step in problem solving meaning

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

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

What Is Problem Solving?

Definition and importance.

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

Problem-Solving Steps

The problem-solving process typically includes the following steps:

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

Defining the Problem

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

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

Generating Solutions

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

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

Evaluating and Selecting Solutions

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

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

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

Implementing and Monitoring the Solution

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

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

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

Problem-Solving Techniques

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

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

Brainstorming

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

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

When brainstorming, remember to:

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

Root Cause Analysis

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

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

SWOT Analysis

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

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

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

Mind Mapping

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

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

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

Examples of Problem Solving in Various Contexts

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

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

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

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

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

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

You might associate problem-solving with the math exercises that a seven-year-old would do at school. But problem-solving isn’t just about math — it’s a crucial skill that helps everyone make better decisions in everyday life or work.

A guide to problem-solving techniques, steps, and skills

Problem-solving involves finding effective solutions to address complex challenges, in any context they may arise.

Unfortunately, structured and systematic problem-solving methods aren’t commonly taught. Instead, when solving a problem, PMs tend to rely heavily on intuition. While for simple issues this might work well, solving a complex problem with a straightforward solution is often ineffective and can even create more problems.

In this article, you’ll learn a framework for approaching problem-solving, alongside how you can improve your problem-solving skills.

The 7 steps to problem-solving

When it comes to problem-solving there are seven key steps that you should follow: define the problem, disaggregate, prioritize problem branches, create an analysis plan, conduct analysis, synthesis, and communication.

1. Define the problem

Problem-solving begins with a clear understanding of the issue at hand. Without a well-defined problem statement, confusion and misunderstandings can hinder progress. It’s crucial to ensure that the problem statement is outcome-focused, specific, measurable whenever possible, and time-bound.

Additionally, aligning the problem definition with relevant stakeholders and decision-makers is essential to ensure efforts are directed towards addressing the actual problem rather than side issues.

2. Disaggregate

Complex issues often require deeper analysis. Instead of tackling the entire problem at once, the next step is to break it down into smaller, more manageable components.

Various types of logic trees (also known as issue trees or decision trees) can be used to break down the problem. At each stage where new branches are created, it’s important for them to be “MECE” – mutually exclusive and collectively exhaustive. This process of breaking down continues until manageable components are identified, allowing for individual examination.

The decomposition of the problem demands looking at the problem from various perspectives. That is why collaboration within a team often yields more valuable results, as diverse viewpoints lead to a richer pool of ideas and solutions.

3. Prioritize problem branches

The next step involves prioritization. Not all branches of the problem tree have the same impact, so it’s important to understand the significance of each and focus attention on the most impactful areas. Prioritizing helps streamline efforts and minimize the time required to solve the problem.

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4. Create an analysis plan

For prioritized components, you may need to conduct in-depth analysis. Before proceeding, a work plan is created for data gathering and analysis. If work is conducted within a team, having a plan provides guidance on what needs to be achieved, who is responsible for which tasks, and the timelines involved.

5. Conduct analysis

Data gathering and analysis are central to the problem-solving process. It’s a good practice to set time limits for this phase to prevent excessive time spent on perfecting details. You can employ heuristics and rule-of-thumb reasoning to improve efficiency and direct efforts towards the most impactful work.

6. Synthesis

After each individual branch component has been researched, the problem isn’t solved yet. The next step is synthesizing the data logically to address the initial question. The synthesis process and the logical relationship between the individual branch results depend on the logic tree used.

7. Communication

The last step is communicating the story and the solution of the problem to the stakeholders and decision-makers. Clear effective communication is necessary to build trust in the solution and facilitates understanding among all parties involved. It ensures that stakeholders grasp the intricacies of the problem and the proposed solution, leading to informed decision-making.

Exploring problem-solving in various contexts

While problem-solving has traditionally been associated with fields like engineering and science, today it has become a fundamental skill for individuals across all professions. In fact, problem-solving consistently ranks as one of the top skills required by employers.

Problem-solving techniques can be applied in diverse contexts:

Individuals — What career path should I choose? Where should I live? These are examples of simple and common personal challenges that require effective problem-solving skills
Organizations — Businesses also face many decisions that are not trivial to answer. Should we expand into new markets this year? How can we enhance the quality of our product development? Will our office accommodate the upcoming year’s growth in terms of capacity?
Societal issues — The biggest world challenges are also complex problems that can be addressed with the same technique. How can we minimize the impact of climate change? How do we fight cancer?

Despite the variation in domains and contexts, the fundamental approach to solving these questions remains the same. It starts with gaining a clear understanding of the problem, followed by decomposition, conducting analysis of the decomposed branches, and synthesizing it into a result that answers the initial problem.

Real-world examples of problem-solving

Let’s now explore some examples where we can apply the problem solving framework.

Problem: In the production of electronic devices, you observe an increasing number of defects. How can you reduce the error rate and improve the quality?

Before delving into analysis, you can deprioritize branches that you already have information for or ones you deem less important. For instance, while transportation delays may occur, the resulting material degradation is likely negligible. For other branches, additional research and data gathering may be necessary.

Once results are obtained, synthesis is crucial to address the core question: How can you decrease the defect rate?

While all factors listed may play a role, their significance varies. Your task is to prioritize effectively. Through data analysis, you may discover that altering the equipment would bring the most substantial positive outcome. However, executing a solution isn’t always straightforward. In prioritizing, you should consider both the potential impact and the level of effort needed for implementation.

By evaluating impact and effort, you can systematically prioritize areas for improvement, focusing on those with high impact and requiring minimal effort to address. This approach ensures efficient allocation of resources towards improvements that offer the greatest return on investment.

Problem : What should be my next job role?

When breaking down this problem, you need to consider various factors that are important for your future happiness in the role. This includes aspects like the company culture, our interest in the work itself, and the lifestyle that you can afford with the role.

However, not all factors carry the same weight for us. To make sense of the results, we can assign a weight factor to each branch. For instance, passion for the job role may have a weight factor of 1, while interest in the industry may have a weight factor of 0.5, because that is less important for you.

By applying these weights to a specific role and summing the values, you can have an estimate of how suitable that role is for you. Moreover, you can compare two roles and make an informed decision based on these weighted indicators.

Key problem-solving skills

This framework provides the foundation and guidance needed to effectively solve problems. However, successfully applying this framework requires the following:

Creativity — During the decomposition phase, it’s essential to approach the problem from various perspectives and think outside the box to generate innovative ideas for breaking down the problem tree
Decision-making — Throughout the process, decisions must be made, even when full confidence is lacking. Employing rules of thumb to simplify analysis or selecting one tree cut over another requires decisiveness and comfort with choices made
Analytical skills — Analytical and research skills are necessary for the phase following decomposition, involving data gathering and analysis on selected tree branches
Teamwork — Collaboration and teamwork are crucial when working within a team setting. Solving problems effectively often requires collective effort and shared responsibility
Communication — Clear and structured communication is essential to convey the problem solution to stakeholders and decision-makers and build trust

How to enhance your problem-solving skills

Problem-solving requires practice and a certain mindset. The more you practice, the easier it becomes. Here are some strategies to enhance your skills:

Practice structured thinking in your daily life — Break down problems or questions into manageable parts. You don’t need to go through the entire problem-solving process and conduct detailed analysis. When conveying a message, simplify the conversation by breaking the message into smaller, more understandable segments
Regularly challenging yourself with games and puzzles — Solving puzzles, riddles, or strategy games can boost your problem-solving skills and cognitive agility.
Engage with individuals from diverse backgrounds and viewpoints — Conversing with people who offer different perspectives provides fresh insights and alternative solutions to problems. This boosts creativity and helps in approaching challenges from new angles

Final thoughts

Problem-solving extends far beyond mathematics or scientific fields; it’s a critical skill for making informed decisions in every area of life and work. The seven-step framework presented here provides a systematic approach to problem-solving, relevant across various domains.

Now, consider this: What’s one question currently on your mind? Grab a piece of paper and try to apply the problem-solving framework. You might uncover fresh insights you hadn’t considered before.

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1. Precisely Identify Problems

As obvious as it seems, identifying the problem is the first step in the problem-solving process. Pinpointing a problem at the beginning of the process will guide your research, collaboration, and solutions in the right direction.

At this stage, your task is to identify the scope and substance of the problem. Ask yourself a series of questions:

What’s the problem?
How many subsets of issues are underneath this problem?
What subject areas, departments of work, or functions of business can best define this problem?

Although some problems are naturally large in scope, precision is key. Write out the problems as statements in planning sheets . Should information or feedback during a later step alter the scope of your problem, revise the statements.

Framing the problem at this stage will help you stay focused if distractions come up in later stages. Furthermore, how you frame a problem will aid your search for a solution. A strategy of building Lean success, for instance, will emphasize identifying and improving upon inefficient systems.

