problem solving?

Problem solving is a process of finding and implementing a solution to a challenge or obstacle. In most contexts, this means going through a problem solving process that begins with identifying the issue, exploring its root causes, ideating and refining possible solutions before implementing and measuring the impact of that solution.

For simple or small problems, it can be tempting to skip straight to implementing what you believe is the right solution. The danger with this approach is that without exploring the true causes of the issue, it might just occur again or your chosen solution may cause other issues.

Particularly in the world of work, good problem solving means using data to back up each step of the process, bringing in new perspectives and effectively measuring the impact of your solution.

Effective problem solving can help ensure that your team or organization is well positioned to overcome challenges, be resilient to change and create innovation. In my experience, problem solving is a combination of skillset, mindset and process, and it’s especially vital for leaders to cultivate this skill.

What is the seven step problem solving process?

A problem solving process is a step-by-step framework from going from discovering a problem all the way through to implementing a solution.

With practice, this framework can become intuitive, and innovative companies tend to have a consistent and ongoing ability to discover and tackle challenges when they come up.

You might see everything from a four step problem solving process through to seven steps. While all these processes cover roughly the same ground, I’ve found a seven step problem solving process is helpful for making all key steps legible.

We’ll outline that process here and then follow with techniques you can use to explore and work on that step of the problem solving process with a group.

The seven-step problem solving process is:

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.

Be sure to align with your team on the exact definition and nature of the problem you’re solving. An effective process is one where everyone is pulling in the same direction – ensure clarity and alignment now to help avoid misunderstandings later.

2. Problem analysis and refinement

The process of problem analysis means ensuring that the problem you are seeking to solve is  the   right problem . Choosing the right problem to solve means you are on the right path to creating the right solution.

At this stage, you may look deeper at the problem you identified to try and discover the root cause at the level of people or process. You may also spend some time sourcing data, consulting relevant parties and creating and refining a problem statement.

Problem refinement means adjusting scope or focus of the problem you will be aiming to solve based on what comes up during your analysis. As you analyze data sources, you might discover that the root cause means you need to adjust your problem statement. Alternatively, you might find that your original problem statement is too big to be meaningful approached within your current project.

Remember that the goal of any problem refinement is to help set the stage for effective solution development and deployment. Set the right focus and get buy-in from your team here and you’ll be well positioned to move forward with confidence.

3. Solution generation

Once your group has nailed down the particulars of the problem you wish to solve, you want to encourage a free flow of ideas connecting to solving that problem. This can take the form of problem solving games that encourage creative thinking or techniquess designed to produce working prototypes of possible solutions. 

The key to ensuring the success of this stage of the problem solving process is to encourage quick, creative thinking and create an open space where all ideas are considered. The best solutions can often come from unlikely places and by using problem solving techniques that celebrate invention, you might come up with solution gold. 

4. Solution development

No solution is perfect right out of the gate. It’s important to discuss and develop the solutions your group has come up with over the course of following the previous problem solving steps in order to arrive at the best possible solution. Problem solving games used in this stage involve lots of critical thinking, measuring potential effort and impact, and looking at possible solutions analytically. 

During this stage, you will often ask your team to iterate and improve upon your front-running solutions and develop them further. Remember that problem solving strategies always benefit from a multitude of voices and opinions, and not to let ego get involved when it comes to choosing which solutions to develop and take further.

Finding the best solution is the goal of all problem solving workshops and here is the place to ensure that your solution is well thought out, sufficiently robust and fit for purpose. 

5. Decision making and planning

Nearly there! Once you’ve got a set of possible, you’ll need to make a decision on which to implement. This can be a consensus-based group decision or it might be for a leader or major stakeholder to decide. You’ll find a set of effective decision making methods below.

Once your group has reached consensus and selected a solution, there are some additional actions that also need to be decided upon. You’ll want to work on allocating ownership of the project, figure out who will do what, how the success of the solution will be measured and decide the next course of action.

Set clear accountabilities, actions, timeframes, and follow-ups for your chosen solution. Make these decisions and set clear next-steps in the problem solving workshop so that everyone is aligned and you can move forward effectively as a group. 

Ensuring that you plan for the roll-out of a solution is one of the most important problem solving steps. Without adequate planning or oversight, it can prove impossible to measure success or iterate further if the problem was not solved. 

6. Solution implementation 

This is what we were waiting for! All problem solving processes have the end goal of implementing an effective and impactful solution that your group has confidence in.

Project management and communication skills are key here – your solution may need to adjust when out in the wild or you might discover new challenges along the way. For some solutions, you might also implement a test with a small group and monitor results before rolling it out to an entire company.

You should have a clear owner for your solution who will oversee the plans you made together and help ensure they’re put into place. This person will often coordinate the implementation team and set-up processes to measure the efficacy of your solution too.

7. Solution evaluation 

So you and your team developed a great solution to a problem and have a gut feeling it’s been solved. Work done, right? Wrong. All problem solving strategies benefit from evaluation, consideration, and feedback.

You might find that the solution does not work for everyone, might create new problems, or is potentially so successful that you will want to roll it out to larger teams or as part of other initiatives. 

None of that is possible without taking the time to evaluate the success of the solution you developed in your problem solving model and adjust if necessary.

Remember that the problem solving process is often iterative and it can be common to not solve complex issues on the first try. Even when this is the case, you and your team will have generated learning that will be important for future problem solving workshops or in other parts of the organization. 

It’s also worth underlining how important record keeping is throughout the problem solving process. If a solution didn’t work, you need to have the data and records to see why that was the case. If you go back to the drawing board, notes from the previous workshop can help save time.

What does an effective problem solving process look like?

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

The format of a workshop ensures that you can get buy-in from your group, encourage free-thinking and solution exploration before making a decision on what to implement following the session.

