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

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

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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36 Problem-solving techniques, methods and tools

When it comes to solving problems, getting ideas is the easy part.

But businesses often forget the other four stages of the problem-solving process that will allow them to find the best solution.

Instead of jumping straight to idea generation, your problem-solving framework should look like this:

Identify the problem
Reveal why it has occurred
Brainstorm ideas
Select the best solution

See how idea generation doesn’t appear until stage 3?!

In this extensive resource, we provide techniques, methodologies and tools to guide you through every stage of the problem-solving process.

Once you’ve finished reading, you’ll possess an extensive problem-solving arsenal that will enable you to overcome your biggest workplace challenges.

11 Problem-solving techniques for clarity and confidence

Before we dive into more comprehensive methodologies for solving problems, there are a few basic techniques you should know.

The following techniques will set you up for a successful problem-solving session with your team, allowing you to take on your biggest challenges with clarity and confidence. ‍

1. Take a moment, take a breath

When a problem or challenge arises, it’s normal to act too quickly or rely on solutions that have worked well in the past. This is known as entrenched thinking.

But acting impulsively, without prior consideration or planning, can cause you to misunderstand the issue and overlook possible solutions to the problem.

Therefore, the first thing you should always do when you encounter a problem is: breathe in and out.

Take a step back and make a clear plan of action before you act. This will help you to take rational steps towards solving a problem. ‍

2. Ask questions to understand the full extent of the issue

Another common mistake people make when attempting to solve a problem is taking action before fully understanding the problem.

Before committing to a theory, ask enough questions to unearth the true root of the issue.

Later in this article, we cover The 5 Why’s problem-solving methodology which you can use to easily identify the root of your problem. Give this a go at your next meeting and see how your initial understanding of a problem can often be wrong. ‍

3. Consider alternative perspectives

A common problem-solving issue is that of myopia—a narrow-minded view or perception of the problem. Myopia can occur when you’re too involved with the problem or your team isn’t diverse enough.

To give yourself the best chance of resolving a problem, gain insight from a wide range of sources. Collaborate with key stakeholders, customers and on-the-ground employees to learn how the problem affects them and whether they have found workarounds or solutions.

To paint the broadest picture, don’t limit your problem-solving team to a specific archetype. Try to include everyone, from the chief executive to the office janitor.

If you’re working with a small team, try the Flip It! problem-solving methodology to view the issue from a fresh angle. ‍

4. Make your office space conducive to problem-solving

The environment in which your host your brainstorming sessions should maximise creativity . When your team members trust each other and feel relaxed, they’re more likely to come up with innovative ideas and solutions to a problem.

Here are a few ways to get your employees’ creative juices flowing:

Play team-building games that maximise trust and build interpersonal relationships
Improve your team’s problem-solving skills with games that encourage critical thinking
Redesign the office with comfortable furniture and collaborative spaces
Boost job satisfaction by creating a positive work-life balance
Improve collaborative skills and learn to resolve conflicts

World Café is a problem-solving method that creates a casual environment conducive to creative thinking.

Keep reading to learn more about how World Café can help your team solve complex organisational problems. ‍

5. Use problem-solving methodologies to guide the process

Because problem-solving is a creative process, it can be hard to keep it on track. As more ideas get banded around, conflicts can arise that derail the session.

That’s why problem-solving methodologies are so helpful. They offer you proven problem-solving frameworks to guide your group sessions and keep them on track.

The Six Thinking Hats problem-solving method is a popular technique that guides the process and helps your team analyse a problem from all angles.

We’re going to take a look at our favourite problem-solving methodologies in the next section of this article, XY Tried and tested problem-solving methodologies. ‍

6. Use analogies to solve complex problems

Sometimes, solving a different problem can help you uncover solutions to another problem!

By stripping back a complex issue and framing it as a simplified analogy , you approach a problem from a different angle, enabling you to come up with alternative ideas.

After solving practice problems, your team might be more aptly equipped to solve real-world issues.

However, coming up with an analogy that reflects your issue can be difficult, so don’t worry if this technique doesn’t work for you.

The Speed Boat diagram is a visual tool that helps your employees view existing challenges as anchors holding back a boat which represents your end goals. By assigning a “weight” to each anchor, your team can prioritise which issues to tackle first. ‍

7. Establish clear constraints

Constraints make a big problem more approachable.

Before you tackle a problem, establish clear boundaries and codes of conduct for the session. This allows your team to focus on the current issue without becoming distracted or veering off on a tangent.

In an article published in the Harvard Business Review, authors Oguz A. Acar, Murat Tarakci, and Daan van Knippenberg wrote, “Constraints … provide focus and a creative challenge that motivates people to search for and connect information from different sources to generate novel ideas for new products, services, or business processes.” (Why Constraints Are Good for Innovation, 2019)

Lightning Decision Jam is a prime example of how constraints can assist the creative process. Here, your team are given strict time constraints and isn’t permitted to discuss ideas until the end. ‍

8. Dislodge preconceived ideas

Humans are creatures of habit.

We defer to strategies that have produced positive results in the past. This is typically beneficial because recalling our previous successes means we don’t need to constantly re-learn similar tasks.

But when it comes to problem-solving, this way of thinking can trip us up. We become fixated on a solution that worked in the past, but when this fails we’re dismayed and left wondering what to do next.

To resolve problems effectively, your employees need to escape the precincts of their imaginations. This helps to eliminate functional fixedness—the belief that an item serves only its predefined function.

Alternative Application is an icebreaker game that encourages employees to think outside the box by coming up with different uses for everyday objects. Try this at your next meeting or team-building event and watch your team tap into their creativity. ‍

9. Level the playing field

Having a diverse group of employees at your brainstorming sessions is a good idea, but there’s one problem: the extroverted members of your team will be more vocal than the introverts.

To ensure you’re gaining insight from every member of your team, you need to give your quieter employees equal opportunities to contribute by eliminating personality biases.

Read more: What icebreaker games and questions work best for introverts?

The obvious solution, then, is to “silence” the louder participants (it’s not as sinister as it sounds, promise)—all you have to do is ban your team from debating suggestions during the ideation process.

The Lightning Decision Jam methodology gives your employees equal opportunities to contribute because much of the problem-solving process is carried out in silence. ‍

10. Take a break from the problem

Have you ever noticed how the best ideas seem to come when you’re not actively working on a problem? You may have spent hours slumped over your desk hashing out a solution, only for the “eureka!” moment to come when you’re walking your dog or taking a shower.

In James Webb Young’s book, A Technique for Producing Ideas , phase three of the process is “stepping away from the problem.” Young proclaims that after putting in the hard work, the information needs to ferment in the mind before any plausible ideas come to you.

So next time you’re in a meeting with your team trying to solve a problem, don’t panic if you don’t uncover groundbreaking ideas there and then. Allow everybody to mull over what they’ve learned, then reconvene at a later date.

The Creativity Dice methodology is a quick-fire brainstorming game that allows your team to incubate ideas while concentrating on another. ‍

11. Limit feedback sessions

The way your team delivers feedback at the end of a successful brainstorming session is critical. Left unsupervised, excessive feedback can undo all of your hard work.

Therefore, it’s wise to put a cap on the amount of feedback your team can provide. One great way of doing this is by using the One Breath Feedback technique.

By limiting your employees to one breath, they’re taught to be concise with their final comments.

16 Tried and tested problem-solving methodologies

Problem-solving methodologies keep your brainstorming session on track and encourage your team to consider all angles of the issue.

Countless methods have wiggled their way into the world of business, each one with a unique strategy and end goal.

Here are 12 of our favourite problem-solving methodologies that will help you find the best-fit solution to your troubles. ‍

12. Six Thinking Hats

Six Thinking Hats is a methodical problem-solving framework that helps your group consider all possible problems, causes, solutions and repercussions by assigning a different coloured hat to each stage of the problem-solving process.

The roles of each hat are as follows:

Blue Hat (Control): This hat controls the session and dictates the order in which the hats will be worn. When wearing the Blue Hat, your group will observe possible solutions, draw conclusions and define a plan of action.
Green Hat (Idea Generation): The Green Hat signifies creativity. At this stage of the methodology, your team will focus their efforts on generating ideas, imagining solutions and considering alternatives.
Red Hat (Intuition and Feelings): It’s time for your employees to communicate their feelings. Here, your team listen to their guts and convey their emotional impulses without justification.
Yellow Hat (Benefits and Values): What are the merits of each idea that has been put forward thus far? What positive impacts could they have?
Black or Grey Hat (Caution): What are the potential risks or shortcomings of each idea? What negative impacts could result from implicating each idea?
White Hat (Information and Data): While wearing The White Hat, your team must determine what information is needed and from where it can be obtained.

For Six Thinking Hats to work effectively, ensure your team acts within the confines of each role.

While wearing The Yellow Hat, for example, your team should only discuss the positives . Any negative implications should be left for the Black or Grey hat.

Note: Feel free to alter the hat colours to align with your cultural context. ‍

13. Lightning Decision Jam (LDJ)

Lightning Decision Jam is a nine-stage problem-solving process designed to uncover a variety of perspectives while keeping the session on track.

The process starts by defining a general topic like the internal design process, interdepartmental communication, the sales funnel, etc.

Then, armed with pens and post-it notes, your team will work through the nine stages in the following order:

Write problems (7 minutes)
Present problems (4 minutes/person)
Select problems (6 minutes)
Reframe the problems (6 minutes)
Offer solutions (7 minutes)
Vote on solutions (10 minutes)
Prioritise solutions (30 seconds)
Decide what to execute (10 minutes)
Create task lists (5 minutes)

The philosophy behind LDJ is that of constraint. By limiting discussion, employees can focus on compiling ideas and coming to democratic decisions that benefit the company without being distracted or going off on a tangent. ‍

14. The 5 Why’s

Root Cause Analysis (RCA) is the process of unearthing a problem and finding the underlying cause. To help you through this process, you can use The 5 Why’s methodology.

The idea is to ask why you’re experiencing a problem, reframe the problem based on the answer, and then ask “ why?” again. If you do this five times , you should come pretty close to the root of your original challenge.

While this might not be a comprehensive end-to-end methodology, it certainly helps you to pin down your core challenges. ‍

15. World Café

If you’ve had enough of uninspiring corporate boardrooms, World Café is the solution.

This problem-solving strategy facilitates casual conversations around given topics, enabling players to speak more openly about their grievances without the pressure of a large group.

Here’s how to do it:

Create a cosy cafe-style setting (try to have at least five or six chairs per table).
As a group, decide on a core problem and mark this as the session topic.
Divide your group into smaller teams by arranging five or six players at a table.
Assign each group a question that pertains to the session topic, or decide on one question for all groups to discuss at once.
Give the groups about 20 minutes to casually talk over each question.
Repeat this with about three or four different questions, making sure to write down key insights from each group.
Share the insights with the whole group.

World Café is a useful way of uncovering hidden causes and pitfalls by having multiple simultaneous conversations about a given topic. ‍

16. Discovery and Action Dialogue (DAD)

Discovery and Actions Dialogues are a collaborative method for employees to share and adopt personal behaviours in response to a problem.

This crowdsourcing approach provides insight into how a problem affects individuals throughout your company and whether some are better equipped than others.

A DAD session is guided by a facilitator who asks seven open-ended questions in succession. Each person is given equal time to participate while a recorder takes down notes and valuable insights.