2. Collect Information and Plan

The second step is to collect information and plan the brainstorming process. This is another foundational step to road mapping your problem-solving process. Data, after all, is useful in identifying the scope and substance of your problems.

Collecting information on the exact details of the problem, however, is done to narrow the brainstorming portion to help you evaluate the outcomes later. Don’t overwhelm yourself with unnecessary information — use the problem statements that you identified in step one as a north star in your research process.

This stage should also include some planning. Ask yourself:

What parties will ultimately decide a solution?
Whose voices and ideas should be heard in the brainstorming process?
What resources are at your disposal for implementing a solution?

Establish a plan and timeline for steps 3-5.

3. Brainstorm Solutions

Brainstorming solutions is the bread and butter of the problem-solving process. At this stage, focus on generating creative ideas. As long as the solution directly addresses the problem statements and achieves your goals, don’t immediately rule it out.

Moreover, solutions are rarely a one-step answer and are more like a roadmap with a set of actions. As you brainstorm ideas, map out these solutions visually and include any relevant factors such as costs involved, action steps, and involved parties.

With Lean success in mind, stay focused on solutions that minimize waste and improve the flow of business ecosystems.

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4. Decide and Implement

The most critical stage is selecting a solution. Easier said than done. Consider the criteria that has arisen in previous steps as you decide on a solution that meets your needs.

Once you select a course of action, implement it.

Practicing due diligence in earlier stages of the process will ensure that your chosen course of action has been evaluated from all angles. Often, efficient implementation requires us to act correctly and successfully the first time, rather than being hurried and sloppy. Further compilations will create more problems, bringing you back to step 1.

5. Evaluate

Exercise humility and evaluate your solution honestly. Did you achieve the results you hoped for? What would you do differently next time?

As some experts note, formulating feedback channels into your evaluation helps solidify future success. A framework like Lean success, for example, will use certain key performance indicators (KPIs) like quality, delivery success, reducing errors, and more. Establish metrics aligned with company goals to assess your solutions.

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The Art of Effective Problem Solving: A Step-by-Step Guide

Daniel Croft

Daniel Croft is an experienced continuous improvement manager with a Lean Six Sigma Black Belt and a Bachelor's degree in Business Management. With more than ten years of experience applying his skills across various industries, Daniel specializes in optimizing processes and improving efficiency. His approach combines practical experience with a deep understanding of business fundamentals to drive meaningful change.

Last Updated: February 6, 2023
Learn Lean Sigma
Problem Solving

Whether we realise it or not, problem solving skills are an important part of our daily lives. From resolving a minor annoyance at home to tackling complex business challenges at work, our ability to solve problems has a significant impact on our success and happiness. However, not everyone is naturally gifted at problem-solving, and even those who are can always improve their skills. In this blog post, we will go over the art of effective problem-solving step by step.

You will learn how to define a problem, gather information, assess alternatives, and implement a solution, all while honing your critical thinking and creative problem-solving skills. Whether you’re a seasoned problem solver or just getting started, this guide will arm you with the knowledge and tools you need to face any challenge with confidence. So let’s get started!

Problem Solving Methodologies

Individuals and organisations can use a variety of problem-solving methodologies to address complex challenges. 8D and A3 problem solving techniques are two popular methodologies in the Lean Six Sigma framework.

Methodology of 8D (Eight Discipline) Problem Solving:

The 8D problem solving methodology is a systematic, team-based approach to problem solving. It is a method that guides a team through eight distinct steps to solve a problem in a systematic and comprehensive manner.

The 8D process consists of the following steps:

Form a team: Assemble a group of people who have the necessary expertise to work on the problem.
Define the issue: Clearly identify and define the problem, including the root cause and the customer impact.
Create a temporary containment plan: Put in place a plan to lessen the impact of the problem until a permanent solution can be found.
Identify the root cause: To identify the underlying causes of the problem, use root cause analysis techniques such as Fishbone diagrams and Pareto charts.
Create and test long-term corrective actions: Create and test a long-term solution to eliminate the root cause of the problem.
Implement and validate the permanent solution: Implement and validate the permanent solution’s effectiveness.
Prevent recurrence: Put in place measures to keep the problem from recurring.
Recognize and reward the team: Recognize and reward the team for its efforts.

Download the 8D Problem Solving Template

A3 Problem Solving Method:

The A3 problem solving technique is a visual, team-based problem-solving approach that is frequently used in Lean Six Sigma projects. The A3 report is a one-page document that clearly and concisely outlines the problem, root cause analysis, and proposed solution.

The A3 problem-solving procedure consists of the following steps:

Determine the issue: Define the issue clearly, including its impact on the customer.
Perform root cause analysis: Identify the underlying causes of the problem using root cause analysis techniques.
Create and implement a solution: Create and implement a solution that addresses the problem’s root cause.
Monitor and improve the solution: Keep an eye on the solution’s effectiveness and make any necessary changes.

Subsequently, in the Lean Six Sigma framework, the 8D and A3 problem solving methodologies are two popular approaches to problem solving. Both methodologies provide a structured, team-based problem-solving approach that guides individuals through a comprehensive and systematic process of identifying, analysing, and resolving problems in an effective and efficient manner.

Step 1 – Define the Problem

The definition of the problem is the first step in effective problem solving. This may appear to be a simple task, but it is actually quite difficult. This is because problems are frequently complex and multi-layered, making it easy to confuse symptoms with the underlying cause. To avoid this pitfall, it is critical to thoroughly understand the problem.

To begin, ask yourself some clarifying questions:

What exactly is the issue?
What are the problem’s symptoms or consequences?
Who or what is impacted by the issue?
When and where does the issue arise?

Answering these questions will assist you in determining the scope of the problem. However, simply describing the problem is not always sufficient; you must also identify the root cause. The root cause is the underlying cause of the problem and is usually the key to resolving it permanently.

Try asking “why” questions to find the root cause:

What causes the problem?
Why does it continue?
Why does it have the effects that it does?

By repeatedly asking “ why ,” you’ll eventually get to the bottom of the problem. This is an important step in the problem-solving process because it ensures that you’re dealing with the root cause rather than just the symptoms.

Once you have a firm grasp on the issue, it is time to divide it into smaller, more manageable chunks. This makes tackling the problem easier and reduces the risk of becoming overwhelmed. For example, if you’re attempting to solve a complex business problem, you might divide it into smaller components like market research, product development, and sales strategies.

To summarise step 1, defining the problem is an important first step in effective problem-solving. You will be able to identify the root cause and break it down into manageable parts if you take the time to thoroughly understand the problem. This will prepare you for the next step in the problem-solving process, which is gathering information and brainstorming ideas.

Step 2 – Gather Information and Brainstorm Ideas

Gathering information and brainstorming ideas is the next step in effective problem solving. This entails researching the problem and relevant information, collaborating with others, and coming up with a variety of potential solutions. This increases your chances of finding the best solution to the problem.

Begin by researching the problem and relevant information. This could include reading articles, conducting surveys, or consulting with experts. The goal is to collect as much information as possible in order to better understand the problem and possible solutions.

Next, work with others to gather a variety of perspectives. Brainstorming with others can be an excellent way to come up with new and creative ideas. Encourage everyone to share their thoughts and ideas when working in a group, and make an effort to actively listen to what others have to say. Be open to new and unconventional ideas and resist the urge to dismiss them too quickly.

Finally, use brainstorming to generate a wide range of potential solutions. This is the place where you can let your imagination run wild. At this stage, don’t worry about the feasibility or practicality of the solutions; instead, focus on generating as many ideas as possible. Write down everything that comes to mind, no matter how ridiculous or unusual it may appear. This can be done individually or in groups.

Once you’ve compiled a list of potential solutions, it’s time to assess them and select the best one. This is the next step in the problem-solving process, which we’ll go over in greater detail in the following section.

Step 3 – Evaluate Options and Choose the Best Solution

Once you’ve compiled a list of potential solutions, it’s time to assess them and select the best one. This is the third step in effective problem solving, and it entails weighing the advantages and disadvantages of each solution, considering their feasibility and practicability, and selecting the solution that is most likely to solve the problem effectively.

To begin, weigh the advantages and disadvantages of each solution. This will assist you in determining the potential outcomes of each solution and deciding which is the best option. For example, a quick and easy solution may not be the most effective in the long run, whereas a more complex and time-consuming solution may be more effective in solving the problem in the long run.

Consider each solution’s feasibility and practicability. Consider the following:

Can the solution be implemented within the available resources, time, and budget?
What are the possible barriers to implementing the solution?
Is the solution feasible in today’s political, economic, and social environment?

You’ll be able to tell which solutions are likely to succeed and which aren’t by assessing their feasibility and practicability.

Finally, choose the solution that is most likely to effectively solve the problem. This solution should be based on the criteria you’ve established, such as the advantages and disadvantages of each solution, their feasibility and practicability, and your overall goals.

