explain the problem solving cycle

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• The Three Stages of the Problem-Solving Cycle

Essentially every problem-solving heuristic in mathematics goes back to George Polya’s How to Solve It ; my approach is no exception. However, this cyclic description might help to keep the process cognitively present.

A few months ago, I produced a video describing this the three stages of the problem-solving cycle: Understand, Strategize, and Implement. That is, we must first understand the problem, then we think of strategies that might help solve the problem, and finally we implement those strategies and see where they lead us. During two decades of observing myself and others in the teaching and learning process, I’ve noticed that the most neglected phase is often the first one—understanding the problem.

The Three Stages Explained

• What am I looking for?
• What is the unknown?
• Do I understand every word and concept in the problem?
• Am I familiar with the units in which measurements are given?
• Is there information that seems missing?
• Is there information that seems superfluous?
• Is the source of information bona fide? (Think about those instances when a friend gives you a puzzle to solve and you suspect there’s something wrong with the way the puzzle is posed.)
• Logical reasoning
• Pattern recognition
• Working backwards
• Adopting a different point of view
• Considering extreme cases
• Solving a simpler analogous problem
• Organizing data
• Making a visual representation
• Accounting for all possibilities
• Intelligent guessing and testing

I have produced videos explaining each one of these strategies individually using problems we have solved at the Chapel Hill Math Circle.

• Implementing : We now implement our strategy or set of strategies. As we progress, we check our reasoning and computations (if any). Many novice problem-solvers make the mistake of “doing something” before understanding (or at least thinking they understand) the problem. For instance, if you ask them “What are you looking for?”, they might not be able to answer. Certainly, it is possible to have an incorrect understanding of the problem, but that is different from not even realizing that we have to understand the problem before we attempt to solve it!

As we implement our strategies, we might not be able to solve the problem, but we might refine our understanding of the problem. As we refine our understanding of the problem, we can refine our strategy. As we refine our strategy and implement a new approach, we get closer to solving the problem, and so on. Of course, even after several iterations of this cycle spanning across hours, days, or even years, one may still not be able to solve a particular problem. That’s part of the enchanting beauty of mathematics.

I invite you to observe your own thinking—and that of your students—as you move along the problem-solving cycle!

[1] Problem-Solving Strategies in Mathematics , Posamentier and Krulik, 2015.

About the author: You may contact Hector Rosario at [email protected].

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Article • 7 min read

What Is Problem Solving?

By the Mind Tools Content Team

We all spend a lot of our time solving problems, both at work and in our personal lives.

Some problems are small, and we can quickly sort them out ourselves. But others are complex challenges that take collaboration, creativity, and a considerable amount of effort to solve.

At work, the types of problems we face depend largely on the organizations we're in and the jobs we do. A manager in a cleaning company, for example, might spend their day untangling staffing issues, resolving client complaints, and sorting out problems with equipment and supplies. An aircraft designer, on the other hand, might be grappling with a problem about aerodynamics, or trying to work out why a new safety feature isn't working. Meanwhile, a politician might be exploring solutions to racial injustice or climate change.

But whatever issues we face, there are some common ways to tackle them effectively. And we can all boost our confidence and ability to succeed by building a strong set of problem-solving skills.

Mind Tools offers a large collection of resources to help you do just that!

How Well Do You Solve Problems?

Start by taking an honest look at your existing skills. What's your current approach to solving problems, and how well is it working? Our quiz, How Good Is Your Problem Solving? lets you analyze your abilities, and signposts ways to address any areas of weakness.

Define Every Problem

The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem – not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work. However, if you look a bit deeper, the real issue might be a general lack of training, or an unreasonable workload across the team.

Tools like 5 Whys , Appreciation and Root Cause Analysis get you asking the right questions, and help you to work through the layers of a problem to uncover what's really going on.

However, defining a problem doesn't mean deciding how to solve it straightaway. It's important to look at the issue from a variety of perspectives. If you commit yourself too early, you can end up with a short-sighted solution. The CATWOE checklist provides a powerful reminder to look at many elements that may contribute to the problem, keeping you open to a variety of possible solutions.

Understanding Complexity

As you define your problem, you'll often discover just how complicated it is. There are likely several interrelated issues involved. That's why it's important to have ways to visualize, simplify and make sense of this tangled mess!

Affinity Diagrams are great for organizing many different pieces of information into common themes, and for understanding the relationships between them.

Another popular tool is the Cause-and-Effect Diagram . To generate viable solutions, you need a solid understanding of what's causing the problem.

When your problem occurs within a business process, creating a Flow Chart , Swim Lane Diagram or a Systems Diagram will help you to see how various activities and inputs fit together. This may well highlight a missing element or bottleneck that's causing your problem.

Quite often, what seems to be a single problem turns out to be a whole series of problems. The Drill Down technique prompts you to split your problem into smaller, more manageable parts.

General Problem-Solving Tools

When you understand the problem in front of you, you’re ready to start solving it. With your definition to guide you, you can generate several possible solutions, choose the best one, then put it into action. That's the four-step approach at the heart of good problem solving.

There are various problem-solving styles to use. For example:

• Constructive Controversy is a way of widening perspectives and energizing discussions.
• Inductive Reasoning makes the most of people’s experiences and know-how, and can speed up solution finding.
• Means-End Analysis can bring extra clarity to your thinking, and kick-start the process of implementing solutions.

Specific Problem-Solving Systems

Some particularly complicated or important problems call for a more comprehensive process. Again, Mind Tools has a range of approaches to try, including:

• Simplex , which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your organization.
• Appreciative Inquiry , which is a uniquely positive way of solving problems by examining what's working well in the areas surrounding them.
• Soft Systems Methodology , which takes you through four stages to uncover more details about what's creating your problem, and then define actions that will improve the situation.

Further Problem-Solving Strategies

Good problem solving requires a number of other skills – all of which are covered by Mind Tools.

For example, we have a large section of resources to improve your Creativity , so that you come up with a range of possible solutions.

By strengthening your Decision Making , you'll be better at evaluating the options, selecting the best ones, then choosing how to implement them.

And our Project Management collection has valuable advice for strengthening the whole problem-solving process. The resources there will help you to make effective changes – and then keep them working long term.

Problems are an inescapable part of life, both in and out of work. So we can all benefit from having strong problem-solving skills.

It's important to understand your current approach to problem solving, and to know where and how to improve.

Define every problem you encounter – and understand its complexity, rather than trying to solve it too soon.

There's a range of general problem-solving approaches, helping you to generate possible answers, choose the best ones, and then implement your solution.

Some complicated or serious problems require more specific problem-solving systems, especially when they relate to business processes.

By boosting your creativity, decision-making and project-management skills, you’ll become even better at solving all the problems you face.

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Problem-Solving Strategies and Obstacles

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

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

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

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

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

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

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

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

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

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

National Alliance on Mental Illness. Warning signs and symptoms .

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

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

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

Continuous Improvement Toolkit

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Applying the PDCA Cycle: A Blueprint for Continuous Improvement

• 5 MINUTES READ

Also known as Shewhart Cycle and Deming Wheel.

Variants include PDSA Cycle and OPDCA.

The Plan-Do-Check-Act Cycle (PDCA Cycle) is a four-step model for systematic problem solving and continuous improvement. It offers a simple and structured way for resolving business-related issues and creating positive change . This framework is widely recognized as the basis for enhancing the quality of processes, products, and services by following a logical sequence of four steps: Plan, Do, Check, and Act.