This is a particularly effective method for uncovering preexisting ideas, behaviours and solutions from the people who face problems daily. ‍

17. Design Sprint 2.0

The Design Sprint 2.0 model by Jake Knapp helps your team to focus on finding, developing measuring a solution within four days . Because theorising is all well and good, but sometimes you can learn more by getting an idea off the ground and observing how it plays out in the real world.

Here’s the basic problem-solving framework:

Day 1: Map out or sketch possible solutions
Day 2: Choose the best solutions and storyboard your strategy going forward
Day 3: Create a living, breathing prototype
Day 4: Test and record how it performs in the real world

This technique is great for testing the viability of new products or expanding and fixing the features of an existing product. ‍

18. Open Space Technology

Open Space Technology is a method for large groups to create a problem-solving agenda around a central theme. It works best when your group is comprised of subject-matter experts and experienced individuals with a sufficient stake in the problem.

Open Space Technology works like this:

Establish a core theme for your team to centralise their efforts.
Ask the participants to consider their approach and write it on a post-it note.
Everybody writes a time and place for discussion on their note and sticks it to the wall.
The group is then invited to join the sessions that most interest them.
Everybody joins and contributes to their chosen sessions
Any significant insights and outcomes are recorded and presented to the group.

This methodology grants autonomy to your team and encourages them to take ownership of the problem-solving process. ‍

19. Round-Robin Brainstorming Technique

While not an end-to-end problem-solving methodology, the Round-Robin Brainstorming Technique is an effective way of squeezing every last ounce of creativity from your ideation sessions.

Here’s how it works:

Decide on a problem that needs to be solved
Sitting in a circle, give each employee a chance to offer an idea
Have somebody write down each idea as they come up
Participants can pass if they don’t have anything to contribute
The brainstorming session ends once everybody has passed

Once you’ve compiled a long list of ideas, it’s up to you how you move forward. You could, for example, borrow techniques from other methodologies, such as the “vote on solutions” phase of the Lightning Decision Jam. ‍

20. Failure Modes and Effects Analysis (FMEA)

Failure Modes and Effects Analysis is a method for preventing and mitigating problems within your business processes.

This technique starts by examining the process in question and asking, “What could go wrong?” From here, your team starts to brainstorm a list of potential failures.

Then, going through the list one by one, ask your participants, “Why would this failure happen?”

Once you’ve answered this question for each list item, ask yourselves, “What would the consequences be of this failure?”

This proactive method focuses on prevention rather than treatment. Instead of waiting for a problem to occur and reacting, you’re actively searching for future shortcomings. ‍

21. Flip It!

The Flip It! Methodology teaches your team to view their concerns in a different light and frame them instead as catalysts for positive change.

The game works like this:

Select a topic your employees are likely to be concerned about, like market demand for your product or friction between departments.
Give each participant a pile of sticky notes and ask them to write down all their fears about the topic.
Take the fears and stick them to an area of the wall marked “fears.”
Then, encourage your team to look at these fears and ask them to reframe them as “hope” by writing new statements on different sticky notes.
Take these “hope” statements and stick them to an area of the wall marked “hope.”
Discuss the statements, then ask them to vote on the areas they feel they can start to take action on. They can do this by drawing a dot on the corner of the sticky note.
Move the notes with the most votes to a new area of the wall marked “traction.”
Discuss the most popular statements as a group and brainstorm actionable items related to each.
Write down the actions that need to be made and discuss them again as a group.

This brainstorming approach teaches your employees the danger of engrained thinking and helps them to reframe their fears as opportunities. ‍

22. The Creativity Dice

The Creativity Dice teaches your team to incubate ideas as they focus on different aspects of a problem. As we mentioned earlier in the article, giving ideas time to mature can be a highly effective problem-solving strategy. Here’s how the game works:

Choose a topic to focus on, It can be as specific or open-ended as you like. Write this down as a word or sentence. Roll the die, start a timer of three minutes and start writing down ideas within the confines of what that number resembles. The roles of each number are as follows:

Specification: Write down goals you want to achieve.
Investigation: Write down existing factual information you know about the topic.
Ideation: Write down creative or practical ideas related to the topic.
Incubation: Do something else unrelated to the problem.
Iteration: Look at what you’ve already written and come up with related ideas (roll again if you didn’t write anything yet). ‍
Integration: Look at everything you have written and try to create something cohesive from your ideas like a potential new product or actionable next step.

Once you’ve finished the activity, review your findings and decide what you want to take with you. ‍

23. SWOT Analysis

The SWOT Analysis is a long-standing method for analysing the current state of your business and considering how this affects the desired end state.

The basic idea is this:

Before the meeting, come up with a “Desired end state” and draw a picture that represents this on a flipchart or whiteboard.
Divide a large piece of paper into quadrants marked “Strengths”, “Weaknesses”, “Opportunities” and “Threats.”
Starting with “Strengths”, work through the quadrants, coming up with ideas that relate to the desired end state.
Ask your team to vote for the statements or ideas of each category that they feel are most relevant to the desired end state.
As a group, discuss the implications that these statements have on the desired end state. Spark debate by asking thought-provoking and open-ended questions.

The SWOT Analysis is an intuitive method for understanding which parts of your business could be affecting your long-term goals. ‍

24. The Journalistic Six

When learning to cover every aspect of a story, journalists are taught to ask themselves six essential questions:

Now, this approach has been adopted by organisations to help understand every angle of a problem. All you need is a clear focus question, then you can start working through the six questions with your team until you have a 360-degree view of what has, can and needs to be done. ‍

25. Gamestorming

Gamestorming is a one-stop creative-thinking framework that uses various games to help your team come up with innovative ideas.

Originally published as a book 10 years ago, Gamestorming contained a selection of creative games used by Silicon Valley’s top-performing businesses to develop groundbreaking products and services.

This collection of resources, plucked from the minds of founders and CEOs like Jeff Bezos and Steve Jobs, allows you to tap into the potentially genius ideas lying dormant in the minds of your employees. ‍

26. Four-Step Sketch

The Four-Step Sketch is a visual brainstorming that provides an alternative to traditional discussion-based ideation techniques .

This methodology requires prior discussion to clarify the purpose of the activity. Imagine you’re on a startup retreat , for example, and your team is taking part in a design sprint or hackathon.

Once you’ve brainstormed a list of ideas with your team, participants can look at the suggestions and take down any relevant notes. They then take these notes and turn them into rough sketches that resemble the idea.

Then, as a warm-up, give each participant eight minutes to produce eight alternative sketches (eight minutes per sketch) of the idea. These ideas are not to be shared with the group.

Finally, participants create new sketches based on their favourite ideas and share them with the group. The group can then vote on the ideas they think offer the best solution. ‍

27. 15% Solutions

15% Solutions is a problem-solving strategy for motivating and inspiring your employees. By encouraging your team to gain small victories, you pave the way for bigger changes.

First, ask your participants to think about things they can personally do within the confines of their role.

Then, arrange your team into small groups of three to four and give them time to share their ideas and consult with each other.

This simple problem-solving process removes negativity and powerlessness and teaches your team to take responsibility for change.

9 Problem-solving tools for gathering and selecting ideas

Problem-solving tools support your meeting with easy-to-use graphs, visualisations and techniques.

By implementing a problem-solving tool, you break the cycle of mundane verbal discussion, enabling you to maintain engagement throughout the session. ‍

28. Fishbone Diagram

The Fishbone Diagram (otherwise known as the Ishikawa Diagram or Cause and Effect Diagram), is a tool for identifying the leading causes of a problem. You can then consolidate these causes into a comprehensive “Problem Statement.”

The term “Fishbone Diagram” is derived from the diagram’s structure. The problem itself forms the tail, possible causes radiate from the sides to form the fish skeleton while the final “Problem Statement” appears as the “head” of the fish.

Example: A fast-food chain is investigating the declining quality of their food. As the team brainstorms potential causes, they come up with reasons like “poorly trained personnel”, “lack of quality control”, and “incorrect quantity of spices.” Together with other causes, the group summarises that these problems lead to “bad burgers.” They write this as the Problem Statement and set about eliminating the main contributing factors. ‍

29. The Problem Tree

A Problem Tree is a useful tool for assessing the importance or relevance of challenges concerning the core topic. If you’re launching a new product, for example, gather your team and brainstorm the current issues, roadblocks and bottlenecks that are hindering the process.

Then, work together to decide which of these are most pressing. Place the most relevant issues closer to the core topic and less relevant issues farther away. ‍

30. SQUID Diagram

The Squid Diagram is an easy-to-use tool that charts the progress of ideas and business developments as they unfold. Your SQUID Diagram can remain on a wall for your team to add to over time.

Write down a core theme on a sticky note such as “customer service” or “Innovation”—this will be the “head” of your SQUID.
Hand two sets of different coloured sticky notes to your participants and choose one colour to represent “questions” and the other to represent “answers.”
Ask your team to write down questions pertaining to the success of the main topic. In the case of “Innovation,” your team might write things like “How can we improve collaboration between key stakeholders?”
Then, using the other coloured sticky notes, ask your team to write down possible answers to these questions. In the example above, this might be “Invest in open innovation software.”
Over time, you’ll develop a spawling SQUID Diagram that reflects the creative problem-solving process. ‍

31. The Speed Boat

The Speed Boat Diagram is a visual metaphor used to help your team identify and solve problems in the way of your goals.

Here’s how it works:

Draw a picture of a boat and name it after the core objective.
With your team, brainstorm things that are slowing progress and draw each one as an anchor beneath the boat.
Discuss possible solutions to each problem on the diagram.

This is an easy-to-use tool that sparks creative solutions. If you like, your team can assign a “weight” to each anchor which determines the impact each problem has on the end goal. ‍

32. The LEGO Challenge

LEGO is an excellent creative-thinking and problem-solving tool used regularly by event facilitators to help teams overcome challenges.

In our article 5 and 10-minute Team-Building Activities , we introduce Sneak a Peek —a collaborative team-building game that develops communication and leadership skills. ‍

33. The Three W’s: What? So What? Now What?

Teams aren’t always aligned when it comes to their understanding of a problem. While the problem remains the same for everyone, they might have differing opinions as to how it occurred at the implications it had.

Asking “ What? So What? Now What?” Helps you to understand different perspectives around a problem.

It goes like this:

Alone or in small groups, ask your employees to consider and write What happened. This should take between five and 10 minutes.
Then ask So What? What occurred because of this? Why was what happened important? What might happen if this issue is left unresolved?
Finally, ask your team Now What? What might be a solution to the problem? What actions do you need to take to avoid this happening again?

This approach helps your team understand how problems affect individuals in different ways and uncovers a variety of ways to overcome them. ‍

34. Now-How-Wow Matrix

Gathering ideas is easy—but selecting the best ones? That’s a different story.

If you’ve got a bunch of ideas, try the Now-How-Wow Matrix to help you identify which ones you should implement now and which ones should wait until later.

Simply draw a two-axis graph with “implementation difficulty” on the Y axis and “idea originality” on the X axis. Divide this graph into quadrants and write “Now!” in the bottom left panel, “Wow!” in the bottom right panel, and “How?” in the top right panel. You can leave the top left panel blank.

Then, take your ideas and plot them on the graph depending on their implementation difficulty and level of originality.

By the end, you’ll have a clearer picture of which ideas to ignore, which ones to implement now, and which ones to add to the pipeline for the future. ‍

35. Impact-Effort Matrix

The Impact-Effort Matrix is a variation of the Now-How-Wow Matrix where the Y axis is marked “Impact” and the X axis is marked “Effort.”