It is critical to remember that there is no one-size-fits-all solution to problems. What is effective for one person or situation may not be effective for another. This is why it is critical to consider a wide range of solutions and evaluate each one based on its ability to effectively solve the problem.

Step 4 – Implement and Monitor the Solution

Communication the missing peice from Lean Six Sigma - Learnleansigma

When you’ve decided on the best solution, it’s time to put it into action. The fourth and final step in effective problem solving is to put the solution into action, monitor its progress, and make any necessary adjustments.

To begin, implement the solution. This may entail delegating tasks, developing a strategy, and allocating resources. Ascertain that everyone involved understands their role and responsibilities in the solution’s implementation.

Next, keep an eye on the solution’s progress. This may entail scheduling regular check-ins, tracking metrics, and soliciting feedback from others. You will be able to identify any potential roadblocks and make any necessary adjustments in a timely manner if you monitor the progress of the solution.

Finally, make any necessary modifications to the solution. This could entail changing the solution, altering the plan of action, or delegating different tasks. Be willing to make changes if they will improve the solution or help it solve the problem more effectively.

It’s important to remember that problem solving is an iterative process, and there may be times when you need to start from scratch. This is especially true if the initial solution does not effectively solve the problem. In these situations, it’s critical to be adaptable and flexible and to keep trying new solutions until you find the one that works best.

To summarise, effective problem solving is a critical skill that can assist individuals and organisations in overcoming challenges and achieving their objectives. Effective problem solving consists of four key steps: defining the problem, generating potential solutions, evaluating alternatives and selecting the best solution, and implementing the solution.

You can increase your chances of success in problem solving by following these steps and considering factors such as the pros and cons of each solution, their feasibility and practicability, and making any necessary adjustments. Furthermore, keep in mind that problem solving is an iterative process, and there may be times when you need to go back to the beginning and restart. Maintain your adaptability and try new solutions until you find the one that works best for you.

Novick, L.R. and Bassok, M., 2005. Problem Solving . Cambridge University Press.

Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.

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What Is Problem-Solving? How to Use Problem-Solving Skills to Resolve Issues

What is problem-solving, what is the general process of problem-solving, the best problem-solving strategies and tools, what to do when a problem feels too big to solve.

Great businesses don’t exist to simply grow and make money. Instead, they solve the world’s problems , from tiny issues to giant dilemmas. Problem-solving is essentially the main function of organizations. An effective organization will have systems and processes in place to reach their goals and solve problems. If a company has team members and leaders who have poor problem-solving skills, that means they’re ineffective at one of the core functions of a business.

You need to be good at both external problem-solving (solving problems for others) and internal problem-solving (solving problems before or when they arise within the business). An organization that can solve problems will see its teams come closer together as they bond over providing solutions to serious issues. Companies that solve problems well will also be able to carry out their purpose more efficiently.

Learn the steps you can follow to solve problems both great and small. Additionally, discover some real-world methods and problem-solving skills successful business leaders use to solve problems of their own.

Problem-solving involves the search for solutions that follow an effective process of discovery, identification, ideation, and execution. Problem-solving usually requires overcoming numerous obstacles that stand in the way of reaching your goal. Often, the act of problem-solving includes coming up with solutions to many smaller problems before eventually solving the main issue that prompted the process in the first place.

The key to cultivating excellent problem-solving skills is having a distinct process designed to produce solutions. While it may seem like problem-solving involves a complex strategy, it features several steps that are easy to follow. The following steps represent a general problem-solving process you can use when you need to find a solution.

1. Define the Problem

The first step to take as part of the problem-solving process involves defining what that problem is. While this may seem like a simple idea to follow, the key is to get to the root of the problem . Only once you’re able to identify the root issue you’re tackling through a root cause analysis can you be sure you’re on the right path. Sometimes the surface issue isn’t what you need to address. Just like an earthquake, organizational issues have an epicenter—complete with shockwaves that negatively impact the business. If you don’t resolve the core problem, it can expand , and the damage becomes detrimental. All problem-solving jobs begin with this important first step.

If your organization has a problem with employee retention , you may think you’ll solve it by increasing pay or perks. However, that might not address the root of the issue. If you were to investigate further, you may discover that a manager is creating a toxic work environment, causing good employees to find work elsewhere.

2. Brainstorm Possible Solutions

Once you have a solid idea of what the real problem is, you can proceed to create possible solutions you can pursue. Take the time to brainstorm different solutions. No two problems are the same, and each one will require a creative approach. Make sure you write down the alternative solutions so you can research them in depth. During the course of your brainstorming, you may stumble upon a solution you wouldn’t have thought of otherwise.

As you follow this step, you may need to find the best way to inspire your critical thinking skills. Think about when and where you generate ideas and get the creative juices flowing. Then, try to put yourself in that environment as often as possible.

Sara Blakely , the founder of SPANX®, says her most productive creative thinking happens when she’s driving in her car . Even though she doesn’t have a real commute, she gets in the car and makes one up. “I live really close to Spanx,” she said on the “Masters of Scale” podcast, “so I’ve created what my friends call my ‘fake commute,’ and I get up an hour early before I’m supposed to go to Spanx, and I drive around aimlessly in Atlanta with my commute so that I can have my thoughts come to me.” As a result, she sets time aside for developing her best problem-solving strategies every single day.

3. Research Several Options

After you’ve come up with several possible alternative solutions, pick two or three that seem the most promising using your analytical skills. Then you’ll need to buckle down and do some research to see which one to pursue. Conduct your research using primary and secondary resources.

Conduct primary research by:

Having a discussion with a mentor
Interviewing a person who’s successfully solved this problem before
Strategizing with team members closest to the issue

Great secondary sources include:

Trustworthy online articles and news sources from credible websites
Leadership books from experts who have written about the problem
Business podcast interviews on the issue
YouTube videos featuring established leaders

4. Select a Solution

At the conclusion of your research, you’ll be better equipped to select the right solution. Evaluate the data you have gathered. To ensure you make a good pick, you’ll need to keep several considerations in mind.

Here are some good questions to ask when picking a solution:

Is this solution in line with the company’s core values?
Is it a realistic option?
Could it lead to additional problems?
Will everyone involved accept the solution?
Does it truly solve the problem, or does it only delay negative effects?

As you employ your creative thinking skills in answering these questions, you’ll eventually need to settle on a single solution. Adhering to a decision-making process helps you objectively choose the best solution out of many options. Don’t make a quick decision you may later regret. Be deliberate in your analysis, and try to remain as objective as possible.

In order to make the most objective decision:

Get into a humble mindset and make sure you’re willing to listen and learn.
Don’t let emotions influence the choice.
Reverse-engineer the possible outcome of any given solution.
Weigh the pros and cons of each choice.
Seek wise counsel from trusted mentors, leaders, and team members.

5. Develop an Action Plan

Once you’ve settled on a solution, you’ll be ready to pursue it. Before moving too quickly, revisit step one and make sure your choice aligns with the main objective . If it doesn’t, although it may be a valid choice, it’s most likely not the best for your team. If this is the case, don’t get discouraged. Creative problem-solving takes time.

When the right choice is made, and the solution is placed into the overall strategy, start developing an action plan . Lay out the “who,” “what,” “when,” “why,” and “how.” Visualize exactly what success looks like with this new plan. When working through the problem-solving process, write all the details down. This helps leaders construct action items and delegate them accordingly. Never leave this part of the process empty-handed. Your team needs a clear picture of expectations so they can properly implement the solution. And if everything works, you can use this problem-solving model in the future.

You will undoubtedly encounter many problems that need to be solved in your life. There are a variety of ways to solve those problems. With all the problem-solving techniques out there, it can be helpful to learn some of them so you can employ the best one at the right moment. The following are just a few examples of what these strategies and problem-solving tools look like in the real world.

One of the best ways to discover the root cause of a problem is by utilizing the 5 Whys method. This strategy was developed by Sakichi Toyoda, founder of Toyota Industries. It’s as simple as it sounds. When a problem occurs, ask why it happened five times. In theory, the last answer should get to the heart of the issue.

Here’s an example of how the 5 Whys work in action:

When business leaders use the 5 Whys method , problems are given more context. Uncovering how, when, and why they happen helps company owners and executives identify the organization’s core issues.

First Principles Thinking

When one engages in first principles thinking , they end up questioning what everyone just assumes to be true. It effectively removes those assumptions , breaking things down into their most basic elements that are probably true. It’s all about getting to that core foundation of truth and building out from there. Problem-solving skills should always include first principles thinking.

Elon Musk most famously pursued this strategy when it comes to space travel. Instead of accepting that building a rocket was too expensive, he got to the fundamental truths of construction, all the way down to pricing each component. Musk once explained that he follows first principles thinking by following three simple steps .