This Design Sprint 2.0 template is an effective problem solving process from top agency AJ&Smart. It’s a great format for the entire problem solving process, with four-days of workshops designed to surface issues, explore solutions and even test a solution.

Check it for an example of how you might structure and run a problem solving process and feel free to copy and adjust it your needs!

For a shorter process you can run in a single afternoon, this remote problem solving agenda will guide you effectively in just a couple of hours.

Whatever the length of your workshop, by using 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!

Complete problem-solving methods

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

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.

The Six Thinking Hats   #creative thinking   #meeting facilitation   #problem solving   #issue resolution   #idea generation   #conflict resolution   The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

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   It doesn’t matter where you work and what your job role is, if you work with other people together as a team, you will always encounter the same challenges: Unclear goals and miscommunication that cause busy work and overtime Unstructured meetings that leave attendants tired, confused and without clear outcomes. Frustration builds up because internal challenges to productivity are not addressed Sudden changes in priorities lead to a loss of focus and momentum Muddled compromise takes the place of clear decision- making, leaving everybody to come up with their own interpretation. In short, a lack of structure leads to a waste of time and effort, projects that drag on for too long and frustrated, burnt out teams. AJ&Smart has worked with some of the most innovative, productive companies in the world. What sets their teams apart from others is not better tools, bigger talent or more beautiful offices. The secret sauce to becoming a more productive, more creative and happier team is simple: Replace all open discussion or brainstorming with a structured process that leads to more ideas, clearer decisions and better outcomes. When a good process provides guardrails and a clear path to follow, it becomes easier to come up with ideas, make decisions and solve problems. This is why AJ&Smart created Lightning Decision Jam (LDJ). It’s a simple and short, but powerful group exercise that can be run either in-person, in the same room, or remotely with distributed teams.

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.

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.

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.

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.

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.

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!

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.

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.

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.

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.

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.

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.

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.

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.

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!

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 brainstorming solutions

Now you have the context and background of the problem you are trying to solving, now comes the time to start ideating and thinking about how you’ll solve the issue.

Here, you’ll want to encourage creative, free thinking and speed. Get as many ideas out as possible and explore different perspectives so you have the raw material for the next step.

Looking at a problem from a new angle can be one of the most effective ways of creating an effective solution. TRIZ is a problem-solving tool that asks the group to consider what they must not do in order to solve a challenge.

By reversing the discussion, new topics and taboo subjects often emerge, allowing the group to think more deeply and create ideas that confront the status quo in a safe and meaningful way. If you’re working on a problem that you’ve tried to solve before, TRIZ is a great problem-solving method to help your team get unblocked.

Making Space with TRIZ   #issue analysis   #liberating structures   #issue resolution   You can clear space for innovation by helping a group let go of what it knows (but rarely admits) limits its success and by inviting creative destruction. TRIZ makes it possible to challenge sacred cows safely and encourages heretical thinking. The question “What must we stop doing to make progress on our deepest purpose?” induces seriously fun yet very courageous conversations. Since laughter often erupts, issues that are otherwise taboo get a chance to be aired and confronted. With creative destruction come opportunities for renewal as local action and innovation rush in to fill the vacuum. Whoosh!

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.

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.

Idea and Concept Development

Brainstorming without structure can quickly become chaotic or frustrating. In a problem-solving context, having an ideation framework to follow can help ensure your team is both creative and disciplined.

In this method, you’ll find an idea generation process that encourages your group to brainstorm effectively before developing their ideas and begin clustering them together. By using concepts such as Yes and…, more is more and postponing judgement, you can create the ideal conditions for brainstorming with ease.

Idea & Concept Development   #hyperisland   #innovation   #idea generation   Ideation and Concept Development is a process for groups to work creatively and collaboratively to generate creative ideas. It’s a general approach that can be adapted and customized to suit many different scenarios. It includes basic principles for idea generation and several steps for groups to work with. It also includes steps for idea selection and development.

Problem-solving techniques for developing and refining 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 develop and refine your ideas in order to bring them closer to a solution that actually solves the problem.

Use these problem-solving techniques when you want to help your team think through their ideas and refine them as part of your problem solving process.

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.

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

Ensuring that everyone in a group is able to contribute to a discussion is vital during any problem solving process. Not only does this ensure all bases are covered, but its then easier to get buy-in and accountability when people have been able to contribute to the process.

1-2-4-All is a tried and tested facilitation technique where participants are asked to first brainstorm on a topic on their own. Next, they discuss and share ideas in a pair before moving into a small group. Those groups are then asked to present the best idea from their discussion to the rest of the team.

This method can be used in many different contexts effectively, though I find it particularly shines in the idea development stage of the process. Giving each participant time to concretize their ideas and develop them in progressively larger groups can create a great space for both innovation and psychological safety.

1-2-4-All   #idea generation   #liberating structures   #issue analysis   With this facilitation technique you can immediately include everyone regardless of how large the group is. You can generate better ideas and more of them faster than ever before. You can tap the know-how and imagination that is distributed widely in places not known in advance. Open, generative conversation unfolds. Ideas and solutions are sifted in rapid fashion. Most importantly, participants own the ideas, so follow-up and implementation is simplified. No buy-in strategies needed! Simple and elegant!

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.

Problem-solving techniques for making decisions and planning

After your group is happy with the possible solutions you’ve developed, now comes the time to choose which to implement. There’s more than one way to make a decision and the best option is often dependant on the needs and set-up of your group.

Sometimes, it’s the case that you’ll want to vote as a group on what is likely to be the most impactful solution. Other times, it might be down to a decision maker or major stakeholder to make the final decision. Whatever your process, here’s some techniques you can use to help you make a decision during your problem solving process.

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.

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.

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.

Straddling the gap between decision making and planning, MoSCoW is a simple and effective method that allows a group team to easily prioritize a set of possible options.