Then, divide the graph into quadrants and plot your ideas.

Top left section = Excellent, implement immediately
Top right section = Risky, but worth a try
Bottom left section = Low risk, but potentially ineffective
Bottom right section = Bad idea, ignore

The Impact-Effort Matrix is a simple way for your team to weigh the benefits of an idea against the amount of investment required. ‍

36. Dot Voting

Once you’ve gathered a substantial list of ideas from your employees, you need to sort the good from the bad.

Dot voting is a simple tool used by problem-solving facilitators as a fast and effective way for large groups to vote on their favourite ideas . You’ll have seen this method used in problem-solving methods like Flip It! and Lightning Decision Jam .

Participants write their ideas on sticky notes and stick them to the wall or a flipchart.
When asked, participants draw a small dot on the corner of the idea they like the most.
Participants can be given as many votes as necessary.
When voting ends, arrange the notes from “most popular” to “least popular.”

This provides an easy-to-use visual representation of the best and worst ideas put forward by your team.

Give your problems the attention they deserve at an offsite retreat

While working from home or at the office, your team is often too caught up in daily tasks to take on complex problems.

By escaping the office and uniting at an offsite location, you can craft a purposeful agenda of team-building activities and problem-solving sessions. This special time away from the office can prove invaluable when it comes to keeping your business on track.

If you have problems that need fixing (who doesn’t?), reach out to Surf Office and let us put together a fully-customised offsite retreat for you.

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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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How to improve your problem solving skills and build effective problem solving strategies

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What is a problem solving process?

What are the problem solving steps I need to follow?

Problem solving strategies

What skills do i need to be an effective problem solver, how can i improve my problem solving skills.

Solving problems is like baking a cake. You can go straight into the kitchen without a recipe or the right ingredients and do your best, but the end result is unlikely to be very tasty!

Using a process to bake a cake allows you to use the best ingredients without waste, collect the right tools, account for allergies, decide whether it is a birthday or wedding cake, and then bake efficiently and on time. The result is a better cake that is fit for purpose, tastes better and has created less mess in the kitchen. Also, it should have chocolate sprinkles. Having a step by step process to solve organizational problems allows you to go through each stage methodically and ensure you are trying to solve the right problems and select the most appropriate, effective solutions.

What are the problem solving steps I need to follow?

All problem solving processes go through a number of steps in order to move from identifying a problem to resolving it.

Depending on your problem solving model and who you ask, there can be anything between four and nine problem solving steps you should follow in order to find the right solution. Whatever framework you and your group use, there are some key items that should be addressed in order to have an effective process.

We’ve looked at problem solving processes from sources such as the American Society for Quality and their four step approach , and Mediate ‘s six step process. By reflecting on those and our own problem solving processes, we’ve come up with a sequence of seven problem solving steps we feel best covers everything you need in order to effectively solve problems.

1. Problem identification

The first stage of any problem solving process is to identify the problem or problems you might want to solve. Effective problem solving strategies always begin by allowing a group scope to articulate what they believe the problem to be and then coming to some consensus over which problem they approach first. Problem solving activities used at this stage often have a focus on creating frank, open discussion so that potential problems can be brought to the surface.

2. Problem analysis

Though this step is not a million miles from problem identification, problem analysis deserves to be considered separately. It can often be an overlooked part of the process and is instrumental when it comes to developing effective solutions.

The process of problem analysis means ensuring that the problem you are seeking to solve is the right problem . As part of this stage, you may look deeper and try to find the root cause of a specific problem at a team or organizational level.

Remember that problem solving strategies should not only be focused on putting out fires in the short term but developing long term solutions that deal with the root cause of organizational challenges.

Whatever your approach, analyzing a problem is crucial in being able to select an appropriate solution and the problem solving skills deployed in this stage are beneficial for the rest of the process and ensuring the solutions you create are fit for purpose.

3. Solution generation

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

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

4. Solution development

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

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

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

5. Decision making

Nearly there! Once your group has reached consensus and selected a solution that applies to the problem at hand you have some decisions to make. You will want to work on allocating ownership of the project, figure out who will do what, how the success of the solution will be measured and decide the next course of action.

The decision making stage is a part of the problem solving process that can get missed or taken as for granted. Fail to properly allocate roles and plan out how a solution will actually be implemented and it less likely to be successful in solving the problem.

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

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

6. Solution implementation

This is what we were waiting for! All problem solving strategies have the end goal of implementing a solution and solving a problem in mind.

Remember that in order for any solution to be successful, you need to help your group through all of the previous problem solving steps thoughtfully. Only then can you ensure that you are solving the right problem but also that you have developed the correct solution and can then successfully implement and measure the impact of that solution.

Project management and communication skills are key here – your solution may need to adjust when out in the wild or you might discover new challenges along the way.

7. Solution evaluation

So you and your team developed a great solution to a problem and have a gut feeling its been solved. Work done, right? Wrong. All problem solving strategies benefit from evaluation, consideration, and feedback. You might find that the solution does not work for everyone, might create new problems, or is potentially so successful that you will want to roll it out to larger teams or as part of other initiatives.

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

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

It’s worth underlining how important record keeping is throughout the problem solving process. If a solution didn’t work, you need to have the data and records to see why that was the case. If you go back to the drawing board, notes from the previous workshop can help save time. Data and insight is invaluable at every stage of the problem solving process and this one is no different.

Problem solving workshops made easy

Problem solving strategies are methods of approaching and facilitating the process of problem-solving with a set of techniques , actions, and processes. Different strategies are more effective if you are trying to solve broad problems such as achieving higher growth versus more focused problems like, how do we improve our customer onboarding process?

Broadly, the problem solving steps outlined above should be included in any problem solving strategy though choosing where to focus your time and what approaches should be taken is where they begin to differ. You might find that some strategies ask for the problem identification to be done prior to the session or that everything happens in the course of a one day workshop.

The key similarity is that all good problem solving strategies are structured and designed. Four hours of open discussion is never going to be as productive as a four-hour workshop designed to lead a group through a problem solving process.

Good problem solving strategies are tailored to the team, organization and problem you will be attempting to solve. Here are some example problem solving strategies you can learn from or use to get started.

Use a workshop to lead a team through a group process

Often, the first step to solving problems or organizational challenges is bringing a group together effectively. Most teams have the tools, knowledge, and expertise necessary to solve their challenges – they just need some guidance in how to use leverage those skills and a structure and format that allows people to focus their energies.

Facilitated workshops are one of the most effective ways of solving problems of any scale. By designing and planning your workshop carefully, you can tailor the approach and scope to best fit the needs of your team and organization.

Problem solving workshop

Creating a bespoke, tailored process
Tackling problems of any size
Building in-house workshop ability and encouraging their use

Workshops are an effective strategy for solving problems. By using tried and test facilitation techniques and methods, you can design and deliver a workshop that is perfectly suited to the unique variables of your organization. You may only have the capacity for a half-day workshop and so need a problem solving process to match.

By using our session planner tool and importing methods from our library of 700+ facilitation techniques, you can create the right problem solving workshop for your team. It might be that you want to encourage creative thinking or look at things from a new angle to unblock your groups approach to problem solving. By tailoring your workshop design to the purpose, you can help ensure great results.

One of the main benefits of a workshop is the structured approach to problem solving. Not only does this mean that the workshop itself will be successful, but many of the methods and techniques will help your team improve their working processes outside of the workshop.

We believe that workshops are one of the best tools you can use to improve the way your team works together. Start with a problem solving workshop and then see what team building, culture or design workshops can do for your organization!

Run a design sprint

Great for:

aligning large, multi-discipline teams
quickly designing and testing solutions
tackling large, complex organizational challenges and breaking them down into smaller tasks

By using design thinking principles and methods, a design sprint is a great way of identifying, prioritizing and prototyping solutions to long term challenges that can help solve major organizational problems with quick action and measurable results.

Some familiarity with design thinking is useful, though not integral, and this strategy can really help a team align if there is some discussion around which problems should be approached first.

The stage-based structure of the design sprint is also very useful for teams new to design thinking. The inspiration phase, where you look to competitors that have solved your problem, and the rapid prototyping and testing phases are great for introducing new concepts that will benefit a team in all their future work.

It can be common for teams to look inward for solutions and so looking to the market for solutions you can iterate on can be very productive. Instilling an agile prototyping and testing mindset can also be great when helping teams move forwards – generating and testing solutions quickly can help save time in the long run and is also pretty exciting!

Break problems down into smaller issues

Organizational challenges and problems are often complicated and large scale in nature. Sometimes, trying to resolve such an issue in one swoop is simply unachievable or overwhelming. Try breaking down such problems into smaller issues that you can work on step by step. You may not be able to solve the problem of churning customers off the bat, but you can work with your team to identify smaller effort but high impact elements and work on those first.

This problem solving strategy can help a team generate momentum, prioritize and get some easy wins. It’s also a great strategy to employ with teams who are just beginning to learn how to approach the problem solving process. If you want some insight into a way to employ this strategy, we recommend looking at our design sprint template below!

Use guiding frameworks or try new methodologies

Some problems are best solved by introducing a major shift in perspective or by using new methodologies that encourage your team to think differently.

Props and tools such as Methodkit , which uses a card-based toolkit for facilitation, or Lego Serious Play can be great ways to engage your team and find an inclusive, democratic problem solving strategy. Remember that play and creativity are great tools for achieving change and whatever the challenge, engaging your participants can be very effective where other strategies may have failed.

LEGO Serious Play

Improving core problem solving skills
Thinking outside of the box
Encouraging creative solutions

LEGO Serious Play is a problem solving methodology designed to get participants thinking differently by using 3D models and kinesthetic learning styles. By physically building LEGO models based on questions and exercises, participants are encouraged to think outside of the box and create their own responses.

Collaborate LEGO Serious Play exercises are also used to encourage communication and build problem solving skills in a group. By using this problem solving process, you can often help different kinds of learners and personality types contribute and unblock organizational problems with creative thinking.

Problem solving strategies like LEGO Serious Play are super effective at helping a team solve more skills-based problems such as communication between teams or a lack of creative thinking. Some problems are not suited to LEGO Serious Play and require a different problem solving strategy.

Card Decks and Method Kits

New facilitators or non-facilitators
Approaching difficult subjects with a simple, creative framework
Engaging those with varied learning styles

Card decks and method kids are great tools for those new to facilitation or for whom facilitation is not the primary role. Card decks such as the emotional culture deck can be used for complete workshops and in many cases, can be used right out of the box. Methodkit has a variety of kits designed for scenarios ranging from personal development through to personas and global challenges so you can find the right deck for your particular needs.

Having an easy to use framework that encourages creativity or a new approach can take some of the friction or planning difficulties out of the workshop process and energize a team in any setting. Simplicity is the key with these methods. By ensuring everyone on your team can get involved and engage with the process as quickly as possible can really contribute to the success of your problem solving strategy.

Source external advice

Looking to peers, experts and external facilitators can be a great way of approaching the problem solving process. Your team may not have the necessary expertise, insights of experience to tackle some issues, or you might simply benefit from a fresh perspective. Some problems may require bringing together an entire team, and coaching managers or team members individually might be the right approach. Remember that not all problems are best resolved in the same manner.