The PDCA cycle model can be applied in most kinds of projects and improvement activities, whether they are breakthrough changes or smaller incremental enhancements. For example, it can be effectively utilized when aiming to enhance employee skill levels within an organization, change the supplier of a product or service, or increase the quality of care and patient engagement within a hospital.

A common practical example of the PDCA cycle can be illustrated when dealing with customer complaints. This scenario involves steps like reviewing, categorizing, and prioritizing the existing complaints, generating potential solutions for addressing the most frequent complaints, conducting pilot surveys with sample customers to test new options, collecting and analyzing customer data and feedback, and ultimately implementing lessons learned on a larger scale. The above steps represent the PDCA cycle in action.

The Four Phases of the PDCA Cycle

The PDCA cycle begins with the Planning phase which involves the identification of the problem and objectives. During this phase, a collaborative effort is made to agrees on the problem to be solved or the process to be improved. Subsequently, an in-depth analysis of the existing as-is situation is conducted, alternative solutions are identified, and the most promising solution is selected and scheduled for implementation.

In the Do phase, the selected solution is put into action on a limited scale. This phase also involves ongoing progress measurement, data collection, and feedback gathering to facilitate subsequent analyses.

The Check phase involves analyzing the collected data and feedback and comparing the outcome against pre-established objectives. This phase allows to evaluate how well the solution has worked and where further enhancement may be needed. Additionally, it involves the identification of unexpected issues and the gathering of key learnings. It is important to note that the Do and Check phases may need to be repeated until the desired results are achieved.

The Act phase is the point at which the chosen solution is fully integrated. This phase requires taking actions based on the insights acquired from the Check phase. A plan for full-scale implementation is carried out, taking into account the associated costs and benefits. The Act phase also concerned with standardizing , documenting, sustaining the improved process, as well as integrating it into the organization’s system.

The utilization of the PDCA cycle doesn’t necessarily stop once the Act phase is completed. The improved process often becomes the new baseline, which may prompt a return to the Plan phase. Multiple iterations of the PDCA cycle may be essential for a permanent resolution of the problem and the attainment of the desired future state. Each cycle brings one closer to their goals and extends their knowledge further.

A common example often used to illustrate the PDCA cycle is when a team is initiating a new product development.

Another example is when a lab team is planning to solve a customer complaint about the delayed test results at a laboratory.

In the 1990s, a modified version of the PDCA cycle was introduced. It was called PDSA cycle where ‘S’ stands for Study. It is believed that data analysis is important for any improvement effort, and “Checking” does not really imply studying and analyzing the data.

OPDCA is another version of PDCA where ‘O’ stands for Observe . The Observe is added at the front of the cycle to emphasize the need to observe before creating any plan. The goal of observation is to find out what is really happening and what can be improved.

You may find it useful to use the following tools in each phase of the PDCA/PDSA cycle:

• Plan – process mapping , brainstorming, waste analysis , prioritization matrix , improvement roadmap , gap analysis , and force field analysis .
• Do – Gantt chart , dashboard, data collection methods , sampling, observation , check sheet , and control chart.
• Check/Study – graphical analysis , statistical analysis, 5 whys , fishbone diagram , Pareto analysis , root cause analysis, and decision-making techniques .
• Act – process mapping , Gantt chart , dashboard, control chart, control plan, visual management , and standard work .

Several tools are available to aid in planning and monitoring project activities using the PDCA model. One of the most straightforward methods is to use this  PDCA template .

Wrapping Up

PDCA represents the logical way of thinking we tend to follow when resolving problems and implementing continuous improvement. The objective is to make significant progress towards achieving the intended goal. Furthermore, it is important to note that the PDCA model stands at the core of almost all quality management systems. TQM, ISO standards and the A3 thinking process are all based around the PDCA philosophy.

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Problem Solving Cycle

This tool would be taught to the students at the beginning of the year, and then a poster of the cycle would be put in the room to remind students of the cycle so they can use it when they have a conflict with another student. The cycle is identify the problem, brainstorm ideas, weigh pros and cons, overcome obstacles, action steps, and then to reflect on the whole situation. Each of these steps will allow for students to self-identify the problem, what they think is causing the problem, and steps that need to be taken in order to solve the problem. The teacher should only intervene in the situation if the students are unable to go through the cycle successfully by themselves. This process teaches students to rely on themselves to solve problems rather than just having the teacher solve the problem for them.

This tool is in the corrective phase because it is being used to correct the behaviors and problems between students. This cycle also restores the conflicts in hope of starting a better relationship between students. Students will use this tool to solve problems with a student, and then can use the same steps again when another problem arises with perhaps a different student. This tool is mostly student centered but can become collaborative because it is up to the students the first time through the cycle to try to take all the steps to solving the problems themselves. However, if the students unsuccessfully go through the cycle without coming to an agreement on how to solve the problem, the teacher will then help to complete cycle so the students are able to come to an agreement on how to solve the issue.

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• What is the Plan-Do-Check-Act (PDCA) cy ...

What is the Plan-Do-Check-Act (PDCA) cycle?

The PDCA cycle is a useful technique for addressing, analyzing, and solving business problems. Because the PDCA cycle is built on the process of continuous improvement, it offers a level of flexibility and iterative improvement. 

PDCA cycle history

The PDCA cycle was first introduced by Walter Shewhart , the father of statistical quality control. In his book, Economic control of quality manufactured product , Shewhart applied the scientific method to economic quality control. 

Shewhart’s thesis was further developed by W. Edwards Deming , who championed Shewhart’s work. Deming expanded on Shewhart’s idea and used the scientific method not only for quality control but also process improvement.

Deming went on to teach the method—which he called the Shewhart cycle—to Japanese engineers. There, the Shewhart cycle mixed with kaizen (the Japanese principle of continuous improvement , which was developed by Kaoru Ishikawa ), the Toyota production system, and lean manufacturing to become what we now call the Plan-Do-Check-Act (PDCA) cycle. 

Nowadays, the Plan-Do-Check-Act cycle is commonly used as part of lean project management .

This methodology has many names, including:

Plan-Do-Check-Act cycle, or PDCA cycle

Deming cycle or Deming wheel

Shewhart cycle

Control cycle

Plan-Do-Study-Act cycle or PDSA cycle 

When should you use the PDCA cycle?

The PDCA cycle is a framework for how to approach and resolve project management and process improvement problems. As a result, it can be implemented for a wide variety of projects. Teams that use the PDCA cycle effectively embrace the element of continuous improvement—rather than using the cycle for an end-to-end process, the PDCA cycle is a way to ensure continuous improvement and implement the iterative process . 

The Plan-Do-Check-Act cycle is particularly useful when you want to:

Streamline and improve a repetitive work process

Develop a new business process

Get started with continuous improvement

Rapidly iterate on change and see immediate results

Minimize errors and maximize outcomes

Test multiple solutions quickly

4 steps to use the PDCA cycle

The four steps of the PDCA process are in the name: planning, doing, checking, and actioning. Notably, this process is a cycle, so as soon as you reach the end, you can start over from the beginning again. 

The first step to any process improvement or project planning is to figure out what you need to do. Like any project plan , this includes a variety of information, including:

The project objectives

Success metrics

The project deliverables or end result

Project stakeholders

The project timeline

Any relevant project risks or constraints

You can use the PDCA cycle for a wide variety of projects. Whether you’re building a new project from scratch or using the PDCA as a quality improvement project, investing in a robust planning phase is a great way to set the project on the right track. 

Keep in mind that PDCA is a cycle. It’s okay if you don’t have all of the answers the first time around, since you’ll probably run this cycle multiple times. Each time you re-run the PDCA cycle, evaluate your project plan to ensure it’s up-to-date and accurate towards your project goals. 