Identify the assumptions
Break down the issue into its core, fundamental components
Innovate by creating new solutions

Other business leaders have engaged in similar strategies, such as Jeff Bezos when he advised the need for finding out key truths for yourself. First principles thinking is an important part of innovating beyond what we assume can’t be changed. It’s a way to use analytical skills to discover potential solutions through constant learning and acquiring new information.

Steve Jobs’ Problem-Solving Method

Steve Jobs gained a reputation for solving problems through Apple. He was always on the lookout for simple solutions to complex problems. He followed his own three-step method that helped him tackle difficult issues.

Zoom Out: When facing a problem, zoom out to get a larger view of the bigger picture. This is another way to help you define the problem and pinpoint the root cause.
Focus In: After defining the problem, focus all your attention on solving it. Concentrate your efforts, and don’t stop until the problem is fixed. Give yourself a period of intense focus and dedication as you bring the solution to life.
Disconnect: If things aren’t proceeding the way you thought they would, it may be time to disconnect. That means walking away and giving yourself a break so you can clear your mind. Sometimes, a break is all you need to approach the problem once more, this time from a fresh angle with your mind fully reenergized.

From increasing sales to engaging in conflict resolution , business leaders have a lot of problems to solve. However, some people may still feel overwhelmed, especially if the problem is large in scope and could even threaten to close the company. Fortunately, there are steps you can take to get in the right mindset as outlined by James Clear, author of Atomic Habits :

Break the bigger problem down into a lot of smaller problems
Focus on one small problem and solve it
Use what you learned from solving that problem to increase your knowledge about the bigger problem
Repeat these steps until the larger problem is solved

Tackling a problem that feels too big to solve requires a can-do, positive mindset. In order to improve your problem-solving, you’ll need to take remember these steps. Imagine what is possible instead of focusing on what seems impossible. As you do so, you’ll become skilled in solving all sorts of problems while also improving your decision-making.

For more help in growing your skillset, check out the following article:

Growth Mindset: Creating an Environment for Innovation

Leaders Media has established sourcing guidelines and relies on relevant, and credible sources for the data, facts, and expert insights and analysis we reference. You can learn more about our mission, ethics, and how we cite sources in our editorial policy .

Abadi, Mark. “The CEO of Spanx Wakes up an Hour Early to Drive around ‘Aimlessly’ on a ‘Fake Commute’ Because She Does Her Best Thinking in the Car.” Insider , 15 Nov. 2018, https://www.businessinsider.com/spanx-ceo-sara-blakely-fake-commute-2018-11.
Oshin, Mayo. “Elon Musks’ ‘3-Step’ First Principles Thinking: How to Think and Solve Difficult Problems Like A….” Mission.Org , 2 Nov. 2020, https://medium.com/the-mission/elon-musks-3-step-first-principles-thinking-how-to-think-and-solve-difficult-problems-like-a-ba1e73a9f6c0.
Clear, James. “How to Solve Big Problems.” James Clear , 25 July 2014, https://jamesclear.com/narrow-focus.
Nast, C. (n.d.). WIRED. https://www.wired.com/2012/10/ff-elon-musk-qa/all/
Just a moment. . . (n.d.). https://www.indeed.com/career-advice/career-development/5-whys-example
inc.com . (n.d.). https://www.inc.com/kelly-main/apple-steve-jobs-problem-solving.html
How to find your big idea . (2022, October 6). Masters of Scale. https://mastersofscale.com/sara-blakely-how-to-find-your-big-idea/
EX-99.1 . (n.d.). https://www.sec.gov/Archives/edgar/data/1018724/000119312517120198/d373368dex991.htm

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Master the 7-Step Problem-Solving Process for Better Decision-Making

Discover the powerful 7-Step Problem-Solving Process to make better decisions and achieve better outcomes. Master the art of problem-solving in this comprehensive guide. Download the Free PowerPoint and PDF Template.

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Master the 7-Step Problem-Solving Process for Better Decision-Making

Introduction

Mastering the art of problem-solving is crucial for making better decisions. Whether you're a student, a business owner, or an employee, problem-solving skills can help you tackle complex issues and find practical solutions. The 7-Step Problem-Solving Process is a proven method that can help you approach problems systematically and efficiently.

The 7-Step Problem-Solving Process involves steps that guide you through the problem-solving process. The first step is to define the problem, followed by disaggregating the problem into smaller, more manageable parts. Next, you prioritize the features and create a work plan to address each. Then, you analyze each piece, synthesize the information, and communicate your findings to others.

By following this process, you can avoid jumping to conclusions, overlooking important details, or making hasty decisions. Instead, you can approach problems with a clear and structured mindset, which can help you make better decisions and achieve better outcomes.

In this article, we'll explore each step of the 7-Step Problem-Solving Process in detail so you can start mastering this valuable skill. At the end of the blog post, you can download the process's free PowerPoint and PDF templates .

Step 1: Define the Problem

The first step in the problem-solving process is to define the problem. This step is crucial because finding a solution is only accessible if the problem is clearly defined. The problem must be specific, measurable, and achievable.

One way to define the problem is to ask the right questions. Questions like "What is the problem?" and "What are the causes of the problem?" can help. Gathering data and information about the issue to assist in the definition process is also essential.

Another critical aspect of defining the problem is identifying the stakeholders. Who is affected by it? Who has a stake in finding a solution? Identifying the stakeholders can help ensure that the problem is defined in a way that considers the needs and concerns of all those affected.

Once the problem is defined, it is essential to communicate the definition to all stakeholders. This helps to ensure that everyone is on the same page and that there is a shared understanding of the problem.

Step 2: Disaggregate

After defining the problem, the next step in the 7-step problem-solving process is to disaggregate the problem into smaller, more manageable parts. Disaggregation helps break down the problem into smaller pieces that can be analyzed individually. This step is crucial in understanding the root cause of the problem and identifying the most effective solutions.

Disaggregation can be achieved by breaking down the problem into sub-problems, identifying the contributing factors, and analyzing the relationships between these factors. This step helps identify the most critical factors that must be addressed to solve the problem.

A tree or fishbone diagram is one effective way to disaggregate a problem. These diagrams help identify the different factors contributing to the problem and how they are related. Another way is to use a table to list the other factors contributing to the situation and their corresponding impact on the issue.

Disaggregation helps in breaking down complex problems into smaller, more manageable parts. It helps understand the relationships between different factors contributing to the problem and identify the most critical factors that must be addressed. By disaggregating the problem, decision-makers can focus on the most vital areas, leading to more effective solutions.

Step 3: Prioritize

After defining the problem and disaggregating it into smaller parts, the next step in the 7-step problem-solving process is prioritizing the issues that need addressing. Prioritizing helps to focus on the most pressing issues and allocate resources more effectively.

There are several ways to prioritize issues, including:

Urgency: Prioritize issues based on their urgency. Problems that require immediate attention should be addressed first.
Impact: Prioritize issues based on their impact on the organization or stakeholders. Problems with a high impact should be given priority.
Resources: Prioritize issues based on the resources required to address them. Problems that require fewer resources should be dealt with first.

It is important to involve stakeholders in the prioritization process, considering their concerns and needs. This can be done through surveys, focus groups, or other forms of engagement.

Once the issues have been prioritized, developing a plan of action to address them is essential. This involves identifying the resources required, setting timelines, and assigning responsibilities.

Prioritizing issues is a critical step in problem-solving. By focusing on the most pressing problems, organizations can allocate resources more effectively and make better decisions.

Step 4: Workplan

After defining the problem, disaggregating, and prioritizing the issues, the next step in the 7-step problem-solving process is to develop a work plan. This step involves creating a roadmap that outlines the steps needed to solve the problem.

The work plan should include a list of tasks, deadlines, and responsibilities for each team member involved in the problem-solving process. Assigning tasks based on each team member's strengths and expertise ensures the work is completed efficiently and effectively.

Creating a work plan can help keep the team on track and ensure everyone is working towards the same goal. It can also help to identify potential roadblocks or challenges that may arise during the problem-solving process and develop contingency plans to address them.

Several tools and techniques can be used to develop a work plan, including Gantt charts, flowcharts, and mind maps. These tools can help to visualize the steps needed to solve the problem and identify dependencies between tasks.

Developing a work plan is a critical step in the problem-solving process. It provides a clear roadmap for solving the problem and ensures everyone involved is aligned and working towards the same goal.

Step 5: Analysis

Once the problem has been defined and disaggregated, the next step is to analyze the information gathered. This step involves examining the data, identifying patterns, and determining the root cause of the problem.

Several methods can be used during the analysis phase, including:

Root cause analysis
Pareto analysis
SWOT analysis

Root cause analysis is a popular method used to identify the underlying cause of a problem. This method involves asking a series of "why" questions to get to the root cause of the issue.

Pareto analysis is another method that can be used during the analysis phase. This method involves identifying the 20% of causes responsible for 80% of the problems. By focusing on these critical causes, organizations can make significant improvements.