If you’re a solo entrepreneur, peer groups, coaches and mentors can also be invaluable at not only solving specific business problems, but in providing a support network for resolving future challenges. One great approach is to join a Mastermind Group and link up with like-minded individuals and all grow together. Remember that however you approach the sourcing of external advice, do so thoughtfully, respectfully and honestly. Reciprocate where you can and prepare to be surprised by just how kind and helpful your peers can be!

Mastermind Group

Solo entrepreneurs or small teams with low capacity
Peer learning and gaining outside expertise
Getting multiple external points of view quickly

Problem solving in large organizations with lots of skilled team members is one thing, but how about if you work for yourself or in a very small team without the capacity to get the most from a design sprint or LEGO Serious Play session?

A mastermind group – sometimes known as a peer advisory board – is where a group of people come together to support one another in their own goals, challenges, and businesses. Each participant comes to the group with their own purpose and the other members of the group will help them create solutions, brainstorm ideas, and support one another.

Mastermind groups are very effective in creating an energized, supportive atmosphere that can deliver meaningful results. Learning from peers from outside of your organization or industry can really help unlock new ways of thinking and drive growth. Access to the experience and skills of your peers can be invaluable in helping fill the gaps in your own ability, particularly in young companies.

A mastermind group is a great solution for solo entrepreneurs, small teams, or for organizations that feel that external expertise or fresh perspectives will be beneficial for them. It is worth noting that Mastermind groups are often only as good as the participants and what they can bring to the group. Participants need to be committed, engaged and understand how to work in this context.

Coaching and mentoring

Focused learning and development
Filling skills gaps
Working on a range of challenges over time

Receiving advice from a business coach or building a mentor/mentee relationship can be an effective way of resolving certain challenges. The one-to-one format of most coaching and mentor relationships can really help solve the challenges those individuals are having and benefit the organization as a result.

A great mentor can be invaluable when it comes to spotting potential problems before they arise and coming to understand a mentee very well has a host of other business benefits. You might run an internal mentorship program to help develop your team’s problem solving skills and strategies or as part of a large learning and development program. External coaches can also be an important part of your problem solving strategy, filling skills gaps for your management team or helping with specific business issues.

Now we’ve explored the problem solving process and the steps you will want to go through in order to have an effective session, let’s look at the skills you and your team need to be more effective problem solvers.

Problem solving skills are highly sought after, whatever industry or team you work in. Organizations are keen to employ people who are able to approach problems thoughtfully and find strong, realistic solutions. Whether you are a facilitator , a team leader or a developer, being an effective problem solver is a skill you’ll want to develop.

Problem solving skills form a whole suite of techniques and approaches that an individual uses to not only identify problems but to discuss them productively before then developing appropriate solutions.

Here are some of the most important problem solving skills everyone from executives to junior staff members should learn. We’ve also included an activity or exercise from the SessionLab library that can help you and your team develop that skill.

If you’re running a workshop or training session to try and improve problem solving skills in your team, try using these methods to supercharge your process!

Active listening

Active listening is one of the most important skills anyone who works with people can possess. In short, active listening is a technique used to not only better understand what is being said by an individual, but also to be more aware of the underlying message the speaker is trying to convey. When it comes to problem solving, active listening is integral for understanding the position of every participant and to clarify the challenges, ideas and solutions they bring to the table.

Some active listening skills include:

Paying complete attention to the speaker.
Removing distractions.
Avoid interruption.
Taking the time to fully understand before preparing a rebuttal.
Responding respectfully and appropriately.
Demonstrate attentiveness and positivity with an open posture, making eye contact with the speaker, smiling and nodding if appropriate. Show that you are listening and encourage them to continue.
Be aware of and respectful of feelings. Judge the situation and respond appropriately. You can disagree without being disrespectful.
Observe body language.
Paraphrase what was said in your own words, either mentally or verbally.
Remain neutral.
Reflect and take a moment before responding.
Ask deeper questions based on what is said and clarify points where necessary.

Active Listening #hyperisland #skills #active listening #remote-friendly This activity supports participants to reflect on a question and generate their own solutions using simple principles of active listening and peer coaching. It’s an excellent introduction to active listening but can also be used with groups that are already familiar with it. Participants work in groups of three and take turns being: “the subject”, the listener, and the observer.

Analytical skills

All problem solving models require strong analytical skills, particularly during the beginning of the process and when it comes to analyzing how solutions have performed.

Analytical skills are primarily focused on performing an effective analysis by collecting, studying and parsing data related to a problem or opportunity.

It often involves spotting patterns, being able to see things from different perspectives and using observable facts and data to make suggestions or produce insight.

Analytical skills are also important at every stage of the problem solving process and by having these skills, you can ensure that any ideas or solutions you create or backed up analytically and have been sufficiently thought out.

Nine Whys #innovation #issue analysis #liberating structures With breathtaking simplicity, you can rapidly clarify for individuals and a group what is essentially important in their work. You can quickly reveal when a compelling purpose is missing in a gathering and avoid moving forward without clarity. When a group discovers an unambiguous shared purpose, more freedom and more responsibility are unleashed. You have laid the foundation for spreading and scaling innovations with fidelity.

Collaboration

Trying to solve problems on your own is difficult. Being able to collaborate effectively, with a free exchange of ideas, to delegate and be a productive member of a team is hugely important to all problem solving strategies.

Remember that whatever your role, collaboration is integral, and in a problem solving process, you are all working together to find the best solution for everyone.

Marshmallow challenge with debriefing #teamwork #team #leadership #collaboration In eighteen minutes, teams must build the tallest free-standing structure out of 20 sticks of spaghetti, one yard of tape, one yard of string, and one marshmallow. The marshmallow needs to be on top. The Marshmallow Challenge was developed by Tom Wujec, who has done the activity with hundreds of groups around the world. Visit the Marshmallow Challenge website for more information. This version has an extra debriefing question added with sample questions focusing on roles within the team.

Communication

Being an effective communicator means being empathetic, clear and succinct, asking the right questions, and demonstrating active listening skills throughout any discussion or meeting.

In a problem solving setting, you need to communicate well in order to progress through each stage of the process effectively. As a team leader, it may also fall to you to facilitate communication between parties who may not see eye to eye. Effective communication also means helping others to express themselves and be heard in a group.

Bus Trip #feedback #communication #appreciation #closing #thiagi #team This is one of my favourite feedback games. I use Bus Trip at the end of a training session or a meeting, and I use it all the time. The game creates a massive amount of energy with lots of smiles, laughs, and sometimes even a teardrop or two.

Creative problem solving skills can be some of the best tools in your arsenal. Thinking creatively, being able to generate lots of ideas and come up with out of the box solutions is useful at every step of the process.

The kinds of problems you will likely discuss in a problem solving workshop are often difficult to solve, and by approaching things in a fresh, creative manner, you can often create more innovative solutions.

Having practical creative skills is also a boon when it comes to problem solving. If you can help create quality design sketches and prototypes in record time, it can help bring a team to alignment more quickly or provide a base for further iteration.

The paper clip method #sharing #creativity #warm up #idea generation #brainstorming The power of brainstorming. A training for project leaders, creativity training, and to catalyse getting new solutions.

Critical thinking

Critical thinking is one of the fundamental problem solving skills you’ll want to develop when working on developing solutions. Critical thinking is the ability to analyze, rationalize and evaluate while being aware of personal bias, outlying factors and remaining open-minded.

Defining and analyzing problems without deploying critical thinking skills can mean you and your team go down the wrong path. Developing solutions to complex issues requires critical thinking too – ensuring your team considers all possibilities and rationally evaluating them.

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

Data analysis

Though it shares lots of space with general analytical skills, data analysis skills are something you want to cultivate in their own right in order to be an effective problem solver.

Being good at data analysis doesn’t just mean being able to find insights from data, but also selecting the appropriate data for a given issue, interpreting it effectively and knowing how to model and present that data. Depending on the problem at hand, it might also include a working knowledge of specific data analysis tools and procedures.

Having a solid grasp of data analysis techniques is useful if you’re leading a problem solving workshop but if you’re not an expert, don’t worry. Bring people into the group who has this skill set and help your team be more effective as a result.

Decision making

All problems need a solution and all solutions require that someone make the decision to implement them. Without strong decision making skills, teams can become bogged down in discussion and less effective as a result.

Making decisions is a key part of the problem solving process. It’s important to remember that decision making is not restricted to the leadership team. Every staff member makes decisions every day and developing these skills ensures that your team is able to solve problems at any scale. Remember that making decisions does not mean leaping to the first solution but weighing up the options and coming to an informed, well thought out solution to any given problem that works for the whole team.

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

Dependability

Most complex organizational problems require multiple people to be involved in delivering the solution. Ensuring that the team and organization can depend on you to take the necessary actions and communicate where necessary is key to ensuring problems are solved effectively.

Being dependable also means working to deadlines and to brief. It is often a matter of creating trust in a team so that everyone can depend on one another to complete the agreed actions in the agreed time frame so that the team can move forward together. Being undependable can create problems of friction and can limit the effectiveness of your solutions so be sure to bear this in mind throughout a project.

Team Purpose & Culture #team #hyperisland #culture #remote-friendly This is an essential process designed to help teams define their purpose (why they exist) and their culture (how they work together to achieve that purpose). Defining these two things will help any team to be more focused and aligned. With support of tangible examples from other companies, the team members work as individuals and a group to codify the way they work together. The goal is a visual manifestation of both the purpose and culture that can be put up in the team’s work space.

Emotional intelligence

Emotional intelligence is an important skill for any successful team member, whether communicating internally or with clients or users. In the problem solving process, emotional intelligence means being attuned to how people are feeling and thinking, communicating effectively and being self-aware of what you bring to a room.

There are often differences of opinion when working through problem solving processes, and it can be easy to let things become impassioned or combative. Developing your emotional intelligence means being empathetic to your colleagues and managing your own emotions throughout the problem and solution process. Be kind, be thoughtful and put your points across care and attention.

Being emotionally intelligent is a skill for life and by deploying it at work, you can not only work efficiently but empathetically. Check out the emotional culture workshop template for more!

Facilitation

As we’ve clarified in our facilitation skills post, facilitation is the art of leading people through processes towards agreed-upon objectives in a manner that encourages participation, ownership, and creativity by all those involved. While facilitation is a set of interrelated skills in itself, the broad definition of facilitation can be invaluable when it comes to problem solving. Leading a team through a problem solving process is made more effective if you improve and utilize facilitation skills – whether you’re a manager, team leader or external stakeholder.

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

Flexibility

Being flexible is a vital skill when it comes to problem solving. This does not mean immediately bowing to pressure or changing your opinion quickly: instead, being flexible is all about seeing things from new perspectives, receiving new information and factoring it into your thought process.

Flexibility is also important when it comes to rolling out solutions. It might be that other organizational projects have greater priority or require the same resources as your chosen solution. Being flexible means understanding needs and challenges across the team and being open to shifting or arranging your own schedule as necessary. Again, this does not mean immediately making way for other projects. It’s about articulating your own needs, understanding the needs of others and being able to come to a meaningful compromise.

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

Working in any group can lead to unconscious elements of groupthink or situations in which you may not wish to be entirely honest. Disagreeing with the opinions of the executive team or wishing to save the feelings of a coworker can be tricky to navigate, but being honest is absolutely vital when to comes to developing effective solutions and ensuring your voice is heard.

Remember that being honest does not mean being brutally candid. You can deliver your honest feedback and opinions thoughtfully and without creating friction by using other skills such as emotional intelligence.