Once you’ve ironed out your project plan, the next step is to try it out. Like most types of lean project management, PDCA embraces small, incremental changes. During the Do phase of the PDCA cycle, implement the project plan on a small scale to ensure it works. 

Review the test you ran during the Do phase of the PDCA cycle to ensure everything went according to plan. More likely than not, you will identify things to improve on during the Do phase. After all, it isn’t called continuous improvement for nothing! The Check phase is critical to finding these small things before they get too big and problematic. 

If necessary, revisit your project plan to ensure your project is still hitting your project objectives. Alternatively, if you realized you need to make a change to the project plan, you can also do so now. 

After the check, move to the Act phase, which includes rolling out the full project or process improvement. Don’t forget that the PDCA cycle is a cycle. If you need to, return to the Plan phase to continuously improve your project or processes. 

Pros and cons of the Plan-Do-Check-Act cycle

The PDCA cycle is a powerful tool to continuously improve, but there are also some disadvantages to using this system as well. Take a look at the pros and cons of the PDCA cycle: 

Helpful for teams looking to get started with continuous improvement

Flexible methodology for virtually any project

Quickly implement change and see results

Use the PDCA as your standard operating procedure to increase org-wide standardization without the use of a project management office (PMO)

Proven continuous improvement methodology

You need support from senior management in order for the PDCA cycle to be particularly effective

Value comes from running the cycle over and over again. Not an effective methodology if you only plan on doing it once. 

Requires time to implement and learn

Isn’t a great solution for urgent projects, since you typically expect to run the cycle multiple times

Planned-Done-Checked-Actioned

The PDCA cycle is an effective way to implement continuous improvement and problem solving. To get the most out of the PDCA cycle, set your projects up for success with project planning tools . Plan, manage, and track your team’s projects to hit your deliverables on time. 

Related resources

Unmanaged business goals don’t work. Here’s what does.

How Asana uses work management to drive product development

How Asana uses work management to streamline project intake processes

How Asana uses work management for smoother creative production

7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

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by TickTick

PDCA Cycle Explained: 4 Steps for Continuous Learning and Improvement

The Meaning of PDCA Cycle

PDCA Cycle (also known as PDSA Cycle or Deming Cycle), is a problem-solving method used for the continuous learning and improvement of a process or product. 

There are 4 basic steps in PDCA Cycle:

• Plan : identify a problem and possible solutions
• Do : execute the plan and test the solution(s)
• Check : evaluate the results and lessons learned
• Act : improve the plan/process for better solutions

These four steps incorporate inductive-deductive interplay and have been a simple and scientific approach for problem-solving (process-improving). It follows the curve of how we acquire knowledge through constant reflection, standardization, and modification.

The PDCA framework begins with a planning phase where a problem or a process to be improved is identified. This involves not only the goal setting and finding possible solutions, but also hypothesizing methods that can be used to reach the ultimate goal. Another thing that needs special attention is defining the success metrics. This simply means a clear evaluation matrix is ideally to be set beforehand.

Then, the solution(s) will be tested in the Do process. To detach the Do, there could be two steps: making the Do multiple To-Dos by splitting the task and defining them with a specific time, personnel, and steps, and collecting real-time data and feedback. 

Check includes analyzing the results and comparing them to the hypothesis in the Plan stage: how well the solution worked, how much the goal has been achieved, and whether the methods were proven feasible. If there are any unexpected issues, you may also need to find the causes and possible solutions. Note that there might be forth and back between Do and check.

The Act step closes the cycle, which involves adjustment on the initial goal or solutions and integration of all key learnings by the entire process, to standardize successful parts and avoid error recurrence. In a nutshell, the Act phase summarizes the current cycle and prepares for the next.

However, the PDCA cycle doesn’t stop here. Instead, it can repeat from the beginning with a modified version of the Plan. There is no end to it and sustainability should be its main pitch.

How PDCA Has Evolved

Usually used interchangeably with “PDSA Cycle”, “Deming Cycle”, “Deming wheel”, “Shewhart Cycle” etc, the PDCA model has indeed confronted some misunderstanding and confusion. It remains unexplained in most cases how PDCA became what it is today and what’s the difference between those mysterious terminologies and how they interact. According to Ronald D. Moen & Clifford L. Norman , its evolution could be summarized like the following:

Shewhart cycle (1939): Specification - Production - Inspection . 

He brought up this method from the viewpoint of Quality Control.

Deming Wheel (1950): Design the product - Make the product - Sell it - Test it .

Deming built off the Shewhart cycle and emphasized the four steps should be rotated constantly to aim for the product quality. This has gained increasing popularity when Deming participated in the Japanese Union of Scientists and Engineers (JUSE).

PDCA Cycle (the 1950s):  Plan - Do - Check - Act.

A Japanese executive reworked the Deming Wheel and translated it into the PDCA Cycle for problem-solving. PDCA emphasizes more on the establishment of standards during the process and the ongoing modification of those standards. 

Extended PDCA Cycle (1985): Plan - Do - Check - Act .

Kaoru Ishikawa refined the PDCA model to include more steps in the Plan and Do steps: Identify the goals and methods to use; involve in training and education during implementation.

PDSA Cycle (1985): Plan - Do - Study - Act .

Deming claimed that the ownership of PDCA Cycle was never recognized by anyone and the word “check” was used incorrectly because it means “to hold back”. Therefore, he replaced it with “study” to emphasize the importance of the continuous learning-improvement model.

How to Implement - PDCA Examples

Now, you’ve got a clear idea of what the PDCA Cycle is and how it changes over time. As a simple and structured method widely adopted in Quality Control and Total Quality Management, can it also be applied in wider areas, such as personal growth and business development? Yes, I’ll give you a couple of examples.

Benefits of PDCA Cycle

Among all those other methods, why does the PDCA model shade some lights in the history, especially known for the “Japanese Quality” and is still widely used today? Some key benefits of it need to be valued.

PDCA methodology emphasizes minimizing errors and maximizing outcomes. When applied to business development, e.g. a product’s iterations, it could ensure a developing path where the product is shaped better and better to the market and customers. It’s the same when it comes to personal growth. It also leaves space for constant check and reflection, which can avoid wasting time on the mistakes or making the same mistakes.

PDCA framework follows a learning curve and enhances the learning-improvement process continually. This is the key factor defining PDCA as a scientific and methodical way to gain knowledge. With knowledge building up, people’s ability goes up. 

PDCA model encourages a growth mindset. Seeing continuous improvements is a good way to enhance individuals’ self-esteem levels and bring a great sense of accomplishment. People tend to find meaning in the things they do. Imagine if one stops making progress, they would stay in the static and lose meaning in repetitive work and life. 

• PDCA Cycle is a simple and scientific way for problem-solving and process improvement.
• PDCA Cycle involves four key steps: Plan, Do, Check and Act.
• PDCA works slightly differently from Deming Cycle, Shewhart Cycle, and PDSA.
• PDCA Cycle is a never-ending process that can be used on a continual basis.
• PDCA Cycle can be used for quality control, business development, and personal growth.

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Exploring the Problem Solving Cycle in Computer Science – Strategies, Techniques, and Tools

• Post author By bicycle-u
• Post date 08.12.2023

The world of computer science is built on the foundation of problem solving. Whether it’s finding a solution to a complex algorithm or analyzing data to make informed decisions, the problem solving cycle is at the core of every computer science endeavor.