Use this method in a problem solving process by collecting and summarizing all your possible solutions and then categorize them into 4 sections: “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”.

This method is particularly useful when its less about choosing one possible solution and more about prioritorizing which to do first and which may not fit in the scope of your project. In my experience, complex challenges often require multiple small fixes, and this method can be a great way to move from a pile of things you’d all like to do to a structured plan.

MoSCoW   #define intentions   #create   #design   #action   #remote-friendly   MoSCoW is a method that allows the team to prioritize the different features that they will work on. Features are then categorized into “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”. To be used at the beginning of a timeslot (for example during Sprint planning) and when planning is needed.

When it comes to managing the rollout of a solution, clarity and accountability are key factors in ensuring the success of the project. The RAACI chart is a simple but effective model for setting roles and responsibilities as part of a planning session.

Start by listing each person involved in the project and put them into the following groups in order to make it clear who is responsible for what during the rollout of your solution.

• Responsibility  (Which person and/or team will be taking action?)
• Authority  (At what “point” must the responsible person check in before going further?)
• Accountability  (Who must the responsible person check in with?)
• Consultation  (Who must be consulted by the responsible person before decisions are made?)
• Information  (Who must be informed of decisions, once made?)

Ensure this information is easily accessible and use it to inform who does what and who is looped into discussions and kept up to date.

RAACI   #roles and responsibility   #teamwork   #project management   Clarifying roles and responsibilities, levels of autonomy/latitude in decision making, and levels of engagement among diverse stakeholders.

Problem-solving warm-up activities

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

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.

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.

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.

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.

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.

Closing activities for a problem-solving process

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

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.

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.

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.

Tips for 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.

Create psychologically safe spaces for discussion

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 tough for people to stand up and contribute if the problems or challenges are emotive or personal in nature. Try and create a psychologically safe space for these kinds of discussions and where possible, create regular opportunities for challenges to be brought up organically.

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!

Save time and effort creating an effective problem solving process

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

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

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

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

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of 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! 

James Smart is Head of Content at SessionLab. He’s also a creative facilitator who has run workshops and designed courses for establishments like the National Centre for Writing, UK. He especially enjoys working with young people and empowering others in their creative practice.

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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

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• Foundations

Problem-Solving

Foundations for implementation.

Problem-Solving Process

The problem-solving process uses data to plan, deliver, and evaluate a multi-tiered system of supports. It is a structured process that includes:

• The people who are affected by the problem, working with people who can help
• A deliberate focus on using each step of the process with fidelity
• Analysis that focuses on things people can control
• Follow-up that includes a review of data to make sure the strategies made a difference

Problem-Solving Model

The problem-solving model is an evidence-based way of work that can be applied to any level:

• individual/inter-personal
• small groups
• organizations (schools, districts, state)

When used with fidelity, the problem-solving process has been shown to improve student outcomes (Bahr, Fernstrom, Fuchs, Fush, & Stecker, 1990; Burns, Vanderwood & Ruby, 2005; Curtis, Castillo, Cohen, 2008; Fuchs & Fuchs, 1989; Gutkin & Curtis, 2009; Kovaleski, Gickling, Morrow, & Swank, 1999; Ruby, Crosby-Cooper, & Vanderwood, 2011) .

The number of steps in a problem solving process may vary, but all structured problem solving follows a general sequence of activities:

Problem Identification

• Describe the difference between current and desired levels of performance
• Define that difference (the problem) in observable and measurable terms

Problem Analysis

• Develop multiple ideas about why the problem is occurring, focusing on things people can control
• Determine which of those ideas have supporting evidence, which sometimes means  collecting or examining additional data 

Intervention Design

• Create a plan to address the reason for the problem, using strategies that are likely to work (e.g., “evidence-based”)
• Identify ways to monitor how accurately the plan was followed, the effectiveness of the plan, and the resources needed to implement the plan
• Implement the plan
• Evaluate whether the plan was effective, revisiting the problem solving process as needed

Additional Reading

Florida’s Guiding Questions for Tier 1 summarize this process within the 4-step problem solving framework.

• For more in-depth instruction on how data-based problem solving is used in Florida schools, review the Guiding Tools for Instructional Problem Solving - Revised (GTIPS-R) .
• Data Entry and Analysis Plan

Diagram Tool

Business Use

Individual Use

A Visual Guide to Problem-Solving: How to Do A Tape Diagram Using 4 Methods

Tape diagrams, also called bar models or strip diagrams, are awesome visual aids that can make it easier for you to get and solve math problems. They show numbers as rectangles or bars, giving you a clear picture of how things are related and making it simpler to figure things out. In this guide, we will look at different ways how to do a tape diagram , so you can get the hang of this super useful trick for solving problems. Whether you're a student, teacher, or just a parent helping out, getting the hang of tape diagrams can boost your math skills and confidence. Let's jump into the tape diagrams and see how they can make solving math problems a piece of cake.

Part 1. What is a Tape Diagram

Part 2. how to use a tape diagram, part 3. how to do a tape diagram with mindonmap, part 4. how to do a tape diagram with 3 other tools, part 5. faqs on how to do a tape diagram.

A tape diagram is a handy tool in math for illustrating problems with numbers, ratios, and how different amounts are related to each other. It's made up of bars or tapes drawn to look like real-life sizes, with each bar showing a certain value or amount.

Key Points About Tape Diagrams

• It makes it easy to see how numbers and quantities are related, helping you better understand and solve math problems. • They're great for showing the parts representing a different amount. • It is really good for comparing the amount of one thing compared to another, especially when dealing with ratios and proportions. • Breaking down tricky problems into smaller, easier-to-see parts makes solving math problems feel less daunting.

This guide will show you how to draw a tape diagram to tackle math problems. By getting the hang of making and looking at tape diagrams, you can better solve problems and better grasp math ideas.