Explore your Values #hyperisland #skills #values #remote-friendly Your Values is an exercise for participants to explore what their most important values are. It’s done in an intuitive and rapid way to encourage participants to follow their intuitive feeling rather than over-thinking and finding the “correct” values. It is a good exercise to use to initiate reflection and dialogue around personal values.

Initiative

The problem solving process is multi-faceted and requires different approaches at certain points of the process. Taking initiative to bring problems to the attention of the team, collect data or lead the solution creating process is always valuable. You might even roadtest your own small scale solutions or brainstorm before a session. Taking initiative is particularly effective if you have good deal of knowledge in that area or have ownership of a particular project and want to get things kickstarted.

That said, be sure to remember to honor the process and work in service of the team. If you are asked to own one part of the problem solving process and you don’t complete that task because your initiative leads you to work on something else, that’s not an effective method of solving business challenges.

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

Impartiality

A particularly useful problem solving skill for product owners or managers is the ability to remain impartial throughout much of the process. In practice, this means treating all points of view and ideas brought forward in a meeting equally and ensuring that your own areas of interest or ownership are not favored over others.

There may be a stage in the process where a decision maker has to weigh the cost and ROI of possible solutions against the company roadmap though even then, ensuring that the decision made is based on merit and not personal opinion.

Empathy map #frame insights #create #design #issue analysis An empathy map is a tool to help a design team to empathize with the people they are designing for. You can make an empathy map for a group of people or for a persona. To be used after doing personas when more insights are needed.

Being a good leader means getting a team aligned, energized and focused around a common goal. In the problem solving process, strong leadership helps ensure that the process is efficient, that any conflicts are resolved and that a team is managed in the direction of success.

It’s common for managers or executives to assume this role in a problem solving workshop, though it’s important that the leader maintains impartiality and does not bulldoze the group in a particular direction. Remember that good leadership means working in service of the purpose and team and ensuring the workshop is a safe space for employees of any level to contribute. Take a look at our leadership games and activities post for more exercises and methods to help improve leadership in your organization.

Leadership Pizza #leadership #team #remote-friendly This leadership development activity offers a self-assessment framework for people to first identify what skills, attributes and attitudes they find important for effective leadership, and then assess their own development and initiate goal setting.

In the context of problem solving, mediation is important in keeping a team engaged, happy and free of conflict. When leading or facilitating a problem solving workshop, you are likely to run into differences of opinion. Depending on the nature of the problem, certain issues may be brought up that are emotive in nature.

Being an effective mediator means helping those people on either side of such a divide are heard, listen to one another and encouraged to find common ground and a resolution. Mediating skills are useful for leaders and managers in many situations and the problem solving process is no different.

Conflict Responses #hyperisland #team #issue resolution A workshop for a team to reflect on past conflicts, and use them to generate guidelines for effective conflict handling. The workshop uses the Thomas-Killman model of conflict responses to frame a reflective discussion. Use it to open up a discussion around conflict with a team.

Planning

Solving organizational problems is much more effective when following a process or problem solving model. Planning skills are vital in order to structure, deliver and follow-through on a problem solving workshop and ensure your solutions are intelligently deployed.

Planning skills include the ability to organize tasks and a team, plan and design the process and take into account any potential challenges. Taking the time to plan carefully can save time and frustration later in the process and is valuable for ensuring a team is positioned for success.

3 Action Steps #hyperisland #action #remote-friendly This is a small-scale strategic planning session that helps groups and individuals to take action toward a desired change. It is often used at the end of a workshop or programme. The group discusses and agrees on a vision, then creates some action steps that will lead them towards that vision. The scope of the challenge is also defined, through discussion of the helpful and harmful factors influencing the group.

Prioritization

As organisations grow, the scale and variation of problems they face multiplies. Your team or is likely to face numerous challenges in different areas and so having the skills to analyze and prioritize becomes very important, particularly for those in leadership roles.

A thorough problem solving process is likely to deliver multiple solutions and you may have several different problems you wish to solve simultaneously. Prioritization is the ability to measure the importance, value, and effectiveness of those possible solutions and choose which to enact and in what order. The process of prioritization is integral in ensuring the biggest challenges are addressed with the most impactful solutions.

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

Project management

Some problem solving skills are utilized in a workshop or ideation phases, while others come in useful when it comes to decision making. Overseeing an entire problem solving process and ensuring its success requires strong project management skills.

While project management incorporates many of the other skills listed here, it is important to note the distinction of considering all of the factors of a project and managing them successfully. Being able to negotiate with stakeholders, manage tasks, time and people, consider costs and ROI, and tie everything together is massively helpful when going through the problem solving process.

Record keeping

Working out meaningful solutions to organizational challenges is only one part of the process. Thoughtfully documenting and keeping records of each problem solving step for future consultation is important in ensuring efficiency and meaningful change.

For example, some problems may be lower priority than others but can be revisited in the future. If the team has ideated on solutions and found some are not up to the task, record those so you can rule them out and avoiding repeating work. Keeping records of the process also helps you improve and refine your problem solving model next time around!

Personal Kanban #gamestorming #action #agile #project planning Personal Kanban is a tool for organizing your work to be more efficient and productive. It is based on agile methods and principles.

Research skills

Conducting research to support both the identification of problems and the development of appropriate solutions is important for an effective process. Knowing where to go to collect research, how to conduct research efficiently, and identifying pieces of research are relevant are all things a good researcher can do well.

In larger groups, not everyone has to demonstrate this ability in order for a problem solving workshop to be effective. That said, having people with research skills involved in the process, particularly if they have existing area knowledge, can help ensure the solutions that are developed with data that supports their intention. Remember that being able to deliver the results of research efficiently and in a way the team can easily understand is also important. The best data in the world is only as effective as how it is delivered and interpreted.

Customer experience map #ideation #concepts #research #design #issue analysis #remote-friendly Customer experience mapping is a method of documenting and visualizing the experience a customer has as they use the product or service. It also maps out their responses to their experiences. To be used when there is a solution (even in a conceptual stage) that can be analyzed.

Risk management

Managing risk is an often overlooked part of the problem solving process. Solutions are often developed with the intention of reducing exposure to risk or solving issues that create risk but sometimes, great solutions are more experimental in nature and as such, deploying them needs to be carefully considered.

Managing risk means acknowledging that there may be risks associated with more out of the box solutions or trying new things, but that this must be measured against the possible benefits and other organizational factors.

Be informed, get the right data and stakeholders in the room and you can appropriately factor risk into your decision making process.

Decisions, Decisions… #communication #decision making #thiagi #action #issue analysis When it comes to decision-making, why are some of us more prone to take risks while others are risk-averse? One explanation might be the way the decision and options were presented. This exercise, based on Kahneman and Tversky’s classic study , illustrates how the framing effect influences our judgement and our ability to make decisions . The participants are divided into two groups. Both groups are presented with the same problem and two alternative programs for solving them. The two programs both have the same consequences but are presented differently. The debriefing discussion examines how the framing of the program impacted the participant’s decision.

Team-building

No single person is as good at problem solving as a team. Building an effective team and helping them come together around a common purpose is one of the most important problem solving skills, doubly so for leaders. By bringing a team together and helping them work efficiently, you pave the way for team ownership of a problem and the development of effective solutions.

In a problem solving workshop, it can be tempting to jump right into the deep end, though taking the time to break the ice, energize the team and align them with a game or exercise will pay off over the course of the day.

Remember that you will likely go through the problem solving process multiple times over an organization’s lifespan and building a strong team culture will make future problem solving more effective. It’s also great to work with people you know, trust and have fun with. Working on team building in and out of the problem solving process is a hallmark of successful teams that can work together to solve business problems.

9 Dimensions Team Building Activity #ice breaker #teambuilding #team #remote-friendly 9 Dimensions is a powerful activity designed to build relationships and trust among team members. There are 2 variations of this icebreaker. The first version is for teams who want to get to know each other better. The second version is for teams who want to explore how they are working together as a team.

Time management

The problem solving process is designed to lead a team from identifying a problem through to delivering a solution and evaluating its effectiveness. Without effective time management skills or timeboxing of tasks, it can be easy for a team to get bogged down or be inefficient.

By using a problem solving model and carefully designing your workshop, you can allocate time efficiently and trust that the process will deliver the results you need in a good timeframe.

Time management also comes into play when it comes to rolling out solutions, particularly those that are experimental in nature. Having a clear timeframe for implementing and evaluating solutions is vital for ensuring their success and being able to pivot if necessary.

Improving your skills at problem solving is often a career-long pursuit though there are methods you can use to make the learning process more efficient and to supercharge your problem solving skillset.

Remember that the skills you need to be a great problem solver have a large overlap with those skills you need to be effective in any role. Investing time and effort to develop your active listening or critical thinking skills is valuable in any context. Here are 7 ways to improve your problem solving skills.

Share best practices

Remember that your team is an excellent source of skills, wisdom, and techniques and that you should all take advantage of one another where possible. Best practices that one team has for solving problems, conducting research or making decisions should be shared across the organization. If you have in-house staff that have done active listening training or are data analysis pros, have them lead a training session.

Your team is one of your best resources. Create space and internal processes for the sharing of skills so that you can all grow together.

Ask for help and attend training

Once you’ve figured out you have a skills gap, the next step is to take action to fill that skills gap. That might be by asking your superior for training or coaching, or liaising with team members with that skill set. You might even attend specialized training for certain skills – active listening or critical thinking, for example, are business-critical skills that are regularly offered as part of a training scheme.

Whatever method you choose, remember that taking action of some description is necessary for growth. Whether that means practicing, getting help, attending training or doing some background reading, taking active steps to improve your skills is the way to go.

Learn a process

Problem solving can be complicated, particularly when attempting to solve large problems for the first time. Using a problem solving process helps give structure to your problem solving efforts and focus on creating outcomes, rather than worrying about the format.

Tools such as the seven-step problem solving process above are effective because not only do they feature steps that will help a team solve problems, they also develop skills along the way. Each step asks for people to engage with the process using different skills and in doing so, helps the team learn and grow together. Group processes of varying complexity and purpose can also be found in the SessionLab library of facilitation techniques . Using a tried and tested process and really help ease the learning curve for both those leading such a process, as well as those undergoing the purpose.

Effective teams make decisions about where they should and shouldn’t expend additional effort. By using a problem solving process, you can focus on the things that matter, rather than stumbling towards a solution haphazardly.

Create a feedback loop

Some skills gaps are more obvious than others. It’s possible that your perception of your active listening skills differs from those of your colleagues.

It’s valuable to create a system where team members can provide feedback in an ordered and friendly manner so they can all learn from one another. Only by identifying areas of improvement can you then work to improve them.

Remember that feedback systems require oversight and consideration so that they don’t turn into a place to complain about colleagues. Design the system intelligently so that you encourage the creation of learning opportunities, rather than encouraging people to list their pet peeves.

While practice might not make perfect, it does make the problem solving process easier. If you are having trouble with critical thinking, don’t shy away from doing it. Get involved where you can and stretch those muscles as regularly as possible.

Problem solving skills come more naturally to some than to others and that’s okay. Take opportunities to get involved and see where you can practice your skills in situations outside of a workshop context. Try collaborating in other circumstances at work or conduct data analysis on your own projects. You can often develop those skills you need for problem solving simply by doing them. Get involved!

Use expert exercises and methods

Learn from the best. Our library of 700+ facilitation techniques is full of activities and methods that help develop the skills you need to be an effective problem solver. Check out our templates to see how to approach problem solving and other organizational challenges in a structured and intelligent manner.