At its essence, problem solving in computer science involves breaking down a complex problem into smaller, more manageable parts. This allows for a systematic approach to finding a solution by analyzing each part individually. The process typically starts with gathering and understanding the data or information related to the problem at hand.

Once the data is collected, computer scientists use various techniques and algorithms to analyze and explore possible solutions. This involves evaluating different approaches and considering factors such as efficiency, accuracy, and scalability. During this analysis phase, it is crucial to think critically and creatively to come up with innovative solutions.

After a thorough analysis, the next step in the problem solving cycle is designing and implementing a solution. This involves creating a detailed plan of action, selecting the appropriate tools and technologies, and writing the necessary code to bring the solution to life. Attention to detail and precision are key in this stage to ensure that the solution functions as intended.

The final step in the problem solving cycle is evaluating the solution and its effectiveness. This includes testing the solution against different scenarios and data sets to ensure its reliability and performance. If any issues or limitations are discovered, adjustments and optimizations are made to improve the solution.

In conclusion, the problem solving cycle is a fundamental process in computer science, involving analysis, data exploration, algorithm development, solution implementation, and evaluation. It is through this cycle that computer scientists are able to tackle complex problems and create innovative solutions that drive progress in the field of computer science.

Understanding the Importance

In computer science, problem solving is a crucial skill that is at the core of the problem solving cycle. The problem solving cycle is a systematic approach to analyzing and solving problems, involving various stages such as problem identification, analysis, algorithm design, implementation, and evaluation. Understanding the importance of this cycle is essential for any computer scientist or programmer.

Data Analysis and Algorithm Design

The first step in the problem solving cycle is problem identification, which involves recognizing and defining the issue at hand. Once the problem is identified, the next crucial step is data analysis. This involves gathering and examining relevant data to gain insights and understand the problem better. Data analysis helps in identifying patterns, trends, and potential solutions.

After data analysis, the next step is algorithm design. An algorithm is a step-by-step procedure or set of rules to solve a problem. Designing an efficient algorithm is crucial as it determines the effectiveness and efficiency of the solution. A well-designed algorithm takes into consideration the constraints, resources, and desired outcomes while implementing the solution.

Implementation and Evaluation

Once the algorithm is designed, the next step in the problem solving cycle is implementation. This involves translating the algorithm into a computer program using a programming language. The implementation phase requires coding skills and expertise in a specific programming language.

After implementation, the solution needs to be evaluated to ensure that it solves the problem effectively. Evaluation involves testing the program and verifying its correctness and efficiency. This step is critical to identify any errors or issues and to make necessary improvements or adjustments.

In conclusion, understanding the importance of the problem solving cycle in computer science is essential for any computer scientist or programmer. It provides a systematic and structured approach to analyze and solve problems, ensuring efficient and effective solutions. By following the problem solving cycle, computer scientists can develop robust algorithms, implement them in efficient programs, and evaluate their solutions to ensure their correctness and efficiency.

Identifying the Problem

In the problem solving cycle in computer science, the first step is to identify the problem that needs to be solved. This step is crucial because without a clear understanding of the problem, it is impossible to find a solution.

Identification of the problem involves a thorough analysis of the given data and understanding the goals of the task at hand. It requires careful examination of the problem statement and any constraints or limitations that may affect the solution.

During the identification phase, the problem is broken down into smaller, more manageable parts. This can involve breaking the problem down into sub-problems or identifying the different aspects or components that need to be addressed.

Identifying the problem also involves considering the resources and tools available for solving it. This may include considering the specific tools and programming languages that are best suited for the problem at hand.

By properly identifying the problem, computer scientists can ensure that they are focused on the right goals and are better equipped to find an effective and efficient solution. It sets the stage for the rest of the problem solving cycle, including the analysis, design, implementation, and evaluation phases.

Gathering the Necessary Data

Before finding a solution to a computer science problem, it is essential to gather the necessary data. Whether it’s writing a program or developing an algorithm, data serves as the backbone of any solution. Without proper data collection and analysis, the problem-solving process can become inefficient and ineffective.

The Importance of Data

In computer science, data is crucial for a variety of reasons. First and foremost, it provides the information needed to understand and define the problem at hand. By analyzing the available data, developers and programmers can gain insights into the nature of the problem and determine the most efficient approach for solving it.

Additionally, data allows for the evaluation of potential solutions. By collecting and organizing relevant data, it becomes possible to compare different algorithms or strategies and select the most suitable one. Data also helps in tracking progress and measuring the effectiveness of the chosen solution.

Data Gathering Process

The process of gathering data involves several steps. Firstly, it is necessary to identify the type of data needed for the particular problem. This may include numerical values, textual information, or other types of data. It is important to determine the sources of data and assess their reliability.

Once the required data has been identified, it needs to be collected. This can be done through various methods, such as surveys, experiments, observations, or by accessing existing data sets. The collected data should be properly organized, ensuring its accuracy and validity.

Data cleaning and preprocessing are vital steps in the data gathering process. This involves removing any irrelevant or erroneous data and transforming it into a suitable format for analysis. Properly cleaned and preprocessed data will help in generating reliable and meaningful insights.

Data Analysis and Interpretation

After gathering and preprocessing the data, the next step is data analysis and interpretation. This involves applying various statistical and analytical methods to uncover patterns, trends, and relationships within the data. By analyzing the data, programmers can gain valuable insights that can inform the development of an effective solution.

During the data analysis process, it is crucial to remain objective and unbiased. The analysis should be based on sound reasoning and logical thinking. It is also important to communicate the findings effectively, using visualizations or summaries to convey the information to stakeholders or fellow developers.

In conclusion, gathering the necessary data is a fundamental step in solving computer science problems. It provides the foundation for understanding the problem, evaluating potential solutions, and tracking progress. By following a systematic and rigorous approach to data gathering and analysis, developers can ensure that their solutions are efficient, effective, and well-informed.

Analyzing the Data

Once you have collected the necessary data, the next step in the problem-solving cycle is to analyze it. Data analysis is a crucial component of computer science, as it helps us understand the problem at hand and develop effective solutions.

To analyze the data, you need to break it down into manageable pieces and examine each piece closely. This process involves identifying patterns, trends, and outliers that may be present in the data. By doing so, you can gain insights into the problem and make informed decisions about the best course of action.

There are several techniques and tools available for data analysis in computer science. Some common methods include statistical analysis, data visualization, and machine learning algorithms. Each approach has its own strengths and limitations, so it’s essential to choose the most appropriate method for the problem you are solving.

Statistical Analysis

Statistical analysis involves using mathematical models and techniques to analyze data. It helps in identifying correlations, distributions, and other statistical properties of the data. By applying statistical tests, you can determine the significance and validity of your findings.

Data Visualization

Data visualization is the process of presenting data in a visual format, such as charts, graphs, or maps. It allows for a better understanding of complex data sets and facilitates the communication of findings. Through data visualization, patterns and trends can become more apparent, making it easier to derive meaningful insights.

Machine Learning Algorithms

Machine learning algorithms are powerful tools for analyzing large and complex data sets. These algorithms can automatically detect patterns and relationships in the data, leading to the development of predictive models and solutions. By training the algorithm on a labeled dataset, it can learn from the data and make accurate predictions or classifications.

In conclusion, analyzing the data is a critical step in the problem-solving cycle in computer science. It helps us gain a deeper understanding of the problem and develop effective solutions. Whether through statistical analysis, data visualization, or machine learning algorithms, data analysis plays a vital role in transforming raw data into actionable insights.