Figure out what numbers matter in the situation. Decide which number is the total and which is the pieces.

Draw a shape like a rectangle or bar to show the total amount. Then, split the shape into pieces according to the given information.

Write down what each piece is worth or how much it is. Check out the picture to see how the numbers relate.

Use the diagram to make up equations or do the math.

MindOnMap is the best online tool that makes it easy to sort out your thoughts, ideas, and projects visually. Whether you're just throwing out ideas, planning your next move, or trying to figure something out, it's great for making mind maps, flowcharts, and all sorts of diagrams. People from all walks of life, like students, teachers, workers, and teams, love it because it's a simple yet effective way to make complicated stuff easier to understand by breaking it down into clear, easy-to-see diagrams. What sets MindOnMap apart is its easy use, even if you need to improve at making mind maps and diagrams. It has features like working on things together in real-time, picking from different templates, and working on it from anywhere with your device. MindOnMap is perfect for getting things done faster, better-grasping things, and sharing your thoughts with others. Whether you're using it for personal stuff, school projects, or working with a team, MindOnMap makes it a breeze to see and organise all

Secure Download

Steps on how to use tape diagrams in MindOnMap

Search MindOnMap in the search engine. You can download or use it free online. Arrange your data. Make sure you're clear on what numbers or values you're dealing with, and choose the Flowchart.

Choose a big rectangle or line to show the total amount. Break it down into smaller sections to show the different parts. You can change the colours and themes. After that, you can use brackets to separate it.

Label your data and create a formula to sum it up.

Once you've looked over all the info and possible fixes, click the Save button to save your project.

How do you make a tape diagram? Tape diagrams are super helpful visual aids that make it easier to get and solve math problems. They show numbers as rectangles or bars, clearly showing how things are connected and simplifying the problem-solving process. This guide will look at three go-to tools for making tape diagrams: EdrawMax Online, Creately, and Lucidchart. Each tool has features, so you can pick the one that fits what you need and like the most. By making tape diagrams, you'll get better at solving problems and understanding math concepts more deeply. Let's jump into the tape diagram and see why these tools are awesome.

Option 1. EdrawMax Online

EdrawMax Online is a handy tool for making all sorts of diagrams. It comes with many different templates, shapes, and ways to tweak them. Even though it's not made just for tape diagrams, its ability to do many things makes it a good fit for making these kinds of visual guides.

Search the tool and begin by making a new document.

Choose rectangles or lines from the shape library to show the tape and its sections. Use the tools to make the rectangles the right lengths for your data. Use text boxes to mark the different sections of the tape diagram.

Change the colours, fonts, and other elements to make your tape diagram your own.

Save your work if you are satisfied with your tape diagram.

Option 2. Creately

Creately is a strong drawing tool with many templates, shapes, and customisation options. Although it's not made just for tape diagrams, its flexibility makes it a good fit for creating these visual maps.

Steps on how to do a tape diagram with Creately

Go to the Creately website and create a diagram using a basic rectangular shape and connector to represent the tape and its divisions.

Use the resizing tools to adjust the lengths of the rectangles to match your data. Label the different parts of the tape diagram using text boxes.

Change colours, fonts, and other visual elements to personalise your tape diagram.

You can now save your tape diagram in Creately. Just click Export.

OpenAI Announces a New AI Model, Code-Named Strawberry, That Solves Difficult Problems Step by Step

OpenAI made the last big breakthrough in artificial intelligence by increasing the size of its models to dizzying proportions, when it introduced GPT-4 last year. The company today announced a new advance that signals a shift in approach—a model that can “reason” logically through many difficult problems and is significantly smarter than existing AI without a major scale-up.

The new model, dubbed OpenAI o1, can solve problems that stump existing AI models, including OpenAI’s most powerful existing model, GPT-4o . Rather than summon up an answer in one step, as a large language model normally does, it reasons through the problem, effectively thinking out loud as a person might, before arriving at the right result.

“This is what we consider the new paradigm in these models,” Mira Murati , OpenAI’s chief technology officer, tells WIRED. “It is much better at tackling very complex reasoning tasks.”

The new model was code-named Strawberry within OpenAI, and it is not a successor to GPT-4o but rather a complement to it, the company says.

Murati says that OpenAI is currently building its next master model, GPT-5, which will be considerably larger than its predecessor. But while the company still believes that scale will help wring new abilities out of AI, GPT-5 is likely to also include the reasoning technology introduced today. “There are two paradigms,” Murati says. “The scaling paradigm and this new paradigm. We expect that we will bring them together.”

LLMs typically conjure their answers from huge neural networks fed vast quantities of training data. They can exhibit remarkable linguistic and logical abilities, but traditionally struggle with surprisingly simple problems such as rudimentary math questions that involve reasoning.

Murati says OpenAI o1 uses reinforcement learning, which involves giving a model positive feedback when it gets answers right and negative feedback when it does not, in order to improve its reasoning process. “The model sharpens its thinking and fine tunes the strategies that it uses to get to the answer,” she says. Reinforcement learning has enabled computers to play games with superhuman skill and do useful tasks like designing computer chips . The technique is also a key ingredient for turning an LLM into a useful and well-behaved chatbot.

Mark Chen, vice president of research at OpenAI, demonstrated the new model to WIRED, using it to solve several problems that its prior model, GPT-4o, cannot. These included an advanced chemistry question and the following mind-bending mathematical puzzle: “A princess is as old as the prince will be when the princess is twice as old as the prince was when the princess’s age was half the sum of their present age. What is the age of the prince and princess?” (The correct answer is that the prince is 30, and the princess is 40).

“The [new] model is learning to think for itself, rather than kind of trying to imitate the way humans would think,” as a conventional LLM does, Chen says.