There is no single approach to improving problem solving skills, but by using the techniques employed by others you can learn from their example and develop processes that have seen proven results.

Try new ways of thinking and change your mindset

Using tried and tested exercises that you know well can help deliver results, but you do run the risk of missing out on the learning opportunities offered by new approaches. As with the problem solving process, changing your mindset can remove blockages and be used to develop your problem solving skills.

Most teams have members with mixed skill sets and specialties. Mix people from different teams and share skills and different points of view. Teach your customer support team how to use design thinking methods or help your developers with conflict resolution techniques. Try switching perspectives with facilitation techniques like Flip It! or by using new problem solving methodologies or models. Give design thinking, liberating structures or lego serious play a try if you want to try a new approach. You will find that framing problems in new ways and using existing skills in new contexts can be hugely useful for personal development and improving your skillset. It’s also a lot of fun to try new things. Give it a go!

Encountering business challenges and needing to find appropriate solutions is not unique to your organization. Lots of very smart people have developed methods, theories and approaches to help develop problem solving skills and create effective solutions. Learn from them!

Books like The Art of Thinking Clearly , Think Smarter, or Thinking Fast, Thinking Slow are great places to start, though it’s also worth looking at blogs related to organizations facing similar problems to yours, or browsing for success stories. Seeing how Dropbox massively increased growth and working backward can help you see the skills or approach you might be lacking to solve that same problem. Learning from others by reading their stories or approaches can be time-consuming but ultimately rewarding.

A tired, distracted mind is not in the best position to learn new skills. It can be tempted to burn the candle at both ends and develop problem solving skills outside of work. Absolutely use your time effectively and take opportunities for self-improvement, though remember that rest is hugely important and that without letting your brain rest, you cannot be at your most effective.

Creating distance between yourself and the problem you might be facing can also be useful. By letting an idea sit, you can find that a better one presents itself or you can develop it further. Take regular breaks when working and create a space for downtime. Remember that working smarter is preferable to working harder and that self-care is important for any effective learning or improvement process.

Want to design better group processes?

Over to you

Now we’ve explored some of the key problem solving skills and the problem solving steps necessary for an effective process, you’re ready to begin developing more effective solutions and leading problem solving workshops.

Need more inspiration? Check out our post on problem solving activities you can use when guiding a group towards a great solution in your next workshop or meeting. Have questions? Did you have a great problem solving technique you use with your team? Get in touch in the comments below. We’d love to chat!

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Problem Solving

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Problem-Solving Strategies and Obstacles

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

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Application
Improvement

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

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

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

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

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

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

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

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

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

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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The Oxford Handbook of Cognitive Psychology

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48 Problem Solving

Department of Psychological and Brain Sciences, University of California, Santa Barbara

Published: 03 June 2013
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Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or nonroutine, and as well defined or ill defined. The major cognitive processes in problem solving are representing, planning, executing, and monitoring. The major kinds of knowledge required for problem solving are facts, concepts, procedures, strategies, and beliefs. Classic theoretical approaches to the study of problem solving are associationism, Gestalt, and information processing. Current issues and suggested future issues include decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific thinking, everyday thinking, and the cognitive neuroscience of problem solving. Common themes concern the domain specificity of problem solving and a focus on problem solving in authentic contexts.

The study of problem solving begins with defining problem solving, problem, and problem types. This introduction to problem solving is rounded out with an examination of cognitive processes in problem solving, the role of knowledge in problem solving, and historical approaches to the study of problem solving.

Definition of Problem Solving

Problem solving refers to cognitive processing directed at achieving a goal for which the problem solver does not initially know a solution method. This definition consists of four major elements (Mayer, 1992 ; Mayer & Wittrock, 2006 ):

Cognitive —Problem solving occurs within the problem solver’s cognitive system and can only be inferred indirectly from the problem solver’s behavior (including biological changes, introspections, and actions during problem solving). Process —Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of a new mental representation. Directed —Problem solving is aimed at achieving a goal. Personal —Problem solving depends on the existing knowledge of the problem solver so that what is a problem for one problem solver may not be a problem for someone who already knows a solution method.

The definition is broad enough to include a wide array of cognitive activities such as deciding which apartment to rent, figuring out how to use a cell phone interface, playing a game of chess, making a medical diagnosis, finding the answer to an arithmetic word problem, or writing a chapter for a handbook. Problem solving is pervasive in human life and is crucial for human survival. Although this chapter focuses on problem solving in humans, problem solving also occurs in nonhuman animals and in intelligent machines.

How is problem solving related to other forms of high-level cognition processing, such as thinking and reasoning? Thinking refers to cognitive processing in individuals but includes both directed thinking (which corresponds to the definition of problem solving) and undirected thinking such as daydreaming (which does not correspond to the definition of problem solving). Thus, problem solving is a type of thinking (i.e., directed thinking).

Reasoning refers to problem solving within specific classes of problems, such as deductive reasoning or inductive reasoning. In deductive reasoning, the reasoner is given premises and must derive a conclusion by applying the rules of logic. For example, given that “A is greater than B” and “B is greater than C,” a reasoner can conclude that “A is greater than C.” In inductive reasoning, the reasoner is given (or has experienced) a collection of examples or instances and must infer a rule. For example, given that X, C, and V are in the “yes” group and x, c, and v are in the “no” group, the reasoning may conclude that B is in “yes” group because it is in uppercase format. Thus, reasoning is a type of problem solving.

Definition of Problem

A problem occurs when someone has a goal but does not know to achieve it. This definition is consistent with how the Gestalt psychologist Karl Duncker ( 1945 , p. 1) defined a problem in his classic monograph, On Problem Solving : “A problem arises when a living creature has a goal but does not know how this goal is to be reached.” However, today researchers recognize that the definition should be extended to include problem solving by intelligent machines. This definition can be clarified using an information processing approach by noting that a problem occurs when a situation is in the given state, the problem solver wants the situation to be in the goal state, and there is no obvious way to move from the given state to the goal state (Newell & Simon, 1972 ). Accordingly, the three main elements in describing a problem are the given state (i.e., the current state of the situation), the goal state (i.e., the desired state of the situation), and the set of allowable operators (i.e., the actions the problem solver is allowed to take). The definition of “problem” is broad enough to include the situation confronting a physician who wishes to make a diagnosis on the basis of preliminary tests and a patient examination, as well as a beginning physics student trying to solve a complex physics problem.

Types of Problems

It is customary in the problem-solving literature to make a distinction between routine and nonroutine problems. Routine problems are problems that are so familiar to the problem solver that the problem solver knows a solution method. For example, for most adults, “What is 365 divided by 12?” is a routine problem because they already know the procedure for long division. Nonroutine problems are so unfamiliar to the problem solver that the problem solver does not know a solution method. For example, figuring out the best way to set up a funding campaign for a nonprofit charity is a nonroutine problem for most volunteers. Technically, routine problems do not meet the definition of problem because the problem solver has a goal but knows how to achieve it. Much research on problem solving has focused on routine problems, although most interesting problems in life are nonroutine.

Another customary distinction is between well-defined and ill-defined problems. Well-defined problems have a clearly specified given state, goal state, and legal operators. Examples include arithmetic computation problems or games such as checkers or tic-tac-toe. Ill-defined problems have a poorly specified given state, goal state, or legal operators, or a combination of poorly defined features. Examples include solving the problem of global warming or finding a life partner. Although, ill-defined problems are more challenging, much research in problem solving has focused on well-defined problems.

Cognitive Processes in Problem Solving

The process of problem solving can be broken down into two main phases: problem representation , in which the problem solver builds a mental representation of the problem situation, and problem solution , in which the problem solver works to produce a solution. The major subprocess in problem representation is representing , which involves building a situation model —that is, a mental representation of the situation described in the problem. The major subprocesses in problem solution are planning , which involves devising a plan for how to solve the problem; executing , which involves carrying out the plan; and monitoring , which involves evaluating and adjusting one’s problem solving.

For example, given an arithmetic word problem such as “Alice has three marbles. Sarah has two more marbles than Alice. How many marbles does Sarah have?” the process of representing involves building a situation model in which Alice has a set of marbles, there is set of marbles for the difference between the two girls, and Sarah has a set of marbles that consists of Alice’s marbles and the difference set. In the planning process, the problem solver sets a goal of adding 3 and 2. In the executing process, the problem solver carries out the computation, yielding an answer of 5. In the monitoring process, the problem solver looks over what was done and concludes that 5 is a reasonable answer. In most complex problem-solving episodes, the four cognitive processes may not occur in linear order, but rather may interact with one another. Although some research focuses mainly on the execution process, problem solvers may tend to have more difficulty with the processes of representing, planning, and monitoring.

Knowledge for Problem Solving

An important theme in problem-solving research is that problem-solving proficiency on any task depends on the learner’s knowledge (Anderson et al., 2001 ; Mayer, 1992 ). Five kinds of knowledge are as follows:

Facts —factual knowledge about the characteristics of elements in the world, such as “Sacramento is the capital of California” Concepts —conceptual knowledge, including categories, schemas, or models, such as knowing the difference between plants and animals or knowing how a battery works Procedures —procedural knowledge of step-by-step processes, such as how to carry out long-division computations Strategies —strategic knowledge of general methods such as breaking a problem into parts or thinking of a related problem Beliefs —attitudinal knowledge about how one’s cognitive processing works such as thinking, “I’m good at this”

Although some research focuses mainly on the role of facts and procedures in problem solving, complex problem solving also depends on the problem solver’s concepts, strategies, and beliefs (Mayer, 1992 ).

Historical Approaches to Problem Solving

Psychological research on problem solving began in the early 1900s, as an outgrowth of mental philosophy (Humphrey, 1963 ; Mandler & Mandler, 1964 ). Throughout the 20th century four theoretical approaches developed: early conceptions, associationism, Gestalt psychology, and information processing.

Early Conceptions

The start of psychology as a science can be set at 1879—the year Wilhelm Wundt opened the first world’s psychology laboratory in Leipzig, Germany, and sought to train the world’s first cohort of experimental psychologists. Instead of relying solely on philosophical speculations about how the human mind works, Wundt sought to apply the methods of experimental science to issues addressed in mental philosophy. His theoretical approach became structuralism —the analysis of consciousness into its basic elements.

Wundt’s main contribution to the study of problem solving, however, was to call for its banishment. According to Wundt, complex cognitive processing was too complicated to be studied by experimental methods, so “nothing can be discovered in such experiments” (Wundt, 1911/1973 ). Despite his admonishments, however, a group of his former students began studying thinking mainly in Wurzburg, Germany. Using the method of introspection, subjects were asked to describe their thought process as they solved word association problems, such as finding the superordinate of “newspaper” (e.g., an answer is “publication”). Although the Wurzburg group—as they came to be called—did not produce a new theoretical approach, they found empirical evidence that challenged some of the key assumptions of mental philosophy. For example, Aristotle had proclaimed that all thinking involves mental imagery, but the Wurzburg group was able to find empirical evidence for imageless thought .

Associationism

The first major theoretical approach to take hold in the scientific study of problem solving was associationism —the idea that the cognitive representations in the mind consist of ideas and links between them and that cognitive processing in the mind involves following a chain of associations from one idea to the next (Mandler & Mandler, 1964 ; Mayer, 1992 ). For example, in a classic study, E. L. Thorndike ( 1911 ) placed a hungry cat in what he called a puzzle box—a wooden crate in which pulling a loop of string that hung from overhead would open a trap door to allow the cat to escape to a bowl of food outside the crate. Thorndike placed the cat in the puzzle box once a day for several weeks. On the first day, the cat engaged in many extraneous behaviors such as pouncing against the wall, pushing its paws through the slats, and meowing, but on successive days the number of extraneous behaviors tended to decrease. Overall, the time required to get out of the puzzle box decreased over the course of the experiment, indicating the cat was learning how to escape.