Exploring Possible Solutions

Once you have gathered data and completed the analysis, the next step in the problem-solving cycle is to explore possible solutions. This is where the true power of computer science comes into play. With the use of algorithms and the application of scientific principles, computer scientists can develop innovative solutions to complex problems.

During this stage, it is important to consider a variety of potential solutions. This involves brainstorming different ideas and considering their feasibility and potential effectiveness. It may be helpful to consult with colleagues or experts in the field to gather additional insights and perspectives.

Developing an Algorithm

One key aspect of exploring possible solutions is the development of an algorithm. An algorithm is a step-by-step set of instructions that outlines a specific process or procedure. In the context of problem solving in computer science, an algorithm provides a clear roadmap for implementing a solution.

The development of an algorithm requires careful thought and consideration. It is important to break down the problem into smaller, manageable steps and clearly define the inputs and outputs of each step. This allows for the creation of a logical and efficient solution.

Evaluating the Solutions

Once you have developed potential solutions and corresponding algorithms, the next step is to evaluate them. This involves analyzing each solution to determine its strengths, weaknesses, and potential impact. Consider factors such as efficiency, scalability, and resource requirements.

It may be helpful to conduct experiments or simulations to further assess the effectiveness of each solution. This can provide valuable insights and data to support the decision-making process.

Ultimately, the goal of exploring possible solutions is to find the most effective and efficient solution to the problem at hand. By leveraging the power of data, analysis, algorithms, and scientific principles, computer scientists can develop innovative solutions that drive progress and solve complex problems in the world of technology.

Evaluating the Options

Once you have identified potential solutions and algorithms for a problem, the next step in the problem-solving cycle in computer science is to evaluate the options. This evaluation process involves analyzing the potential solutions and algorithms based on various criteria to determine the best course of action.

Consider the Problem

Before evaluating the options, it is important to take a step back and consider the problem at hand. Understand the requirements, constraints, and desired outcomes of the problem. This analysis will help guide the evaluation process.

Analyze the Options

Next, it is crucial to analyze each solution or algorithm option individually. Look at factors such as efficiency, accuracy, ease of implementation, and scalability. Consider whether the solution or algorithm meets the specific requirements of the problem, and if it can be applied to related problems in the future.

Additionally, evaluate the potential risks and drawbacks associated with each option. Consider factors such as cost, time, and resources required for implementation. Assess any potential limitations or trade-offs that may impact the overall effectiveness of the solution or algorithm.

Select the Best Option

Based on the analysis, select the best option that aligns with the specific problem-solving goals. This may involve prioritizing certain criteria or making compromises based on the limitations identified during the evaluation process.

Remember that the best option may not always be the most technically complex or advanced solution. Consider the practicality and feasibility of implementation, as well as the potential impact on the overall system or project.

In conclusion, evaluating the options is a critical step in the problem-solving cycle in computer science. By carefully analyzing the potential solutions and algorithms, considering the problem requirements, and considering the limitations and trade-offs, you can select the best option to solve the problem at hand.

Making a Decision

Decision-making is a critical component in the problem-solving process in computer science. Once you have analyzed the problem, identified the relevant data, and generated a potential solution, it is important to evaluate your options and choose the best course of action.

Consider All Factors

When making a decision, it is important to consider all relevant factors. This includes evaluating the potential benefits and drawbacks of each option, as well as understanding any constraints or limitations that may impact your choice.

In computer science, this may involve analyzing the efficiency of different algorithms or considering the scalability of a proposed solution. It is important to take into account both the short-term and long-term impacts of your decision.

Weigh the Options

Once you have considered all the factors, it is important to weigh the options and determine the best approach. This may involve assigning weights or priorities to different factors based on their importance.

Using techniques such as decision matrices or cost-benefit analysis can help you systematically compare and evaluate different options. By quantifying and assessing the potential risks and rewards, you can make a more informed decision.

Remember: Decision-making in computer science is not purely subjective or based on personal preference. It is crucial to use analytical and logical thinking to select the most optimal solution.

In conclusion, making a decision is a crucial step in the problem-solving process in computer science. By considering all relevant factors and weighing the options using logical analysis, you can choose the best possible solution to a given problem.

Implementing the Solution

Once the problem has been analyzed and a solution has been proposed, the next step in the problem-solving cycle in computer science is implementing the solution. This involves turning the proposed solution into an actual computer program or algorithm that can solve the problem.

In order to implement the solution, computer science professionals need to have a strong understanding of various programming languages and data structures. They need to be able to write code that can manipulate and process data in order to solve the problem at hand.

During the implementation phase, the proposed solution is translated into a series of steps or instructions that a computer can understand and execute. This involves breaking down the problem into smaller sub-problems and designing algorithms to solve each sub-problem.

Computer scientists also need to consider the efficiency of their solution during the implementation phase. They need to ensure that the algorithm they design is able to handle large amounts of data and solve the problem in a reasonable amount of time. This often requires optimization techniques and careful consideration of the data structures used.

Once the code has been written and the algorithm has been implemented, it is important to test and debug the solution. This involves running test cases and checking the output to ensure that the program is working correctly. If any errors or bugs are found, they need to be fixed before the solution can be considered complete.

In conclusion, implementing the solution is a crucial step in the problem-solving cycle in computer science. It requires strong programming skills and a deep understanding of algorithms and data structures. By carefully designing and implementing the solution, computer scientists can solve problems efficiently and effectively.

Testing and Debugging

In computer science, testing and debugging are critical steps in the problem-solving cycle. Testing helps ensure that a program or algorithm is functioning correctly, while debugging analyzes and resolves any issues or bugs that may arise.

Testing involves running a program with specific input data to evaluate its output. This process helps verify that the program produces the expected results and handles different scenarios correctly. It is important to test both the normal and edge cases to ensure the program’s reliability.

Debugging is the process of identifying and fixing errors or bugs in a program. When a program does not produce the expected results or crashes, it is necessary to go through the code to find and fix the problem. This can involve analyzing the program’s logic, checking for syntax errors, and using debugging tools to trace the flow of data and identify the source of the issue.

Data analysis plays a crucial role in both testing and debugging. It helps to identify patterns, anomalies, or inconsistencies in the program’s behavior. By analyzing the data, developers can gain insights into potential issues and make informed decisions on how to improve the program’s performance.

In conclusion, testing and debugging are integral parts of the problem-solving cycle in computer science. Through testing and data analysis, developers can verify the correctness of their programs and identify and resolve any issues that may arise. This ensures that the algorithms and programs developed in computer science are robust, reliable, and efficient.

Iterating for Improvement

In computer science, problem solving often involves iterating through multiple cycles of analysis, solution development, and evaluation. This iterative process allows for continuous improvement in finding the most effective solution to a given problem.

The problem solving cycle starts with problem analysis, where the specific problem is identified and its requirements are understood. This step involves examining the problem from various angles and gathering all relevant information.

Once the problem is properly understood, the next step is to develop an algorithm or a step-by-step plan to solve the problem. This algorithm is a set of instructions that, when followed correctly, will lead to the solution.

After the algorithm is developed, it is implemented in a computer program. This step involves translating the algorithm into a programming language that a computer can understand and execute.

Once the program is implemented, it is then tested and evaluated to ensure that it produces the correct solution. This evaluation step is crucial in identifying any errors or inefficiencies in the program and allows for further improvement.

If any issues or problems are found during testing, the cycle iterates, starting from problem analysis again. This iterative process allows for refinement and improvement of the solution until the desired results are achieved.

Iterating for improvement is a fundamental concept in computer science problem solving. By continually analyzing, developing, and evaluating solutions, computer scientists are able to find the most optimal and efficient approaches to solving problems.