OpenAI says its new model performs markedly better on a number of problem sets, including ones focused on coding, math, physics, biology, and chemistry. On the American Invitational Mathematics Examination (AIME), a test for math students, GPT-4o solved on average 12 percent of the problems while o1 got 83 percent right, according to the company.

The new model is slower than GPT-4o, and OpenAI says it does not always perform better—in part because, unlike GPT-4o, it cannot search the web and it is not multimodal, meaning it cannot parse images or audio.

Improving the reasoning capabilities of LLMs has been a hot topic in research circles for some time. Indeed, rivals are pursuing similar research lines. In July, Google announced AlphaProof , a project that combines language models with reinforcement learning for solving difficult math problems.

AlphaProof was able to learn how to reason over math problems by looking at correct answers. A key challenge with broadening this kind of learning is that there are not correct answers for everything a model might encounter. Chen says OpenAI has succeeded in building a reasoning system that is much more general. “I do think we have made some breakthroughs there; I think it is part of our edge,” Chen says. “It’s actually fairly good at reasoning across all domains.”

Noah Goodman , a professor at Stanford who has published work on improving the reasoning abilities of LLMs, says the key to more generalized training may involve using a “carefully prompted language model and handcrafted data” for training. He adds that being able to consistently trade the speed of results for greater accuracy would be a “nice advance.”

Yoon Kim , an assistant professor at MIT, says how LLMs solve problems currently remains somewhat mysterious, and even if they perform step-by-step reasoning there may be key differences from human intelligence. This could be crucial as the technology becomes more widely used. “These are systems that would be potentially making decisions that affect many, many people,” he says. “The larger question is, do we need to be confident about how a computational model is arriving at the decisions?”

The technique introduced by OpenAI today also may help ensure that AI models behave well. Murati says the new model has shown itself to be better at avoiding producing unpleasant or potentially harmful output by reasoning about the outcome of its actions. “If you think about teaching children, they learn much better to align to certain norms, behaviors, and values once they can reason about why they’re doing a certain thing,” she says.

Oren Etzioni , a professor emeritus at the University of Washington and a prominent AI expert, says it’s “essential to enable LLMs to engage in multi-step problem solving, use tools, and solve complex problems.” He adds, “Pure scale up will not deliver this.” Etzioni says, however, that there are further challenges ahead. “Even if reasoning were solved, we would still have the challenge of hallucination and factuality.”

OpenAI’s Chen says that the new reasoning approach developed by the company shows that advancing AI need not cost ungodly amounts of compute power. “One of the exciting things about the paradigm is we believe that it’ll allow us to ship intelligence cheaper,” he says, “and I think that really is the core mission of our company.”

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JSmol Viewer

Solution of inverse photoacoustic problem for semiconductors via phase neural network.

1. Introduction

2. phase of photoacoustic response of semiconductors—direct pa problem, 3. silicon n-type phase neural network, 4. inverse solution of the photoacoustic problem, 5. discussion and conclusions, author contributions, data availability statement, acknowledgments, conflicts of interest.