Finally, SWOT analysis is a valuable tool for analyzing the internal and external factors that may impact the problem. This method involves identifying the strengths, weaknesses, opportunities, and threats related to the issue.

Overall, the analysis phase is critical for identifying the root cause of the problem and developing practical solutions. By using a combination of methods, organizations can gain a deeper understanding of the issue and make informed decisions.

Step 6: Synthesize

Once the analysis phase is complete, it is time to synthesize the information gathered to arrive at a solution. During this step, the focus is on identifying the most viable solution that addresses the problem. This involves examining and combining the analysis results for a clear and concise conclusion.

One way to synthesize the information is to use a decision matrix. This involves creating a table that lists the potential solutions and the essential criteria for making a decision. Each answer is then rated against each standard, and the scores are tallied to arrive at a final decision.

Another approach to synthesizing the information is to use a mind map. This involves creating a visual representation of the problem and the potential solutions. The mind map can identify the relationships between the different pieces of information and help prioritize the solutions.

During the synthesis phase, it is vital to remain open-minded and consider all potential solutions. Involving all stakeholders in the decision-making process is essential to ensure everyone's perspectives are considered.

Step 7: Communicate

After synthesizing the information, the next step is communicating the findings to the relevant stakeholders. This is a crucial step because it helps to ensure that everyone is on the same page and that the decision-making process is transparent.

One effective way to communicate the findings is through a well-organized report. The report should include the problem statement, the analysis, the synthesis, and the recommended solution. It should be clear, concise, and easy to understand.

In addition to the report, a presentation explaining the findings is essential. The presentation should be tailored to the audience and highlight the report's key points. Visual aids such as tables, graphs, and charts can make the presentation more engaging.

During the presentation, it is essential to be open to feedback and questions from the audience. This helps ensure everyone agrees with the recommended solution and addresses concerns or objections.

Effective communication is vital to ensuring the decision-making process is successful. Stakeholders can make informed decisions and work towards a common goal by communicating the findings clearly and concisely.

The 7-step problem-solving process is a powerful tool for helping individuals and organizations make better decisions. By following these steps, individuals can identify the root cause of a problem, prioritize potential solutions, and develop a clear plan of action. This process can be applied to various scenarios, from personal challenges to complex business problems.

Through disaggregation, individuals can break down complex problems into smaller, more manageable parts. By prioritizing potential solutions, individuals can focus their efforts on the most impactful actions. The work step allows individuals to develop a clear action plan, while the analysis step provides a framework for evaluating possible solutions.

The synthesis step combines all the information gathered to develop a comprehensive solution. Finally, the communication step allows individuals to share their answers with others and gather feedback.

By mastering the 7-step problem-solving process, individuals can become more effective decision-makers and problem-solvers. This process can help individuals and organizations save time and resources while improving outcomes. With practice, individuals can develop the skills to apply this process to a wide range of scenarios and make better decisions in all areas of life.

7-Step Problem-Solving Process PPT Template

Free powerpoint and pdf template, executive summary: the 7-step problem-solving process.

The 7-Step Problem-Solving Process is a robust and systematic method to help individuals and organizations make better decisions by tackling complex issues and finding practical solutions. This process comprises defining the problem, disaggregating it into smaller parts, prioritizing the issues, creating a work plan, analyzing the data, synthesizing the information, and communicating the findings.

By following these steps, individuals can identify the root cause of a problem, break it down into manageable components, and prioritize the most impactful actions. The work plan, analysis, and synthesis steps provide a framework for developing comprehensive solutions, while the communication step ensures transparency and stakeholder engagement.

Mastering this process can improve decision-making and problem-solving capabilities, save time and resources, and improve outcomes in personal and professional contexts.

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The Problem-Solving Process

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

By the Mind Tools Content Team

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

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

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

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

1. Define the Problem

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

2. Analyze the Problem

Ask yourself, and others, the following questions.

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

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

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

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

3. Generate Potential Solutions

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

4. Select Best Solution

When selecting the best solution, consider:

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

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

5. Take Action

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

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

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

6. Monitor and Review

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

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

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

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

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Problem solving techniques: Steps and methods

Posted on May 29, 2019

Constant disruption has become a hallmark of the modern workforce and organisations want problem solving skills to combat this. Employers need people who can respond to change – be that evolving technology, new competitors, different models for doing business, or any of the other transformations that have taken place in recent years.

In addition, problem solving techniques encompass many of the other top skills employers seek . For example, LinkedIn’s list of the most in-demand soft skills of 2019 includes creativity, collaboration and adaptability, all of which fall under the problem-solving umbrella.

Despite its importance, many employees misunderstand what the problem solving method really involves.

What constitutes effective problem solving?

Effective problem solving doesn’t mean going away and coming up with an answer immediately. In fact, this isn’t good problem solving at all, because you’ll be running with the first solution that comes into your mind, which often isn’t the best.

Instead, you should look at problem solving more as a process with several steps involved that will help you reach the best outcome. Those steps are:

Define the problem
List all the possible solutions
Evaluate the options
Select the best solution
Create an implementation plan
Communicate your solution

Let’s look at each step in a little more detail.

It's important you take the time to brainstorm and consider all your options when solving problems.

1. Define the problem

The first step to solving a problem is defining what the problem actually is – sounds simple, right? Well no. An effective problem solver will take the thoughts of everyone involved into account, but different people might have different ideas on what the root cause of the issue really is. It’s up to you to actively listen to everyone without bringing any of your own preconceived notions to the conversation. Learning to differentiate facts from opinion is an essential part of this process.

An effective problem solver will take the opinions of everyone involved into account

The same can be said of data. Depending on what the problem is, there will be varying amounts of information available that will help you work out what’s gone wrong. There should be at least some data involved in any problem, and it’s up to you to gather as much as possible and analyse it objectively.

2. List all the possible solutions

Once you’ve identified what the real issue is, it’s time to think of solutions. Brainstorming as many solutions as possible will help you arrive at the best answer because you’ll be considering all potential options and scenarios. You should take everyone’s thoughts into account when you’re brainstorming these ideas, as well as all the insights you’ve gleaned from your data analysis. It also helps to seek input from others at this stage, as they may come up with solutions you haven’t thought of.

Depending on the type of problem, it can be useful to think of both short-term and long-term solutions, as some of your options may take a while to implement.

One of the best problem solving techniques is brainstorming a number of different solutions and involving affected parties in this process.

3. Evaluate the options

Each option will have pros and cons, and it’s important you list all of these, as well as how each solution could impact key stakeholders. Once you’ve narrowed down your options to three or four, it’s often a good idea to go to other employees for feedback just in case you’ve missed something. You should also work out how each option ties in with the broader goals of the business.

There may be a way to merge two options together in order to satisfy more people.

4. Select an option

Only now should you choose which solution you’re going to go with. What you decide should be whatever solves the problem most effectively while also taking the interests of everyone involved into account. There may be a way to merge two options together in order to satisfy more people.

5. Create an implementation plan

At this point you might be thinking it’s time to sit back and relax – problem solved, right? There are actually two more steps involved if you want your problem solving method to be truly effective. The first is to create an implementation plan. After all, if you don’t carry out your solution effectively, you’re not really solving the problem at all.

Create an implementation plan on how you will put your solution into practice. One problem solving technique that many use here is to introduce a testing and feedback phase just to make sure the option you’ve selected really is the most viable. You’ll also want to include any changes to your solution that may occur in your implementation plan, as well as how you’ll monitor compliance and success.

6. Communicate your solution

There’s one last step to consider as part of the problem solving methodology, and that’s communicating your solution . Without this crucial part of the process, how is anyone going to know what you’ve decided? Make sure you communicate your decision to all the people who might be impacted by it. Not everyone is going to be 100 per cent happy with it, so when you communicate you must give them context. Explain exactly why you’ve made that decision and how the pros mean it’s better than any of the other options you came up with.

Prove your problem solving skills with Deakin

Employers are increasingly seeking soft skills, but unfortunately, while you can show that you’ve got a degree in a subject, it’s much harder to prove you’ve got proficiency in things like problem solving skills. But this is changing thanks to Deakin’s micro-credentials. These are university-level micro-credentials that provide an authoritative and third-party assessment of your capabilities in a range of areas, including problem solving. Reach out today for more information .

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What Is Problem-Solving Therapy?

Arlin Cuncic, MA, is the author of The Anxiety Workbook and founder of the website About Social Anxiety. She has a Master's degree in clinical psychology.

Daniel B. Block, MD, is an award-winning, board-certified psychiatrist who operates a private practice in Pennsylvania.

Verywell / Madelyn Goodnight

Problem-Solving Therapy Techniques

How effective is problem-solving therapy, things to consider, how to get started.

Problem-solving therapy is a brief intervention that provides people with the tools they need to identify and solve problems that arise from big and small life stressors. It aims to improve your overall quality of life and reduce the negative impact of psychological and physical illness.