Documenting the Process

Documenting the problem-solving process in computer science is an essential step to ensure that the cycle is repeated successfully. The process involves gathering information, analyzing the problem, and designing a solution.

During the analysis phase, it is crucial to identify the specific problem at hand and break it down into smaller components. This allows for a more targeted approach to finding the solution. Additionally, analyzing the data involved in the problem can provide valuable insights and help in designing an effective solution.

Once the analysis is complete, it is important to document the findings. This documentation can take various forms, such as written reports, diagrams, or even code comments. The goal is to create a record that captures the problem, the analysis, and the proposed solution.

Documenting the process serves several purposes. Firstly, it allows for easy communication and collaboration between team members or future developers. By documenting the problem, analysis, and solution, others can easily understand the thought process behind the solution and potentially build upon it.

Secondly, documenting the process provides an opportunity for reflection and improvement. By reviewing the documentation, developers can identify areas where the problem-solving cycle can be strengthened or optimized. This continuous improvement is crucial in the field of computer science, as new challenges and technologies emerge rapidly.

In conclusion, documenting the problem-solving process is an integral part of the computer science cycle. It allows for effective communication, collaboration, and reflection on the solutions devised. By taking the time to document the process, developers can ensure a more efficient and successful problem-solving experience.

Communicating the Solution

Once the problem solving cycle is complete, it is important to effectively communicate the solution. This involves explaining the analysis, data, and steps taken to arrive at the solution.

Analyzing the Problem

During the problem solving cycle, a thorough analysis of the problem is conducted. This includes understanding the problem statement, gathering relevant data, and identifying any constraints or limitations. It is important to clearly communicate this analysis to ensure that others understand the problem at hand.

Presenting the Solution

The next step in communicating the solution is presenting the actual solution. This should include a detailed explanation of the steps taken to solve the problem, as well as any algorithms or data structures used. It is important to provide clear and concise descriptions of the solution, so that others can understand and reproduce the results.

Overall, effective communication of the solution in computer science is essential to ensure that others can understand and replicate the problem solving process. By clearly explaining the analysis, data, and steps taken, the solution can be communicated in a way that promotes understanding and collaboration within the field of computer science.

Reflecting and Learning

Reflecting and learning are crucial steps in the problem solving cycle in computer science. Once a problem has been solved, it is essential to reflect on the entire process and learn from the experience. This allows for continuous improvement and growth in the field of computer science.

During the reflecting phase, one must analyze and evaluate the problem solving process. This involves reviewing the initial problem statement, understanding the constraints and requirements, and assessing the effectiveness of the chosen algorithm and solution. It is important to consider the efficiency and accuracy of the solution, as well as any potential limitations or areas for optimization.

By reflecting on the problem solving cycle, computer scientists can gain valuable insights into their own strengths and weaknesses. They can identify areas where they excelled and areas where improvement is needed. This self-analysis helps in honing problem solving skills and becoming a better problem solver.

Learning from Mistakes

Mistakes are an integral part of the problem solving cycle, and they provide valuable learning opportunities. When a problem is not successfully solved, it is essential to analyze the reasons behind the failure and learn from them. This involves identifying errors in the algorithm or solution, understanding the underlying concepts or principles that were misunderstood, and finding alternative approaches or strategies.

Failure should not be seen as a setback, but rather as an opportunity for growth. By learning from mistakes, computer scientists can improve their problem solving abilities and expand their knowledge and understanding of computer science. It is through these failures and the subsequent learning process that new ideas and innovations are often born.

Continuous Improvement

Reflecting and learning should not be limited to individual problem solving experiences, but should be an ongoing practice. As computer science is a rapidly evolving field, it is crucial to stay updated with new technologies, algorithms, and problem solving techniques. Continuous learning and improvement contribute to staying competitive and relevant in the field.

Computer scientists can engage in continuous improvement by seeking feedback from peers, participating in research and development activities, attending conferences and workshops, and actively seeking new challenges and problem solving opportunities. This dedication to learning and improvement ensures that one’s problem solving skills remain sharp and effective.

In conclusion, reflecting and learning are integral parts of the problem solving cycle in computer science. They enable computer scientists to refine their problem solving abilities, learn from mistakes, and continuously improve their skills and knowledge. By embracing these steps, computer scientists can stay at the forefront of the ever-changing world of computer science and contribute to its advancements.

Applying Problem Solving in Real Life

In computer science, problem solving is not limited to the realm of programming and algorithms. It is a skill that can be applied to various aspects of our daily lives, helping us to solve problems efficiently and effectively. By using the problem-solving cycle and applying the principles of analysis, data, solution, algorithm, and cycle, we can tackle real-life challenges with confidence and success.

The first step in problem-solving is to analyze the problem at hand. This involves breaking it down into smaller, more manageable parts and identifying the key issues or goals. By understanding the problem thoroughly, we can gain insights into its root causes and potential solutions.

For example, let’s say you’re facing a recurring issue in your daily commute – traffic congestion. By analyzing the problem, you may discover that the main causes are a lack of alternative routes and a lack of communication between drivers. This analysis helps you identify potential solutions such as using navigation apps to find alternate routes or promoting carpooling to reduce the number of vehicles on the road.

Gathering and Analyzing Data

Once we have identified the problem, it is important to gather relevant data to support our analysis. This may involve conducting surveys, collecting statistics, or reviewing existing research. By gathering data, we can make informed decisions and prioritize potential solutions based on their impact and feasibility.

Continuing with the traffic congestion example, you may gather data on the average commute time, the number of vehicles on the road, and the impact of carpooling on congestion levels. This data can help you analyze the problem more accurately and determine the most effective solutions.

Generating and Evaluating Solutions

After analyzing the problem and gathering data, the next step is to generate potential solutions. This can be done through brainstorming, researching best practices, or seeking input from experts. It is important to consider multiple options and think outside the box to find innovative and effective solutions.

For our traffic congestion problem, potential solutions can include implementing a smart traffic management system that optimizes traffic flow or investing in public transportation to incentivize people to leave their cars at home. By evaluating each solution’s potential impact, cost, and feasibility, you can make an informed decision on the best course of action.

Implementing and Iterating

Once a solution has been chosen, it is time to implement it in real life. This may involve developing a plan, allocating resources, and executing the solution. It is important to monitor the progress and collect feedback to learn from the implementation and make necessary adjustments.

For example, if the chosen solution to address traffic congestion is implementing a smart traffic management system, you would work with engineers and transportation authorities to develop and deploy the system. Regular evaluation and iteration of the system’s performance would ensure that it is effective and making a positive impact on reducing congestion.

By applying the problem-solving cycle derived from computer science to real-life situations, we can approach challenges with a systematic and analytical mindset. This can help us make better decisions, improve our problem-solving skills, and ultimately achieve more efficient and effective solutions.

Building Problem Solving Skills

In the field of computer science, problem-solving is a fundamental skill that is crucial for success. Whether you are a computer scientist, programmer, or student, developing strong problem-solving skills will greatly benefit your work and studies. It allows you to approach challenges with a logical and systematic approach, leading to efficient and effective problem resolution.

The Problem Solving Cycle

Problem-solving in computer science involves a cyclical process known as the problem-solving cycle. This cycle consists of several stages, including problem identification, data analysis, solution development, implementation, and evaluation. By following this cycle, computer scientists are able to tackle complex problems and arrive at optimal solutions.

Importance of Data Analysis

Data analysis is a critical step in the problem-solving cycle. It involves gathering and examining relevant data to gain insights and identify patterns that can inform the development of a solution. Without proper data analysis, computer scientists may overlook important information or make unfounded assumptions, leading to subpar solutions.