• Rosencwaig, A.; Gerscho, A. Photoacoustic Effect with Solids: A Theoretical Treatment. Science 1975 , 190 , 556–557. [ Google Scholar ] [ CrossRef ]
• Rosencwaig, A.; Gersho, A. Theory of the photoacoustic effect with solids. J. Appl. Phys. 1976 , 47 , 64–69. [ Google Scholar ] [ CrossRef ]
• Tam, A.C. Applications of photoacoustic sensing techniques. Rev. Mod. Phys. 1986 , 58 , 381–431. [ Google Scholar ] [ CrossRef ]
• Sarode, A.P.; Mahajan, O.H. Theoretical Aspects of Photoacoustic Effect with Solids: A Review. Int. J. Sci. Adv. Res. Technol. 2018 , 4 , 1237–1242. [ Google Scholar ] [ CrossRef ]
• Park, H.K.; Grigoropoulos, C.P.; Tam, A.C. Optical measurements of thermal diffusivity of a material. Int. J. Thermophys. 1995 , 16 , 973–995. [ Google Scholar ] [ CrossRef ]
• Vargas, H.; Miranda, L.C.M. Photoacoustic and related photothermal techniques. Phys. Rep. 1988 , 161 , 43–101. [ Google Scholar ] [ CrossRef ]
• Bialkowski, S. Photothermal Spectroscopy Methods for Chemical Analysis ; John Wiley: New York, NY, USA, 1996; ISBN 978-1-119-27907-5. [ Google Scholar ]
• Djordjević, K.L.; Galović, S.P.; Popović, M.N.; Nešić, M.V.; Stanimirović, I.P.; Stanimirović, Z.I.; Markushev, D.D. Use neural network in photoacoustic measurement of thermoelastic properties of aluminum foil. Measurement 2022 , 199 , 111537. [ Google Scholar ] [ CrossRef ]
• Rousset, G.; Lepoutre, F.; Bertrand, L. Influence of thermoelastic bending on photoacoustic experiments related to measurements of thermal diffusivity of metals. J. Appl. Phys. 1983 , 54 , 2383–2391. [ Google Scholar ] [ CrossRef ]
• Djordjević, K.L.; Stoisavljević, Z.Z.; Dragaš, M.A.; Stanimirović, I.; Stanimirović, Z.; Suljovrujic, E.; Galović, S.P. Application of neural network to study of frequency range effect to photoacoustic measurement of thermoelastic properties of thin aluminum samples. Measurement 2024 , 236 , 115043. [ Google Scholar ] [ CrossRef ]
• Todorovic, D.; Nikolic, P. Investigation of carrier transport processes in semiconductors by the photoacoustic frequency transmission method. Opt. Eng. 1997 , 36 , 432–445. [ Google Scholar ] [ CrossRef ]
• Mandelis, A.; Hess, P. Semiconductors and Electronic Materials ; SPIE Press: Bellingham, WA, USA, 2000. [ Google Scholar ]
• Lishchuk, P.; Isaiev, M.; Osminkina, L.; Burbelo, R.; Nychyporuk, T.; Timoshenko, V. Photoacoustic characterization of nanowire arrays formed by metal-assisted chemical etching of crystalline silicon substrates with different doping level. Phys. E Low Dimens. Syst. Nanostruct. 2019 , 107 , 131–136. [ Google Scholar ] [ CrossRef ]
• Astrath, N.G.C.; Astrath, F.B.G.; Shen, J.; Lei, C.; Zhou, J.; Sheng Liu, Z.; Navessin, T.; Baesso, M.L.; Bento, A.C. An open-photoacoustic-cell method for thermal characterization of a two-layer system. J. Appl. Phys. 2010 , 107 , 043514. [ Google Scholar ] [ CrossRef ]
• Dubyk, K.; Nychyporuk, T.; Lysenko, V.; Termentzidis, K.; Castanet, G.; Lemoine, F.; Lacroix, D.; Isaiev, M. Thermal properties study of silicon nanostructures by photoacoustic techniques. J. Appl. Phys. 2020 , 127 , 225101. [ Google Scholar ] [ CrossRef ]
• Strzałkowski, K.; Dadarlat, D.; Streza, M.; Zakrzewski, J. Thermal characterization of ZnBeMnSe mixed compounds by means of photopyroelectric and lock-in thermography methods. Appl. Phys. A 2015 , 119 , 1165–1171. [ Google Scholar ] [ CrossRef ]
• Isaiev, M.; Mussabek, G.; Lishchuk, P.; Dubyk, K.; Zhylkybayeva, N.; Yar-Mukhamedova, G.; Lacroix, D.; Lysenko, V. Application of the Photoacoustic Approach in the Characterization of Nanostructured Materials. Nanomaterials 2022 , 12 , 708. [ Google Scholar ] [ CrossRef ]
• Markushev, D.D.; Ordonez-Miranda, J.; Rabasovic, M.D.; Chirtoc, M.; Todorović, D.M.; Bialkowski, S.E.; Korte, D.; Franko, M. Thermal and elastic characterization of glassy carbon thin films by photoacoustic measurements. Eur. Phys. J. Plus 2017 , 132 , 33. [ Google Scholar ] [ CrossRef ]
• Florian, R.; Pelzl, J.; Rosenberg, M.; Vargas, H.; Wernhardt, R. Photoacoustic Detection of Phase Transitions. Phys. Status Solidi A Appl. Res. 1978 , 48 , K35–K38. [ Google Scholar ] [ CrossRef ]
• Olenka, L.; Nogueiran, E.S.; Medina, A.N.; Baesso, M.L.; Bento, A.C.; Muniz, E.C.; Rubira, A.F. Photoacoustic study of PET films and fibers dyed in supercritical CO 2 reactor. Rev. Sci. Instrum. 2003 , 74 , 328–330. [ Google Scholar ] [ CrossRef ]
• Mandelis, A.; Royce, B.S.H. Relaxation time measurements in frequency and time-domain photoacoustic spectroscopy of condensed phases. J. Opt. Soc. Am. 1980 , 70 , 474–480. [ Google Scholar ] [ CrossRef ]
• Djordjevic, K.L.; Milicevic, D.; Galovic, S.P.; Suljovrujic, E.; Jacimovski, S.K.; Furundzic, D.; Popovic, M. Photothermal Response of Polymeric Materials Including Complex Heat Capacity. Int. J. Thermophys. 2022 , 43 , 131–136. [ Google Scholar ] [ CrossRef ]
• Pichardo-Molina, J.L.; Gutiérrez-Juárez, G.; Huerta-Franco, R.; Vargas-Luna, M.; Cholico, P.; Alvarado-Gil, J.J. Open Photoacoustic Cell Technique as a Tool for Thermal and Thermo-Mechanical Characterization of Teeth and Their Restorative Materials. Int. J. Thermophys. 2005 , 26 , 243–253. [ Google Scholar ] [ CrossRef ]