Problem-solving therapy can be used to treat depression , among other conditions. It can be administered by a doctor or mental health professional and may be combined with other treatment approaches.

At a Glance

Problem-solving therapy is a short-term treatment used to help people who are experiencing depression, stress, PTSD, self-harm, suicidal ideation, and other mental health problems develop the tools they need to deal with challenges. This approach teaches people to identify problems, generate solutions, and implement those solutions. Let's take a closer look at how problem-solving therapy can help people be more resilient and adaptive in the face of stress.

Problem-solving therapy is based on a model that takes into account the importance of real-life problem-solving. In other words, the key to managing the impact of stressful life events is to know how to address issues as they arise. Problem-solving therapy is very practical in its approach and is only concerned with the present, rather than delving into your past.

This form of therapy can take place one-on-one or in a group format and may be offered in person or online via telehealth . Sessions can be anywhere from 30 minutes to two hours long.

Key Components

There are two major components that make up the problem-solving therapy framework:

Applying a positive problem-solving orientation to your life
Using problem-solving skills

A positive problem-solving orientation means viewing things in an optimistic light, embracing self-efficacy , and accepting the idea that problems are a normal part of life. Problem-solving skills are behaviors that you can rely on to help you navigate conflict, even during times of stress. This includes skills like:

Knowing how to identify a problem
Defining the problem in a helpful way
Trying to understand the problem more deeply
Setting goals related to the problem
Generating alternative, creative solutions to the problem
Choosing the best course of action
Implementing the choice you have made
Evaluating the outcome to determine next steps

Problem-solving therapy is all about training you to become adaptive in your life so that you will start to see problems as challenges to be solved instead of insurmountable obstacles. It also means that you will recognize the action that is required to engage in effective problem-solving techniques.

Planful Problem-Solving

One problem-solving technique, called planful problem-solving, involves following a series of steps to fix issues in a healthy, constructive way:

Problem definition and formulation : This step involves identifying the real-life problem that needs to be solved and formulating it in a way that allows you to generate potential solutions.
Generation of alternative solutions : This stage involves coming up with various potential solutions to the problem at hand. The goal in this step is to brainstorm options to creatively address the life stressor in ways that you may not have previously considered.
Decision-making strategies : This stage involves discussing different strategies for making decisions as well as identifying obstacles that may get in the way of solving the problem at hand.
Solution implementation and verification : This stage involves implementing a chosen solution and then verifying whether it was effective in addressing the problem.

Other Techniques

Other techniques your therapist may go over include:

Problem-solving multitasking , which helps you learn to think clearly and solve problems effectively even during times of stress
Stop, slow down, think, and act (SSTA) , which is meant to encourage you to become more emotionally mindful when faced with conflict
Healthy thinking and imagery , which teaches you how to embrace more positive self-talk while problem-solving

What Problem-Solving Therapy Can Help With

Problem-solving therapy addresses life stress issues and focuses on helping you find solutions to concrete issues. This approach can be applied to problems associated with various psychological and physiological symptoms.

Mental Health Issues

Problem-solving therapy may help address mental health issues, like:

Chronic stress due to accumulating minor issues
Complications associated with traumatic brain injury (TBI)
Emotional distress
Post-traumatic stress disorder (PTSD)
Problems associated with a chronic disease like cancer, heart disease, or diabetes
Self-harm and feelings of hopelessness
Substance use
Suicidal ideation

Specific Life Challenges

This form of therapy is also helpful for dealing with specific life problems, such as:

Death of a loved one
Dissatisfaction at work
Everyday life stressors
Family problems
Financial difficulties
Relationship conflicts

Your doctor or mental healthcare professional will be able to advise whether problem-solving therapy could be helpful for your particular issue. In general, if you are struggling with specific, concrete problems that you are having trouble finding solutions for, problem-solving therapy could be helpful for you.

Benefits of Problem-Solving Therapy

The skills learned in problem-solving therapy can be helpful for managing all areas of your life. These can include:

Being able to identify which stressors trigger your negative emotions (e.g., sadness, anger)
Confidence that you can handle problems that you face
Having a systematic approach on how to deal with life's problems
Having a toolbox of strategies to solve the issues you face
Increased confidence to find creative solutions
Knowing how to identify which barriers will impede your progress
Knowing how to manage emotions when they arise
Reduced avoidance and increased action-taking
The ability to accept life problems that can't be solved
The ability to make effective decisions
The development of patience (realizing that not all problems have a "quick fix")

Problem-solving therapy can help people feel more empowered to deal with the problems they face in their lives. Rather than feeling overwhelmed when stressors begin to take a toll, this therapy introduces new coping skills that can boost self-efficacy and resilience .

Other Types of Therapy

Other similar types of therapy include cognitive-behavioral therapy (CBT) and solution-focused brief therapy (SFBT) . While these therapies work to change thinking and behaviors, they work a bit differently. Both CBT and SFBT are less structured than problem-solving therapy and may focus on broader issues. CBT focuses on identifying and changing maladaptive thoughts, and SFBT works to help people look for solutions and build self-efficacy based on strengths.

This form of therapy was initially developed to help people combat stress through effective problem-solving, and it was later adapted to address clinical depression specifically. Today, much of the research on problem-solving therapy deals with its effectiveness in treating depression.

Problem-solving therapy has been shown to help depression in:

Older adults
People coping with serious illnesses like cancer

Problem-solving therapy also appears to be effective as a brief treatment for depression, offering benefits in as little as six to eight sessions with a therapist or another healthcare professional. This may make it a good option for someone unable to commit to a lengthier treatment for depression.

Problem-solving therapy is not a good fit for everyone. It may not be effective at addressing issues that don't have clear solutions, like seeking meaning or purpose in life. Problem-solving therapy is also intended to treat specific problems, not general habits or thought patterns .

In general, it's also important to remember that problem-solving therapy is not a primary treatment for mental disorders. If you are living with the symptoms of a serious mental illness such as bipolar disorder or schizophrenia , you may need additional treatment with evidence-based approaches for your particular concern.

Problem-solving therapy is best aimed at someone who has a mental or physical issue that is being treated separately, but who also has life issues that go along with that problem that has yet to be addressed.

For example, it could help if you can't clean your house or pay your bills because of your depression, or if a cancer diagnosis is interfering with your quality of life.

Your doctor may be able to recommend therapists in your area who utilize this approach, or they may offer it themselves as part of their practice. You can also search for a problem-solving therapist with help from the American Psychological Association’s (APA) Society of Clinical Psychology .

If receiving problem-solving therapy from a doctor or mental healthcare professional is not an option for you, you could also consider implementing it as a self-help strategy using a workbook designed to help you learn problem-solving skills on your own.

During your first session, your therapist may spend some time explaining their process and approach. They may ask you to identify the problem you’re currently facing, and they’ll likely discuss your goals for therapy .

Keep In Mind

Problem-solving therapy may be a short-term intervention that's focused on solving a specific issue in your life. If you need further help with something more pervasive, it can also become a longer-term treatment option.

Get Help Now

We've tried, tested, and written unbiased reviews of the best online therapy programs including Talkspace, BetterHelp, and ReGain. Find out which option is the best for you.

Shang P, Cao X, You S, Feng X, Li N, Jia Y. Problem-solving therapy for major depressive disorders in older adults: an updated systematic review and meta-analysis of randomized controlled trials . Aging Clin Exp Res . 2021;33(6):1465-1475. doi:10.1007/s40520-020-01672-3

Cuijpers P, Wit L de, Kleiboer A, Karyotaki E, Ebert DD. Problem-solving therapy for adult depression: An updated meta-analysis . Eur Psychiatry . 2018;48(1):27-37. doi:10.1016/j.eurpsy.2017.11.006

Nezu AM, Nezu CM, D'Zurilla TJ. Problem-Solving Therapy: A Treatment Manual . New York; 2013. doi:10.1891/9780826109415.0001

Owens D, Wright-Hughes A, Graham L, et al. Problem-solving therapy rather than treatment as usual for adults after self-harm: a pragmatic, feasibility, randomised controlled trial (the MIDSHIPS trial) . Pilot Feasibility Stud . 2020;6:119. doi:10.1186/s40814-020-00668-0

Sorsdahl K, Stein DJ, Corrigall J, et al. The efficacy of a blended motivational interviewing and problem solving therapy intervention to reduce substance use among patients presenting for emergency services in South Africa: A randomized controlled trial . Subst Abuse Treat Prev Policy . 2015;10(1):46. doi:doi.org/10.1186/s13011-015-0042-1

Margolis SA, Osborne P, Gonzalez JS. Problem solving . In: Gellman MD, ed. Encyclopedia of Behavioral Medicine . Springer International Publishing; 2020:1745-1747. doi:10.1007/978-3-030-39903-0_208

Kirkham JG, Choi N, Seitz DP. Meta-analysis of problem solving therapy for the treatment of major depressive disorder in older adults . Int J Geriatr Psychiatry . 2016;31(5):526-535. doi:10.1002/gps.4358

Garand L, Rinaldo DE, Alberth MM, et al. Effects of problem solving therapy on mental health outcomes in family caregivers of persons with a new diagnosis of mild cognitive impairment or early dementia: A randomized controlled trial . Am J Geriatr Psychiatry . 2014;22(8):771-781. doi:10.1016/j.jagp.2013.07.007

Noyes K, Zapf AL, Depner RM, et al. Problem-solving skills training in adult cancer survivors: Bright IDEAS-AC pilot study . Cancer Treat Res Commun . 2022;31:100552. doi:10.1016/j.ctarc.2022.100552

Albert SM, King J, Anderson S, et al. Depression agency-based collaborative: effect of problem-solving therapy on risk of common mental disorders in older adults with home care needs . The American Journal of Geriatric Psychiatry . 2019;27(6):619-624. doi:10.1016/j.jagp.2019.01.002

By Arlin Cuncic, MA Arlin Cuncic, MA, is the author of The Anxiety Workbook and founder of the website About Social Anxiety. She has a Master's degree in clinical psychology.