To effectively analyze data, computer scientists can employ various techniques such as data visualization, statistical analysis, and machine learning algorithms. These tools enable them to extract meaningful information from large datasets and make informed decisions during the problem-solving process.

Developing Effective Solutions

Developing effective solutions requires creativity, critical thinking, and logical reasoning. Computer scientists must evaluate multiple approaches, consider various factors, and assess the feasibility of different solutions. They should also consider potential limitations and trade-offs to ensure that the chosen solution addresses the problem effectively.

Furthermore, collaboration and communication skills are vital when building problem-solving skills. Computer scientists often work in teams and need to effectively communicate their ideas, propose solutions, and address any challenges that arise during the problem-solving process. Strong interpersonal skills facilitate collaboration and enhance problem-solving outcomes.

• Mastering programming languages and algorithms
• Staying updated with technological advancements in the field
• Practicing problem solving through coding challenges and projects
• Seeking feedback and learning from mistakes
• Continuing to learn and improve problem-solving skills

By following these strategies, individuals can strengthen their problem-solving abilities and become more effective computer scientists or programmers. Problem-solving is an essential skill in computer science and plays a central role in driving innovation and advancing the field.

Questions and answers:

What is the problem solving cycle in computer science.

The problem solving cycle in computer science refers to a systematic approach that programmers use to solve problems. It involves several steps, including problem definition, algorithm design, implementation, testing, and debugging.

How important is the problem solving cycle in computer science?

The problem solving cycle is extremely important in computer science as it allows programmers to effectively tackle complex problems and develop efficient solutions. It helps in organizing the thought process and ensures that the problem is approached in a logical and systematic manner.

What are the steps involved in the problem solving cycle?

The problem solving cycle typically consists of the following steps: problem definition and analysis, algorithm design, implementation, testing, and debugging. These steps are repeated as necessary until a satisfactory solution is achieved.

Can you explain the problem definition and analysis step in the problem solving cycle?

During the problem definition and analysis step, the programmer identifies and thoroughly understands the problem that needs to be solved. This involves analyzing the requirements, constraints, and possible inputs and outputs. It is important to have a clear understanding of the problem before proceeding to the next steps.

Why is testing and debugging an important step in the problem solving cycle?

Testing and debugging are important steps in the problem solving cycle because they ensure that the implemented solution functions as intended and is free from errors. Through testing, the programmer can identify and fix any issues or bugs in the code, thereby improving the quality and reliability of the solution.

What is the problem-solving cycle in computer science?

The problem-solving cycle in computer science refers to the systematic approach that computer scientists use to solve problems. It involves various steps, including problem analysis, algorithm design, coding, testing, and debugging.

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35 problem-solving techniques and methods for solving complex problems

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

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

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

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

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

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

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

Problem-solving warm-up activities

Closing activities for a problem-solving process.

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

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

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

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

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

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

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

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

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

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

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

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

Tips for more effective problem solving

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

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

Clearly define the problem

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

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

Don’t jump to conclusions

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

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

Try different approaches  

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

Don’t take it personally 

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

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

Get the right people in the room

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

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

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

Document everything

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

Bring a facilitator 

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

Develop your problem-solving skills

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

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

Design a great agenda

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

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

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

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

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

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

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

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

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

2. Lightning Decision Jam

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

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

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

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

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

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

3. Problem Definition Process

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

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

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

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

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

4. The 5 Whys 

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

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

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

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

5. World Cafe

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

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

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

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

6. Discovery & Action Dialogue (DAD)

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

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

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

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

7. Design Sprint 2.0

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

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

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

8. Open space technology

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

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

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

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

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

Techniques to identify and analyze problems

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

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

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

Let’s take a look!

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

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

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

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

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

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

10. The Creativity Dice

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

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

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

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

11. Fishbone Analysis

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

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

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

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

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

12. Problem Tree 

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

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

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

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

13. SWOT Analysis

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

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

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

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

14. Agreement-Certainty Matrix

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

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

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

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

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

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

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

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

16. Speed Boat

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

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

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

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

17. The Journalistic Six

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

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

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

18. LEGO Challenge

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

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

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

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

19. What, So What, Now What?

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

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

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

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

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

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

20. Journalists  

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

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

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

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

Problem-solving techniques for developing solutions 

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

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

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

21. Mindspin  

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

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

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

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

22. Improved Solutions

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

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

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

23. Four Step Sketch

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

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

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

24. 15% Solutions

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

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

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

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

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

25. How-Now-Wow Matrix

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

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

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

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

26. Impact and Effort Matrix

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

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

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

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

27. Dotmocracy

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

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

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

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

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

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

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

28. Check-in / Check-out

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

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

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

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

29. Doodling Together  

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

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

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

30. Show and Tell

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

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

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

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

31. Constellations

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

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

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

32. Draw a Tree

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

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

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

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

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

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

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

• One Breath Feedback
• Who What When Matrix
• Response Cards

How do I conclude a problem-solving process?

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

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

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

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

33. One Breath Feedback

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

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

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

34. Who What When Matrix 

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

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

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

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

35. Response cards

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

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

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

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

Save time and effort discovering the right solutions

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

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

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

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

Over to you

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

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

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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The PDCA cycle or Deming wheel: how and why to use it

Origins of the pdca cycle.

The PDCA (Plan-Do-Check-Act) cycle is often associated with W. Edwards Deming, but its origins can be traced through several significant contributions in the field of quality and management.

Walter A. Shewhart : In the 1920s and 1930s, statistician Walter A. Shewhart, then at Bell Laboratories, developed concepts around statistical process control and introduced a preliminary version of the cycle, often referred to as the Plan-Do-See cycle. Shewhart is often considered the "father of statistical quality control".

W. Edwards Deming : Deming, who was a protégé of Shewhart, adopted and adapted these ideas. Although the cycle is often called the "Deming Cycle", he always acknowledged Shewhart for his original contribution. Deming introduced this cycle in Japan in the 1950s, where it became a central element of post-World War II reconstruction and quality improvement efforts. In Japan, it was named the "PDCA cycle" and is sometimes called the "Deming-Shewhart Cycle".

Adoption in Japan : After World War II, Japan sought to rebuild its industry. As part of this initiative, many experts, including Deming, were invited to give lectures and training. The PDCA cycle was embraced by Japanese companies and became a fundamental component of their continuous improvement efforts, especially within the Total Quality Management (TQM) movement.

Over the years, PDCA has been incorporated into many continuous improvement methodologies and frameworks, such as Six Sigma, Lean Management, and other quality management systems.

It's important to note that, although the PDCA cycle is often attributed to Deming, he always emphasized the importance of Shewhart's work and often preferred to call it the "Shewhart Cycle".

Steps of the PDCA cycle

The four steps of PDCA are:

• Identify a problem or an improvement opportunity.
• Analyze the current situation.
• Set specific objectives.
• Propose solutions and prepare an action plan.
• Implement the action plan on a small scale, in a controlled setting (like a trial or test).
• Gather data to analyze the effects of the changes.
• Analyze the collected data.
• Compare the achieved results with the set objectives.
• Identify deviations and the causes of these deviations.
• If the objectives are met, standardize the changes and deploy on a larger scale.
• If objectives are not met, understand why and return to the "Plan" step to refine or rethink the solution.

The PDCA cycle is designed to be continuously repeated for continuous improvements. By repeating this cycle, organizations can identify and fix issues, improve processes, and ensure that improvements are effective and sustainable.