• Dubyk, K.; Borisova, T.; Paliienko, K.; Krisanova, N.; Isaiev, M.; Alekseev, S.; Skryshevsky, V.; Lysenko, V.; Geloen, A. Bio-distribution of Carbon Nanoparticles Studied by Photoacoustic Measurements. Nanoscale Res. Lett. 2022 , 17 , 127. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Galovic, S.P.; Djordjevic, K.L.; Nesic, M.V.; Popovic, M.N.; Markushev, D.D.; Markushev, D.K.; Todorovic, D.M. Time-domain minimum-volume cell photoacoustic of thin semiconductor layer—Part I: Theory. J. Appl. Phys. 2023 , 133 , 245701. [ Google Scholar ] [ CrossRef ]
• Telenkov, S.; Mandelis, A. Signal-to-noise analysis of biomedical photoacoustic measurements in time and frequency domains. Rev. Sci. Inst. 2010 , 81 , 124901. [ Google Scholar ] [ CrossRef ]
• Wang, X.; Ku, Y.G.; Xie, X.; Stoica, G.; Wang, L.V. Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain. Nat. Biotechnol. 2003 , 21 , 803–806. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Xu, M.; Wang, L.V. Photoacoustic imaging in biomedicine. Rev. Sci. Instrum. 2006 , 77 , 041101. [ Google Scholar ] [ CrossRef ]
• Li, C.; Wang, L.V. Photoacoustic tomography and sensing in biomedicine. Phys. Med. Biol. 2009 , 54 , R59–R97. [ Google Scholar ] [ CrossRef ]
• Todorovic, D.M.; Nikolic, P.M. A novel design of photoacoustic cells for the investigation of semiconductors. In Proceedings of the International Conference on Microelectronics, Nis, Serbia, 12–14 September 1995. [ Google Scholar ] [ CrossRef ]
• Hossain, M.; Chowdhury, M.H. Heat Transfer Simulations on Silicon Thin Film Using Pulsed Laser for Photovoltaics Application. J. Adv. Phys. 2017 , 6 , 326–333. [ Google Scholar ] [ CrossRef ]
• Todorovic, D.M.; Cretin, B.; Song, Y.Q.; Vairac, P. Photothermal elastic vibration method: Investigation of the micro-electro-mechanical-systems. J. Phys. Conf. Ser. 2010 , 214 , 012105. [ Google Scholar ] [ CrossRef ]
• Zhang, Z.; Wang, S.; Ding, L.; Liang, X.; Pei, T.; Shen, J.; Peng, L.M. Self-Aligned Ballistic n-Type Single-Walled Carbon Nanotube Field-Effect Transistors with Adjustable Threshold Voltage. Nano Lett. 2008 , 8 , 3696–3701. [ Google Scholar ] [ CrossRef ]
• Ding, L.; Wang, S.; Zhang, Z.; Zeng, Q.; Wang, Z.; Pei, T.; Peng, L.M. Y-Contacted High-Performance n-Type Single-Walled Carbon Nanotube Field-Effect Transistors: Scaling and Comparison with Sc-Contacted Devices. Nano Lett. 2009 , 9 , 4209–4214. [ Google Scholar ] [ CrossRef ]
• Lj Djordjević, K.; Galović, S.P.; Ćojbašić, Ž.M.; Markushev, D.D.; Markushev, D.K.; Aleksić, S.M.; Pantić, D.S. Electronic characterization of plasma-thick n-type silicon using neural networks and photoacoustic response. Opt. Quantum Electron. 2022 , 54 , 485. [ Google Scholar ] [ CrossRef ]
• Nesic, M.V.; Popovic, M.N.; Galovic, S.P.; Djordjevic, K.L.; Jordovic-Pavlovic, M.I.; Miletic, V.V.; Markushev, D.D. Estimation of linear expansion coefficient and thermal diffusivity by photoacoustic numerical self-consistent procedure. J. Appl. Phys. 2022 , 131 , 105104. [ Google Scholar ] [ CrossRef ]
• Nesic, M.; Popovic, M.; Djordjevic, K.; Miletic, V.; Jordovic-Pavlovic, M.; Markushev, D.; Galovic, S. Development and comparison of the techniques for solving the inverse problem in photoacoustic characterization of semiconductors. Opt. Quantum Electron. 2021 , 53 , 381. [ Google Scholar ] [ CrossRef ]
• Šoškić, Z.; Ćirić-Kostić, S.; Galović, S. An extension to the methodology for characterization of thermal properties of thin solid samples by photoacoustic techniques. Int. J. Therm. Sci. 2016 , 109 , 217–230. [ Google Scholar ] [ CrossRef ]
• Herrmann, K.; Pech, N.W.; Retsch, M. Photoacoustic thermal characterization of low thermal diffusivity thin films. Photoacoustics 2021 , 22 , 100246. [ Google Scholar ] [ CrossRef ]
• Bonno, B.; Zeninari, V.; Joly, L.; Parvitte, B. Study of a Thermophysical System with Two Time Constants Using an Open Photoacoustic Cell. Int. J. Thermophys. 2011 , 32 , 630–640. [ Google Scholar ] [ CrossRef ]
• Lashkari, B.; Mandelis, A. Comparison between pulsed laser and frequency-domain photoacoustic modalities: Signal-to-noise ratio, contrast, resolution, and maximum depth detectivity. Rev. Sci. Instrum. 2011 , 82 , 094903. [ Google Scholar ] [ CrossRef ]
• Nikolić, P.M.; Ðurić, S.; Todorović, D.M.; Vasiljević-Radović, D.; Blagojević, V.; Mihajlović, P.; Urošević, D. Application of the photoacoustic method for characterization of natural galena (PbS). Phys. Chem. Miner. 2001 , 28 , 44–51. [ Google Scholar ] [ CrossRef ]
• Djordjevic, K.L.; Markushev, D.D.; Ćojbašić, Ž.M.; Galović, S.P. Photoacoustic measurements of the thermal and elastic properties of n-type silicon using neural networks. Silicon 2020 , 12 , 1289–1300. [ Google Scholar ] [ CrossRef ]
• Djordjevic, K.L.; Markushev, D.D.; Ćojbašić, Ž.M.; Galović, S.P. Inverse problem solving in semiconductor photoacoustics by neural networks. Inverse Probl. Sci. Eng. 2020 , 29 , 248–262. [ Google Scholar ] [ CrossRef ]
• Jordovic-Pavlovic, M.I.; Kupusinac, A.D.; Djordjevic, K.L.; Galovic, S.P.; Markushev, D.D.; Nesic, M.V.; Popovic, M.N. Computationally intelligent description of a photoacoustic detector. Opt. Quantum Electron. 2020 , 52 , 246. [ Google Scholar ] [ CrossRef ]