Thorndike’s explanation for how the cat learned to solve the puzzle box problem is based on an associationist view: The cat begins with a habit family hierarchy —a set of potential responses (e.g., pouncing, thrusting, meowing, etc.) all associated with the same stimulus (i.e., being hungry and confined) and ordered in terms of strength of association. When placed in the puzzle box, the cat executes its strongest response (e.g., perhaps pouncing against the wall), but when it fails, the strength of the association is weakened, and so on for each unsuccessful action. Eventually, the cat gets down to what was initially a weak response—waving its paw in the air—but when that response leads to accidentally pulling the string and getting out, it is strengthened. Over the course of many trials, the ineffective responses become weak and the successful response becomes strong. Thorndike refers to this process as the law of effect : Responses that lead to dissatisfaction become less associated with the situation and responses that lead to satisfaction become more associated with the situation. According to Thorndike’s associationist view, solving a problem is simply a matter of trial and error and accidental success. A major challenge to assocationist theory concerns the nature of transfer—that is, where does a problem solver find a creative solution that has never been performed before? Associationist conceptions of cognition can be seen in current research, including neural networks, connectionist models, and parallel distributed processing models (Rogers & McClelland, 2004 ).

Gestalt Psychology

The Gestalt approach to problem solving developed in the 1930s and 1940s as a counterbalance to the associationist approach. According to the Gestalt approach, cognitive representations consist of coherent structures (rather than individual associations) and the cognitive process of problem solving involves building a coherent structure (rather than strengthening and weakening of associations). For example, in a classic study, Kohler ( 1925 ) placed a hungry ape in a play yard that contained several empty shipping crates and a banana attached overhead but out of reach. Based on observing the ape in this situation, Kohler noted that the ape did not randomly try responses until one worked—as suggested by Thorndike’s associationist view. Instead, the ape stood under the banana, looked up at it, looked at the crates, and then in a flash of insight stacked the crates under the bananas as a ladder, and walked up the steps in order to reach the banana.

According to Kohler, the ape experienced a sudden visual reorganization in which the elements in the situation fit together in a way to solve the problem; that is, the crates could become a ladder that reduces the distance to the banana. Kohler referred to the underlying mechanism as insight —literally seeing into the structure of the situation. A major challenge of Gestalt theory is its lack of precision; for example, naming a process (i.e., insight) is not the same as explaining how it works. Gestalt conceptions can be seen in modern research on mental models and schemas (Gentner & Stevens, 1983 ).

Information Processing

The information processing approach to problem solving developed in the 1960s and 1970s and was based on the influence of the computer metaphor—the idea that humans are processors of information (Mayer, 2009 ). According to the information processing approach, problem solving involves a series of mental computations—each of which consists of applying a process to a mental representation (such as comparing two elements to determine whether they differ).

In their classic book, Human Problem Solving , Newell and Simon ( 1972 ) proposed that problem solving involved a problem space and search heuristics . A problem space is a mental representation of the initial state of the problem, the goal state of the problem, and all possible intervening states (based on applying allowable operators). Search heuristics are strategies for moving through the problem space from the given to the goal state. Newell and Simon focused on means-ends analysis , in which the problem solver continually sets goals and finds moves to accomplish goals.

Newell and Simon used computer simulation as a research method to test their conception of human problem solving. First, they asked human problem solvers to think aloud as they solved various problems such as logic problems, chess, and cryptarithmetic problems. Then, based on an information processing analysis, Newell and Simon created computer programs that solved these problems. In comparing the solution behavior of humans and computers, they found high similarity, suggesting that the computer programs were solving problems using the same thought processes as humans.

An important advantage of the information processing approach is that problem solving can be described with great clarity—as a computer program. An important limitation of the information processing approach is that it is most useful for describing problem solving for well-defined problems rather than ill-defined problems. The information processing conception of cognition lives on as a keystone of today’s cognitive science (Mayer, 2009 ).

Classic Issues in Problem Solving

Three classic issues in research on problem solving concern the nature of transfer (suggested by the associationist approach), the nature of insight (suggested by the Gestalt approach), and the role of problem-solving heuristics (suggested by the information processing approach).

Transfer refers to the effects of prior learning on new learning (or new problem solving). Positive transfer occurs when learning A helps someone learn B. Negative transfer occurs when learning A hinders someone from learning B. Neutral transfer occurs when learning A has no effect on learning B. Positive transfer is a central goal of education, but research shows that people often do not transfer what they learned to solving problems in new contexts (Mayer, 1992 ; Singley & Anderson, 1989 ).

Three conceptions of the mechanisms underlying transfer are specific transfer , general transfer , and specific transfer of general principles . Specific transfer refers to the idea that learning A will help someone learn B only if A and B have specific elements in common. For example, learning Spanish may help someone learn Latin because some of the vocabulary words are similar and the verb conjugation rules are similar. General transfer refers to the idea that learning A can help someone learn B even they have nothing specifically in common but A helps improve the learner’s mind in general. For example, learning Latin may help people learn “proper habits of mind” so they are better able to learn completely unrelated subjects as well. Specific transfer of general principles is the idea that learning A will help someone learn B if the same general principle or solution method is required for both even if the specific elements are different.

In a classic study, Thorndike and Woodworth ( 1901 ) found that students who learned Latin did not subsequently learn bookkeeping any better than students who had not learned Latin. They interpreted this finding as evidence for specific transfer—learning A did not transfer to learning B because A and B did not have specific elements in common. Modern research on problem-solving transfer continues to show that people often do not demonstrate general transfer (Mayer, 1992 ). However, it is possible to teach people a general strategy for solving a problem, so that when they see a new problem in a different context they are able to apply the strategy to the new problem (Judd, 1908 ; Mayer, 2008 )—so there is also research support for the idea of specific transfer of general principles.

Insight refers to a change in a problem solver’s mind from not knowing how to solve a problem to knowing how to solve it (Mayer, 1995 ; Metcalfe & Wiebe, 1987 ). In short, where does the idea for a creative solution come from? A central goal of problem-solving research is to determine the mechanisms underlying insight.

The search for insight has led to five major (but not mutually exclusive) explanatory mechanisms—insight as completing a schema, insight as suddenly reorganizing visual information, insight as reformulation of a problem, insight as removing mental blocks, and insight as finding a problem analog (Mayer, 1995 ). Completing a schema is exemplified in a study by Selz (Fridja & de Groot, 1982 ), in which people were asked to think aloud as they solved word association problems such as “What is the superordinate for newspaper?” To solve the problem, people sometimes thought of a coordinate, such as “magazine,” and then searched for a superordinate category that subsumed both terms, such as “publication.” According to Selz, finding a solution involved building a schema that consisted of a superordinate and two subordinate categories.

Reorganizing visual information is reflected in Kohler’s ( 1925 ) study described in a previous section in which a hungry ape figured out how to stack boxes as a ladder to reach a banana hanging above. According to Kohler, the ape looked around the yard and found the solution in a flash of insight by mentally seeing how the parts could be rearranged to accomplish the goal.

Reformulating a problem is reflected in a classic study by Duncker ( 1945 ) in which people are asked to think aloud as they solve the tumor problem—how can you destroy a tumor in a patient without destroying surrounding healthy tissue by using rays that at sufficient intensity will destroy any tissue in their path? In analyzing the thinking-aloud protocols—that is, transcripts of what the problem solvers said—Duncker concluded that people reformulated the goal in various ways (e.g., avoid contact with healthy tissue, immunize healthy tissue, have ray be weak in healthy tissue) until they hit upon a productive formulation that led to the solution (i.e., concentrating many weak rays on the tumor).

Removing mental blocks is reflected in classic studies by Duncker ( 1945 ) in which solving a problem involved thinking of a novel use for an object, and by Luchins ( 1942 ) in which solving a problem involved not using a procedure that had worked well on previous problems. Finding a problem analog is reflected in classic research by Wertheimer ( 1959 ) in which learning to find the area of a parallelogram is supported by the insight that one could cut off the triangle on one side and place it on the other side to form a rectangle—so a parallelogram is really a rectangle in disguise. The search for insight along each of these five lines continues in current problem-solving research.

Heuristics are problem-solving strategies, that is, general approaches to how to solve problems. Newell and Simon ( 1972 ) suggested three general problem-solving heuristics for moving from a given state to a goal state: random trial and error , hill climbing , and means-ends analysis . Random trial and error involves randomly selecting a legal move and applying it to create a new problem state, and repeating that process until the goal state is reached. Random trial and error may work for simple problems but is not efficient for complex ones. Hill climbing involves selecting the legal move that moves the problem solver closer to the goal state. Hill climbing will not work for problems in which the problem solver must take a move that temporarily moves away from the goal as is required in many problems.

Means-ends analysis involves creating goals and seeking moves that can accomplish the goal. If a goal cannot be directly accomplished, a subgoal is created to remove one or more obstacles. Newell and Simon ( 1972 ) successfully used means-ends analysis as the search heuristic in a computer program aimed at general problem solving, that is, solving a diverse collection of problems. However, people may also use specific heuristics that are designed to work for specific problem-solving situations (Gigerenzer, Todd, & ABC Research Group, 1999 ; Kahneman & Tversky, 1984 ).

Current and Future Issues in Problem Solving

Eight current issues in problem solving involve decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific problem solving, everyday thinking, and the cognitive neuroscience of problem solving.

Decision Making

Decision making refers to the cognitive processing involved in choosing between two or more alternatives (Baron, 2000 ; Markman & Medin, 2002 ). For example, a decision-making task may involve choosing between getting $240 for sure or having a 25% change of getting $1000. According to economic theories such as expected value theory, people should chose the second option, which is worth $250 (i.e., .25 x $1000) rather than the first option, which is worth $240 (1.00 x $240), but psychological research shows that most people prefer the first option (Kahneman & Tversky, 1984 ).

Research on decision making has generated three classes of theories (Markman & Medin, 2002 ): descriptive theories, such as prospect theory (Kahneman & Tversky), which are based on the ideas that people prefer to overweight the cost of a loss and tend to overestimate small probabilities; heuristic theories, which are based on the idea that people use a collection of short-cut strategies such as the availability heuristic (Gigerenzer et al., 1999 ; Kahneman & Tversky, 2000 ); and constructive theories, such as mental accounting (Kahneman & Tversky, 2000 ), in which people build a narrative to justify their choices to themselves. Future research is needed to examine decision making in more realistic settings.

Intelligence and Creativity

Although researchers do not have complete consensus on the definition of intelligence (Sternberg, 1990 ), it is reasonable to view intelligence as the ability to learn or adapt to new situations. Fluid intelligence refers to the potential to solve problems without any relevant knowledge, whereas crystallized intelligence refers to the potential to solve problems based on relevant prior knowledge (Sternberg & Gregorenko, 2003 ). As people gain more experience in a field, their problem-solving performance depends more on crystallized intelligence (i.e., domain knowledge) than on fluid intelligence (i.e., general ability) (Sternberg & Gregorenko, 2003 ). The ability to monitor and manage one’s cognitive processing during problem solving—which can be called metacognition —is an important aspect of intelligence (Sternberg, 1990 ). Research is needed to pinpoint the knowledge that is needed to support intelligent performance on problem-solving tasks.