For which types of problems is the PDCA cycle suitable?

The PDCA is particularly well-suited to the following situations and problems:

Recurring problems : When an issue recurs frequently and its underlying cause is not clearly identified, the PDCA is useful for diagnosing, addressing, and preventing the issue.

Problems requiring incremental improvements : For situations that benefit from continuous adjustments rather than major overhauls, PDCA offers a framework for iterative improvement.

Situations with quantifiable data : The PDCA works especially well when outcomes or impacts can be quantitatively measured. This allows for objective evaluation during the "Check" phase.

Situations requiring a structured approach : For organizations or teams that struggle with addressing issues in a systematic manner, PDCA offers a clear and structured framework.

Changing environments : In situations where the environment is constantly evolving, PDCA enables organizations to adapt swiftly, adjust their plans, and act accordingly.

Quality improvement projects : Given its origins in quality control, the PDCA is naturally suited to efforts aimed at improving the quality of processes or products.

Here are situations where the PDCA cycle might not be the best method:

Urgent problems requiring immediate action : In crisis situations where swift action is needed, the systematic methodology of PDCA might slow down decision-making.

Highly complex problems with many interdependent variables : Although PDCA can be combined with other tools to address complex issues, on its own, it might oversimplify some situations.

Situations requiring radical innovation : PDCA focuses on continuous improvement, which might limit the "outside-the-box" thinking necessary for major innovations.

In summary, PDCA is a versatile tool suitable for many situations, but it's not universal. It's essential to assess the context and nature of the problem before choosing the best method or approach.

Using PDCA in innovation

PDCA can be employed in innovation, especially when introducing a new product in a production environment or implementing a new production process/equipment. We aren't including the product or process development part, which generally employs more specific methods. Here's how introducing new products or processes in production can be tackled.

Analysis of current capabilities : Examine your current facilities, equipment, and staff skills to determine if any changes are needed to produce the new product or to accommodate the new process/equipment.

Identification of needs : Based on the analysis, identify the requirements in terms of staff training, purchasing additional equipment, or modifications to the facilities.

Resource planning : Create a detailed plan for acquiring the necessary resources, whether it's material, training, labor, or time.

Defining success criteria : Set KPIs (key performance indicators) to measure the success of introducing the new product or process/equipment in production.

Implementation : Acquire the planned resources, train staff if necessary, and start producing the new product or implement the new process/equipment.

Monitoring : During production, ensure you closely monitor operations, especially in the early stages, to quickly identify any issues.

Performance measurement : Use the KPIs established during the planning phase to measure the success of introducing the new product or process/equipment in production.

Feedback collection : Gather feedback from production staff on potential problems, inefficiencies, or areas for improvement. They can often provide valuable insights as they are on the front lines.

Analysis and optimization : Based on measured performance and feedback received, identify areas for improvement or correction. This might include adjustments to machines, changes in workflow, or additional training sessions for staff.

Standardization : Once the new product is efficiently produced or the new process/equipment is fully integrated and working well, document the procedures and train all relevant staff to ensure consistency and efficiency.

Main difference between PDCA and other problem-solving methods

The primary difference between PDCA and other problem-solving methods like DMAIC or 8D lies in two major aspects:

Level of detail and flexibility :

• PDCA is a general, flexible framework that can be adapted to a myriad of situations. Its simplicity allows for rapid and reactive deployment.
• On the other hand, DMAIC and 8D are more prescriptive methodologies with detailed steps, specifically designed to tackle and solve complex problems using specific tools and analyses.

Type of improvement :

• PDCA is oriented towards incremental and continuous improvements, ideal for regular adjustments based on feedback and observations.
• DMAIC and 8D, meanwhile, are often used for more radical transformations or to address specific and complex problems that require deep understanding and a structured solution to ensure lasting resolution.

Thus, while PDCA lends itself to regular adjustments and continuous improvements, DMAIC and 8D cater to more specific and complex challenges with a more rigid structure.

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What are the 7 Steps to Problem-Solving? & Its Examples

7 Steps to Problem-Solving

7 Steps to Problem-Solving is a systematic process that involves analyzing a situation, generating possible solutions, and implementing the best course of action. While different problem-solving models exist, a common approach often involves the following seven steps:

Define the Problem:

• Clearly articulate and understand the nature of the problem. Define the issue, its scope, and its impact on individuals or the organization.

Gather Information:

• Collect relevant data and information related to the problem. This may involve research, observation, interviews, or any other method to gain a comprehensive understanding.

Generate Possible Solutions:

• Brainstorm and generate a variety of potential solutions to the problem. Encourage creativity and consider different perspectives during this phase.

Evaluate Options:

• Assess the strengths and weaknesses of each potential solution. Consider the feasibility, potential risks, and the likely outcomes associated with each option.

Make a Decision:

• Based on the evaluation, choose the most suitable solution. This decision should align with the goals and values of the individual or organization facing the problem.

Implement the Solution:

• Put the chosen solution into action. Develop an implementation plan, allocate resources, and carry out the necessary steps to address the problem effectively.

Evaluate the Results:

• Assess the outcomes of the implemented solution. Did it solve the problem as intended? What can be learned from the process? Use this information to refine future problem-solving efforts.

It’s important to note that these steps are not always linear and may involve iteration. Problem-solving is often an ongoing process, and feedback from the implementation and evaluation stages may lead to adjustments in the chosen solution or the identification of new issues that need to be addressed.

Problem-Solving Example in Education

• Certainly: Let’s consider a problem-solving example in the context of education.
• Problem: Declining Student Engagement in Mathematics Classes

Background:

A high school has noticed a decline in student engagement and performance in mathematics classes over the past few years. Students seem disinterested, and there is a noticeable decrease in test scores. The traditional teaching methods are not effectively capturing students’ attention, and there’s a need for innovative solutions to rekindle interest in mathematics.

Steps in Problem-Solving

Identify the problem:.

• Clearly define the issue: declining student engagement and performance in mathematics classes.
• Gather data on student performance, attendance, and feedback from teachers and students.

Root Cause Analysis

• Conduct surveys, interviews, and classroom observations to identify the root causes of disengagement.
• Identify potential factors such as teaching methods, curriculum relevance, or lack of real-world applications.

Brainstorm Solutions

• Organize a team of educators, administrators, and even students to brainstorm creative solutions.
• Consider integrating technology, real-world applications, project-based learning, or other interactive teaching methods.

Evaluate and Prioritize Solutions

• Evaluate each solution based on feasibility, cost, and potential impact.
• Prioritize solutions that are likely to address the root causes and have a positive impact on student engagement.

Implement the Chosen Solution

• Develop an action plan for implementing the chosen solution.
• Provide training and resources for teachers to adapt to new teaching methods or technologies.

Monitor and Evaluate

• Continuously monitor the implementation of the solution.
• Collect feedback from teachers and students to assess the effectiveness of the changes.

Adjust as Needed

• Be willing to make adjustments based on ongoing feedback and data analysis.
• Fine-tune the solution to address any unforeseen challenges or issues.

Example Solution

• Introduce a project-based learning approach in mathematics classes, where students work on real-world problems that require mathematical skills.
• Incorporate technology, such as educational apps or interactive simulations, to make learning more engaging.
• Provide professional development for teachers to enhance their skills in implementing these new teaching methods.

Expected Outcomes:

• Increased student engagement and interest in mathematics.
• Improvement in test scores and overall academic performance.
• Positive feedback from both teachers and students.

Final Words

This problem-solving approach in education involves a systematic process of identifying, analyzing, and addressing issues to enhance the learning experience for students.

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