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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Use Active Listening to Help a Colleague Make a Hard Decision

Cheryl Strauss Einhorn

Don’t jump straight to problem-solving.

Imagine a colleague is faced with a high-stakes decision. They’re likely stressed, conflicted, and overwhelmed. In these situations, many of us default to the role of problem-solver. We try to support our colleague by providing our opinion or offering a solution. But to effectively support decision makers in your organization, you need to step back from your own ego and just listen . This article outlines practical strategies for exercising four types of active listening: emotional, informational, analytical, and reflective. Active listening can be hard to do, but it’s a great skill to practice. It allows you to strengthen key relationships while giving decision makers the space to make decisions for themselves.

Arnaldo was the chief operating officer at a successful investment firm. Recently, the firm’s results had been underperforming expectations. This poor performance was due to one large investment that the chief investment officer, Russ, was committed to holding. Arnaldo had fielded several calls from investors who wanted Russ to sell the money-losing investment. So, when Russ asked for a meeting to discuss the fund’s performance, Arnaldo’s instinct was to make a pitch to sell — to solve the problem.

Cheryl Strauss Einhorn is the founder and CEO of Decisive, a decision sciences company using her AREA Method decision-making system for individuals, companies, and nonprofits looking to solve complex problems. Decisive offers digital tools and in-person training, workshops, coaching and consulting. Cheryl is a long-time educator teaching at Columbia Business School and Cornell and has won several journalism awards for her investigative news stories. She’s authored two books on complex problem solving, Problem Solved for personal and professional decisions, and Investing In Financial Research about business, financial, and investment decisions. Her new book, Problem Solver, is about the psychology of personal decision-making and Problem Solver Profiles. For more information please watch Cheryl’s TED talk and visit areamethod.com .

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Raising Self-Reliant Kids: 8 Steps To Foster Independence

Raising self-reliant kids is one of the biggest parenting flexes you can have. Our job as parents is to give our kids the skills they need to confidently navigate the world. As much as we want to be there for them, they must learn to rely on themselves and trust their abilities.

Self-reliance starts at home and isn’t as complicated as you might think to encourage. It takes intention, patience, and a bit of modeling as you teach your child how to be confident in themselves.

What Does It Mean for Your Child To Be Self-Reliant?

A self-reliant child is independent and autonomous. They understand their effort is valuable and can help them achieve their goals. Self-reliance lets your child trust their abilities to take on challenges and explore the world around them.

You’ve probably noticed your child striving for independence already. Kids crave autonomy, whether it’s putting on their own pair of shoes or dying their hair. It’s our job to give them the skills they need to build resilience and perseverance.

Benefits of Self-Reliance for Kids

Encouraging independence and self-reliance gives kids a good foundation for success. Self-reliant kids:

Make decisions more easily and usually make better choices
Have the ability to problem-solve and think creatively about situations
Feel more self-confident and have higher self-esteem
Have better emotional regulation

8 Steps To Foster Independence

Without self-reliance, kids depend on parents, teachers, siblings, and friends. Dependent kids rely heavily on others for guidance, problem-solving, and decision-making. On the other hand, self-reliant kids display independence but feel comfortable asking for help when they need it.

1. Speak mindfully

Your words have power. What you say to your child and how you say it becomes their inner voice. You can help them feel empowered and confident or ashamed and inadequate.

Instead of getting frustrated and impatient as your child is busy with a task, praise their progress and effort. It’s easy to be annoyed by how long it takes to tie shoelaces when you’re trying to get out of the door. But when you reframe their behavior and recognize their effort, it makes them feel good and helps you keep your cool.

Some kids struggle to do challenging things. You can use positive reinforcement to encourage them to keep trying. The more you praise their specific efforts, the more of that behavior you’ll see. Positive reinforcement helps your child feel confident as they learn to do things independently.

2. Give age-appropriate responsibilities

Age-appropriate responsibilities empower kids to do things for themselves and contribute to the family and home. You can help your child take ownership of responsibilities by setting them collaboratively. Let them work out how to complete chores before jumping in to tell them how best to do it, and don’t remove obstacles they may face.

They can take ownership of their responsibilities by keeping a chore chart . Keeping track of their progress helps kids take responsibility for the consequences of failing to follow through with tasks.

3. Let them make decisions

How can you expect your child to trust themselves if you always make decisions for them?

If the idea of letting your child call the shots gives you a cold sweat, start with something small. For example, lay out two outfits and let your child choose which one to wear. For older kids, let them decide on a family activity for the weekend.

When you make decisions a normal part of the day, your child won’t find them stressful. They will also learn to assess risk because they make decisions, both good and bad, within the safe parameters you set. Letting kids make decisions, especially in the early years, helps them take risks, accept the outcome of their decisions, and become more independent and self-reliant [ * ].

4. Help them set goals

Kids learn to trust themselves when they set goals and take action to achieve them. Goals can range from small, like saving enough pocket money to buy a Lego set, to significant, like achieving high enough grades to get into a prestigious college. Goals should be:

S - Specific
M - Measurable
A - Achievable
R - Relevant
T - Time-Bound

Encourage your child to set long-term and short-term goals. Reaching short-term goals will give them a sense of achievement, helping them persevere as they work toward the long-term ones. Each time they successfully overcome frustration or tick a task off their list, they learn to trust themselves and their commitment more.

5. Teach Problem-Solving

A big part of self-reliance is learning to think critically and creatively when solving problems. According to some research, kids who can problem-solve have higher levels of self-esteem and confidence and display less challenging behavior [ * ].

You can model problem-solving by ‘thinking out loud.’ When you are trying to solve a problem, talk about it out loud so your child can see the process in action. You can also ask your child for their advice. Start with something simple like dinner. For example, “I was going to make quiche for dinner, but I don’t have enough eggs. What could we make instead?”

If your child has a problem, ask open-ended questions and guide them through the process of finding an answer. Brainstorm together and discuss different solutions. Give your child the opportunity to figure it out for themselves.

6. Encourage a growth mindset

Helping your child develop a growth mindset is invaluable. Kids with a growth mindset see failure as a learning opportunity and aren’t afraid to make mistakes. A growth mindset means your child will be more willing to take on challenging tasks.

For your child to tackle life independently, they must make mistakes, learn from them, and try new things. However, how you view your child’s success or failure can affect their mindset. Some research shows that parents who see failure as a negative focus on outcomes over progress and are more likely to have kids with a fixed mindset [ * ].

7. Foster self-confidence

Self-reliance happens when your child has the confidence to explore and is brave enough to learn new skills. The easiest way for you to foster self-confidence is to teach them practical skills. These may include:

Grocery shopping and budgeting
Prepping and cooking a meal
Caring for pets

Praise your child’s perseverance as they try new things. Be specific by praising their actions. For example, you can tell them. “Wow, the table looks beautiful. I love the flowers you added!”

8. Emotional regulation

Emotional regulation is managing your emotions and responding rather than reacting to situations. To feel confident, independent, and empowered, your child must understand and deal with their feelings.

By embracing difficult situations, you can help your child develop self-reliance and emotional regulation. Scaffolding is an effective way to give your child just enough support to help them get through a challenging situation or task.

For example, if your child struggles with their English homework, help them with one or two questions to give them the confidence to tackle the rest independently.

Be sure to validate your child’s emotions. For example, “I see that you’re struggling. Homework can be hard.” This lets your child feel seen and creates a sense of safety and connection.

The Bottom Line

Self-reliance helps kids and teens become independent, confident people who can deal with challenges healthily and recover from setbacks.

Watching your kids grow up, make mistakes, and learn can be challenging. However, creating a safe space for them to explore and fail is exactly what they need as they learn how to trust themselves and their blossoming independence.