• Radiša, R.; Dučić, N.; Manasijević, S.; Marković, N.; Ćojbašić, Ž. Casting improvement based on metaheuristic optimization and numerical simulation. Facta Univ. Ser. Mech. Eng. 2017 , 15 , 397–411. [ Google Scholar ] [ CrossRef ]
• Ćojbašić, Ž.M.; Nikolić, V.D.; Ćirić, I.T.; Ćojbašić, L.R. Computationally intelligent modeling and control of fluidized bed combustion process. Therm. Sci. 2011 , 15 , 321–338. [ Google Scholar ] [ CrossRef ]
• Djordjević, K.L.; Jordović-Pavlović, M.I.; Ćojbašić, Ž.M.; Galović, S.P.; Popović, M.N.; Nešić, M.V.; Markushev, D.D. Influence of data scaling and normalization on overall neural network performances in photoacoustics. Opt. Quantum Electron. 2022 , 54 , 501. [ Google Scholar ] [ CrossRef ]
• Bento, A.C.; Mansanares, A.M.; Vargas, H.; Miranda, L.C.M. Photoacoustic Measurements of the Thermal Diffusivity of Anisotropic Samples Using the Phase Lag Method. Phys. Chem. Glas. 1989 , 30 , 160–162. [ Google Scholar ]
• Pessoa, O.; Cesar, C.L.; Patel, N.A.; Vargas, H.; Ghizoni, C.C.; Miranda, L.C. Two-beam Photoacoustic Phase Measurement of the Thermal Diffusivity of Solids. J. Appl. Phys. 1986 , 59 , 1316–1318. [ Google Scholar ] [ CrossRef ]
• Cesar, C.L.; Vargas, H.; Miranda, L.C.M. Photoacoustic Microscopy of Layred Samples: Phase Detection Technique. J. Phys. D Appl. Phys. 1985 , 18 , 599–608. [ Google Scholar ] [ CrossRef ]
• Maliński, M. Determination of the thermal diffusivity from the piezoelectric phase spectra. Phys. Status Solidi A 2003 , 198 , 169–175. [ Google Scholar ] [ CrossRef ]
• Chatterjee, A.; Dziczek, D.; Song, P.; Liu, J.; Wieck, A.D.; Pawlak, M. Effect of amplitude measurements on the precision of thermal parameters’ determination in GaAs using frequency-resolved thermoreflectance. J. Appl. Phys. 2024 , 135 , 225101. [ Google Scholar ] [ CrossRef ]
• Todorovic, D.M.; Nikolic, P.M.; Bojicic, A.I.; Radulovic, K.T. Thermoelastic and electronic strain contribution to the frequency transmission photoacoustic effect in semiconductors. Phys. Rev. B 1997 , 55 , 15631–15642. [ Google Scholar ] [ CrossRef ]
• Ivić, Z.; Zeković, S.; Čevizović, D.; Kostić, D. Phonon hardening due to the small-polaron effect. Phys. B Condens. Matter 2005 , 355 , 417–426. [ Google Scholar ] [ CrossRef ]
• Ivić, Z.; Zeković, S.; Čevizović, D.; Kostić, D.; Vujičić, G. Small-polaron resistivity of the narrow band molecular chain: The influence of phonon hardening. Phys. B Condens. Matter 2005 , 362 , 187–192. [ Google Scholar ] [ CrossRef ]
• Čevizović, D.; Ivić, Z.; Galović, S.; Reshetnyak, A.; Chizhov, A. On the vibron nature in the system of two parallel macromolecular chains: The influence of interchain coupling. Phys. B Condens. Matter 2016 , 490 , 9–15. [ Google Scholar ] [ CrossRef ]
• Čevizović, D.; Galović, S.; Zeković, S.; Ivić, Z. Boundary between coherent and noncoherent small polaron motion: Influence of the phonon hardening. Phys. B Condens. Matter 2009 , 404 , 270–274. [ Google Scholar ] [ CrossRef ]
• Chevizovich, D.; Zdravkovic, S. Nonlinear Dynamics of Nanobiophysics , 1st ed.; Springer: New York, NY, USA, 2022; ISBN 978-981-19-5322-4. [ Google Scholar ]
• Bishop, C.M. Training with noise is equivalent to Tikhonov regularization. Neural Comput. 1995 , 7 , 108–116. [ Google Scholar ] [ CrossRef ]
• Djordjevic, K.L.; Galovic, S.P.; Jordovic-Pavlovic, M.I.; Cojbasic, Z.M.; Markushev, D.D. Improvement of Neural Networks Applied to Photoacoustic Signals of Semiconductors with Added Noise. Silicon 2021 , 13 , 2959–2969. [ Google Scholar ] [ CrossRef ]
• Rifai, S.; Glorot, X.; Bengio, Y.; Vincent, P. Adding noise to the input of a model trained with a regularized objective. arXiv 2011 , arXiv:1104.3250. [ Google Scholar ]
• Zur, R.M.; Jiang, Y.; Pesce, L.L.; Drukker, K. Noise injection for training artificial neural networks: A comparison with weight decay and early stopping. Med. Phys. 2009 , 36 , 4810–4818. [ Google Scholar ] [ CrossRef ]
• Wang, C.; Principe, J.C. Training neural networks with additive noise in the desired signal. IEEE Trans. Neural Netw. 1999 , 10 , 1511–1517. [ Google Scholar ] [ CrossRef ]
• An, G. The effects of adding noise during backpropagation training on a generalization performance. Neural Comput. 1996 , 8 , 643–674. [ Google Scholar ] [ CrossRef ]

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Dragas, M.; Galovic, S.; Milicevic, D.; Suljovrujic, E.; Djordjevic, K. Solution of Inverse Photoacoustic Problem for Semiconductors via Phase Neural Network. Mathematics 2024 , 12 , 2858. https://doi.org/10.3390/math12182858

Dragas M, Galovic S, Milicevic D, Suljovrujic E, Djordjevic K. Solution of Inverse Photoacoustic Problem for Semiconductors via Phase Neural Network. Mathematics . 2024; 12(18):2858. https://doi.org/10.3390/math12182858

Dragas, Milica, Slobodanka Galovic, Dejan Milicevic, Edin Suljovrujic, and Katarina Djordjevic. 2024. "Solution of Inverse Photoacoustic Problem for Semiconductors via Phase Neural Network" Mathematics 12, no. 18: 2858. https://doi.org/10.3390/math12182858

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