Awopetu, A. V. (2023, December 22). FOSTERING SELF-RELIANCE AND INDEPENDENCE IN EARLY CHILDHOOD: HOW EXPOSURE TO RISKY ACTIVITIES HELPS THERE. Awopetu | European Journal of Education Studies. https://oapub.org/edu/index.php/ejes/article/view/5141/7773
Fettig, A., Schultz, T. R., & Ostrosky, M. M. (2016, August 1). Storybooks and Beyond. Young Exceptional Children. https://doi.org/10.1177/1096250615576803
Haimovitz, K., & Dweck, C. S. (2016). Parents’ Views of Failure Predict Children’s Fixed and Growth Intelligence Mind-Sets. Psychological Science, 27(6), 859-869. https://doi.org/10.1177/0956797616639727

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Domain and Range of a Function

Understand the concepts of domain and range of a function with this comprehensive guide. Knowing how to determine the domain and range is crucial for analyzing and interpreting functions in mathematics.

Key Takeaways

Introduction to domain and range.

Definition of domain and range.
Importance of understanding the domain and range in mathematical functions.

How to Determine the Domain

Steps to find the domain of a function.
Examples of common functions and their domains.

How to Determine the Range

Steps to find the range of a function.
Examples of common functions and their ranges.

Applications of Domain and Range

Real-life applications of domain and range in various fields.
How understanding domain and range can aid in problem-solving.

The domain of a function is the complete set of possible input values (independent variable) that allow the function to work. The range of a function is the complete set of possible output values (dependent variable) that result from using the function. Understanding these concepts is essential for graphing functions and solving mathematical problems.

Steps to Find the Domain

Identify the Function : Start by understanding the type of function you are dealing with, such as linear, quadratic, polynomial, rational, etc.
Analyze Constraints : Determine any restrictions on the input values. For example, values that make the denominator zero in a rational function or negative values under a square root in a real-valued function.
Set Notation : Express the domain using interval notation or set notation.
Linear Functions : The domain is all real numbers.
Quadratic Functions : The domain is all real numbers.
Rational Functions : Exclude values that make the denominator zero.
Square Root Functions : Include only values that make the expression under the square root non-negative.

Steps to Find the Range

Identify the Function : Understand the type of function you are analyzing.
Determine the Behavior : Analyze how the function behaves as the input values change, considering both end behavior and any critical points.
Solve for Output Values : Determine the set of all possible output values based on the input values within the domain.
Linear Functions : The range is all real numbers.
Quadratic Functions : The range is all real numbers greater than or equal to the vertex's y-coordinate (for upward-facing parabolas) or less than or equal to the vertex's y-coordinate (for downward-facing parabolas).
Rational Functions : Determine the horizontal asymptotes or use limits to find the range.
Square Root Functions : The range includes only non-negative values.

Real-life Applications

Engineering : Analyzing stresses and strains in materials.
Economics : Understanding demand and supply functions.
Science : Modeling population growth or radioactive decay.

Problem-solving

Knowing the domain and range helps in solving equations, optimizing functions, and understanding the behavior of different mathematical models.

By mastering the concepts of domain and range, you can enhance your mathematical skills and apply them to various real-world problems.

For a detailed step-by-step guide, visit the full article at https://www.geeksforgeeks.org/domain-and-range-of-function/ .

Let’s shift from explaining NY’s cannabis problems to solving them (Guest Column)

Published: May. 28, 2024, 7:30 a.m.

SUNY Orange students take part in the school's Horticultural Cannabis class.

Ngiste Abebe | KND Group

Join NY Cannabis Insider for its next industry meetup in Lafayette on June 13, 2024. Tickets available now .

This guest column is from Ngiste Abebe, co-founder of KND Group , vice chair of Virginia’s Cannabis Public Health Advisory Council, and a past president of the NY Medical Cannabis Industry Association . The views and opinions expressed in this article are those of the author, and do not necessarily reflect the views or positions of NY Cannabis Insider.

New York’s implementation of the Marijuana Regulation & Taxation Act (MRTA) has been plagued by many of the same challenges states that have gone before them experienced.

Implementation complications typically begin with the delays in establishing the new regulating body, continue through the adoption of comprehensive regulations, and peak when the (inevitably delayed) license issuance faces litigation landmines.

At the heart of New York’s rejection to take what worked in other states and tweak what didn’t, is what a recent audit conducted by the New York Office of General Services characterized as , “The perceived uniqueness of the agency’s work.”

Translation: politics. It’s unfortunate that every decision-maker involved in New York’s rollout has chosen to politicize the establishment of this emerging regulated market, which has left prospective business owners, licensees, consumers, and taxpayers way behind.

The job of a regulator is to implement the law in an unbiased, consistent way. The politics were already settled with the passage of the benchmark-setting MRTA’s equity provisions. The Office of Cannabis Management did not need to over complicate its mission, just fulfill the equity vision codified in the MRTA: issuing 50% of all licenses to Social and Economic Equity (SEE) business and establishing a marketplace that maximizes tax revenue and the corresponding community reinvestment.

While OCM has made strides in licensing under-represented groups, the SEE programs and support mandated by the MRTA have not been meaningfully provided. So while a dozen or so justice-involved business owners are winning, thousands of SEE applicants are struggling to navigate an ever-shifting regulatory framework and the communities owed reinvestment from tax revenues are once again collateral damage.

While limited in scope ( DASNY deserves a similar review), this report brought some much-needed transparency to license applicants. Now the focus must shift from explaining the problems to solving them.

First and foremost, OCM needs to restore regulatory credibility. The town hall tour OGS recommends is too staff-intensive for an agency that needs to prioritize serious internal reforms.

At this point OCM needs to embody consistent communications reliably backed by actions in public (and behind closed doors). Licensees and applicants should not fear “selective enforcement” from their regulator. Program changes, like this week’s news about DASNY’s loan fund ending , should come with guidance about next steps from the OCM.

Second, simplifying regulations will help streamline processes without compromising OCM’s mission. The unnecessary complexity in New York’s regulations are reflected in the hodge-podge process for license application review. Equity does not require complexity. In fact, the more needlessly byzantine programs are, the less accessible they become.

Last, and most importantly, OCM must focus on all aspects of equity programming. Licensing was only ever one piece of the puzzle. The unregulated cannabis market in New York is estimated to be $7 billion, which means New York’s failure to launch a meaningful regulated market has cost over $600 million of investment into the communities most impacted by the racist enforcement of prohibition.

The CAURD and Seeding Opportunity programs’ floundering starts are meant to support this broader approach to equity. Indeed, this community investment funding was so important that the sponsors of the MRTA held out in negotiations for years to include this historic provision in statute.

It’s time for decision-makers to recognize that the world has changed since the enactment of the MRTA – New York is now facing an enormous, and sophisticated, illicit market that new licensees need to be able to compete with.

Even more of our neighboring states have launched adult-use markets, with another expected to come online next month. It’s a good start for the OCM to review all applications in the November queue and for the Cannabis Control Board to award retail licenses to all eligible applicants with control of a location. New York needs to turn on regulated channels for consumers as soon as possible in order to focus on market conversion.

While cannabis may be a unique consumer good, the backbone of good governance is efficient bureaucracies powered by knowledgeable civil servants. Despite the current challenges, the future of New York’s cannabis industry still has promise if OCM can implement the needed changes.

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Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything ...
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What is Problem Solving? (Steps, Techniques, Examples)

What Is Problem Solving?

Problem-Solving Steps

Defining the Problem

Generating Solutions

Evaluating and Selecting Solutions

Implementing and Monitoring the Solution

Problem-Solving Techniques

Brainstorming

Root Cause Analysis

SWOT Analysis

Mind Mapping

Examples of Problem Solving in Various Contexts

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A guide to problem-solving techniques, steps, and skills

The 7 steps to problem-solving

1. Define the problem

2. Disaggregate

3. Prioritize problem branches

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4. Create an analysis plan

5. Conduct analysis

6. Synthesis

7. Communication

Exploring problem-solving in various contexts

Real-world examples of problem-solving

Key problem-solving skills

How to enhance your problem-solving skills

Final thoughts

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Table of Contents

1. Precisely Identify Problems

2. Collect Information and Plan

3. Brainstorm Solutions

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Problem Solving Methodologies

A3 Problem Solving Method:

Step 1 – Define the Problem

Step 2 – Gather Information and Brainstorm Ideas

Step 3 – Evaluate Options and Choose the Best Solution

Step 4 – Implement and Monitor the Solution

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8D: Tools and Techniques

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What Is Problem-Solving? How to Use Problem-Solving Skills to Resolve Issues

1. Define the Problem

2. Brainstorm Possible Solutions

3. Research Several Options

4. Select a Solution

5. Develop an Action Plan

First Principles Thinking

Steve Jobs’ Problem-Solving Method

Master the 7-Step Problem-Solving Process for Better Decision-Making

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