Creativity refers to the ability to generate ideas that are original (i.e., other people do not think of the same idea) and functional (i.e., the idea works; Sternberg, 1999 ). Creativity is often measured using tests of divergent thinking —that is, generating as many solutions as possible for a problem (Guilford, 1967 ). For example, the uses test asks people to list as many uses as they can think of for a brick. Creativity is different from intelligence, and it is at the heart of creative problem solving—generating a novel solution to a problem that the problem solver has never seen before. An important research question concerns whether creative problem solving depends on specific knowledge or creativity ability in general.

Teaching of Thinking Skills

How can people learn to be better problem solvers? Mayer ( 2008 ) proposes four questions concerning teaching of thinking skills:

What to teach —Successful programs attempt to teach small component skills (such as how to generate and evaluate hypotheses) rather than improve the mind as a single monolithic skill (Covington, Crutchfield, Davies, & Olton, 1974 ). How to teach —Successful programs focus on modeling the process of problem solving rather than solely reinforcing the product of problem solving (Bloom & Broder, 1950 ). Where to teach —Successful programs teach problem-solving skills within the specific context they will be used rather than within a general course on how to solve problems (Nickerson, 1999 ). When to teach —Successful programs teaching higher order skills early rather than waiting until lower order skills are completely mastered (Tharp & Gallimore, 1988 ).

Overall, research on teaching of thinking skills points to the domain specificity of problem solving; that is, successful problem solving depends on the problem solver having domain knowledge that is relevant to the problem-solving task.

Expert Problem Solving

Research on expertise is concerned with differences between how experts and novices solve problems (Ericsson, Feltovich, & Hoffman, 2006 ). Expertise can be defined in terms of time (e.g., 10 years of concentrated experience in a field), performance (e.g., earning a perfect score on an assessment), or recognition (e.g., receiving a Nobel Prize or becoming Grand Master in chess). For example, in classic research conducted in the 1940s, de Groot ( 1965 ) found that chess experts did not have better general memory than chess novices, but they did have better domain-specific memory for the arrangement of chess pieces on the board. Chase and Simon ( 1973 ) replicated this result in a better controlled experiment. An explanation is that experts have developed schemas that allow them to chunk collections of pieces into a single configuration.

In another landmark study, Larkin et al. ( 1980 ) compared how experts (e.g., physics professors) and novices (e.g., first-year physics students) solved textbook physics problems about motion. Experts tended to work forward from the given information to the goal, whereas novices tended to work backward from the goal to the givens using a means-ends analysis strategy. Experts tended to store their knowledge in an integrated way, whereas novices tended to store their knowledge in isolated fragments. In another study, Chi, Feltovich, and Glaser ( 1981 ) found that experts tended to focus on the underlying physics concepts (such as conservation of energy), whereas novices tended to focus on the surface features of the problem (such as inclined planes or springs). Overall, research on expertise is useful in pinpointing what experts know that is different from what novices know. An important theme is that experts rely on domain-specific knowledge rather than solely general cognitive ability.

Analogical Reasoning

Analogical reasoning occurs when people solve one problem by using their knowledge about another problem (Holyoak, 2005 ). For example, suppose a problem solver learns how to solve a problem in one context using one solution method and then is given a problem in another context that requires the same solution method. In this case, the problem solver must recognize that the new problem has structural similarity to the old problem (i.e., it may be solved by the same method), even though they do not have surface similarity (i.e., the cover stories are different). Three steps in analogical reasoning are recognizing —seeing that a new problem is similar to a previously solved problem; abstracting —finding the general method used to solve the old problem; and mapping —using that general method to solve the new problem.

Research on analogical reasoning shows that people often do not recognize that a new problem can be solved by the same method as a previously solved problem (Holyoak, 2005 ). However, research also shows that successful analogical transfer to a new problem is more likely when the problem solver has experience with two old problems that have the same underlying structural features (i.e., they are solved by the same principle) but different surface features (i.e., they have different cover stories) (Holyoak, 2005 ). This finding is consistent with the idea of specific transfer of general principles as described in the section on “Transfer.”

Mathematical and Scientific Problem Solving

Research on mathematical problem solving suggests that five kinds of knowledge are needed to solve arithmetic word problems (Mayer, 2008 ):

Factual knowledge —knowledge about the characteristics of problem elements, such as knowing that there are 100 cents in a dollar Schematic knowledge —knowledge of problem types, such as being able to recognize time-rate-distance problems Strategic knowledge —knowledge of general methods, such as how to break a problem into parts Procedural knowledge —knowledge of processes, such as how to carry our arithmetic operations Attitudinal knowledge —beliefs about one’s mathematical problem-solving ability, such as thinking, “I am good at this”

People generally possess adequate procedural knowledge but may have difficulty in solving mathematics problems because they lack factual, schematic, strategic, or attitudinal knowledge (Mayer, 2008 ). Research is needed to pinpoint the role of domain knowledge in mathematical problem solving.

Research on scientific problem solving shows that people harbor misconceptions, such as believing that a force is needed to keep an object in motion (McCloskey, 1983 ). Learning to solve science problems involves conceptual change, in which the problem solver comes to recognize that previous conceptions are wrong (Mayer, 2008 ). Students can be taught to engage in scientific reasoning such as hypothesis testing through direct instruction in how to control for variables (Chen & Klahr, 1999 ). A central theme of research on scientific problem solving concerns the role of domain knowledge.

Everyday Thinking

Everyday thinking refers to problem solving in the context of one’s life outside of school. For example, children who are street vendors tend to use different procedures for solving arithmetic problems when they are working on the streets than when they are in school (Nunes, Schlieman, & Carraher, 1993 ). This line of research highlights the role of situated cognition —the idea that thinking always is shaped by the physical and social context in which it occurs (Robbins & Aydede, 2009 ). Research is needed to determine how people solve problems in authentic contexts.

Cognitive Neuroscience of Problem Solving

The cognitive neuroscience of problem solving is concerned with the brain activity that occurs during problem solving. For example, using fMRI brain imaging methodology, Goel ( 2005 ) found that people used the language areas of the brain to solve logical reasoning problems presented in sentences (e.g., “All dogs are pets…”) and used the spatial areas of the brain to solve logical reasoning problems presented in abstract letters (e.g., “All D are P…”). Cognitive neuroscience holds the potential to make unique contributions to the study of problem solving.

Problem solving has always been a topic at the fringe of cognitive psychology—too complicated to study intensively but too important to completely ignore. Problem solving—especially in realistic environments—is messy in comparison to studying elementary processes in cognition. The field remains fragmented in the sense that topics such as decision making, reasoning, intelligence, expertise, mathematical problem solving, everyday thinking, and the like are considered to be separate topics, each with its own separate literature. Yet some recurring themes are the role of domain-specific knowledge in problem solving and the advantages of studying problem solving in authentic contexts.

Future Directions

Some important issues for future research include the three classic issues examined in this chapter—the nature of problem-solving transfer (i.e., How are people able to use what they know about previous problem solving to help them in new problem solving?), the nature of insight (e.g., What is the mechanism by which a creative solution is constructed?), and heuristics (e.g., What are some teachable strategies for problem solving?). In addition, future research in problem solving should continue to pinpoint the role of domain-specific knowledge in problem solving, the nature of cognitive ability in problem solving, how to help people develop proficiency in solving problems, and how to provide aids for problem solving.

Anderson L. W. , Krathwohl D. R. , Airasian P. W. , Cruikshank K. A. , Mayer R. E. , Pintrich P. R. , Raths, J., & Wittrock M. C. ( 2001 ). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. New York : Longman.

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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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What is Problem Solving? Process, Techniques, Examples

Home Blog others What is Problem Solving? Process, Techniques, Examples

Whether tackling a technical issue at work or finding our way around a roadblock unnoticed by Google Maps, problem-solving is a daily occurrence for most people. But how prepared are you to overcome life's challenges? Do you rely on a structured process to ensure successful outcomes, or do you navigate through problems impulsively?

Here's the crux: the strength of your problem-solving skills significantly impacts the ease and success of your life, both professionally and personally. Practical problem-solving is a valuable career and life skill. You're in the right place if you're eager to enhance your problem-solving abilities efficiently.

In this blog post, I will delve into what is problem solving the steps, techniques, and exercises of the problem-solving process. Whether seeking to troubleshoot technical issues or navigate life's complexities, mastering organized problem-solving can elevate your capabilities and lead to more favorable outcomes.

What is Problem Solving? And Its Importance

First, let me help you understand what is problem solving. Problem-solving is a comprehensive process involving identifying issues, prioritizing based on urgency and severity, analyzing root causes, gathering pertinent Information, devising and assessing solutions, making informed decisions, and planning and executing implementation strategies.

This skill set also encompasses critical thinking, effective communication, active listening, creativity, research, data analysis, risk assessment, continuous learning, and decision-making abilities. Effective problem-solving strategies mitigate potential losses or damages and enhance self-confidence and reputation. Problem-solving is essential in personal and professional contexts as it allows individuals and teams to navigate obstacles, make informed decisions, and drive progress.

Importance:

Enhances Decision-Making: Effective problem solving leads to better decision-making by evaluating various options and selecting the most suitable solution.
Promotes Innovation: Problem solving encourages innovation and creativity as individuals seek new approaches to tackle challenges.
Improves Efficiency: By resolving issues efficiently, problem solving helps streamline processes and optimize resource allocation.
Builds Resilience: Successfully overcoming obstacles builds confidence and resilience, enabling
individuals and teams to tackle future challenges with greater confidence.

Problem-solving Process

Now that we have a clear understanding of the problem solving definition as to what is problem solving let us now navigate the problem solving process. Effective problem-solving is a valuable skill sought after by employers in various fields. Here's a breakdown of a common problem-solving process, presented in a pointwise manner:

1. Identifying the Problem

The first step in the problem-solving process is clearly defining the issue. This involves gathering relevant Information, observing patterns or trends, and understanding the impact of the problem on stakeholders.

2. Analyzing the Situation

Once the problem is identified, it's essential to analyze its root causes and contributing factors. This may involve conducting research, gathering data, and exploring different perspectives to comprehensively understand the situation.

3. Generating Solutions

With a clear understanding of the problem solving methods, brainstorming potential solutions is the next step. Encouraging creativity and considering various alternatives can lead to innovative ideas. Evaluating each solution based on feasibility, effectiveness, and alignment with goals and values is crucial.

4. Evaluating Options

After generating a list of potential solutions, it's essential to carefully evaluate each option. This involves weighing the pros and cons, considering potential risks and benefits, and assessing the likelihood of success. Consulting with relevant stakeholders or experts can provide valuable insights during this stage.

5. Selecting the Best Solution

Based on the evaluation, one or more solutions are the most viable options. It's essential to prioritize solutions that address the root cause of the problem and have the most significant potential for long-term success. Communicating the chosen solution effectively to stakeholders is crucial for garnering support and buy-in.

6. Implementing the Solution

Once a solution is selected, it's time to put it into action. This involves developing a detailed action plan, allocating resources, and assigning responsibilities. Effective communication, coordination, and monitoring are essential during the implementation phase to ensure smooth execution and timely resolution of the problem.

7. Monitoring and Reviewing

After implementing the solution, it's essential to monitor its progress and evaluate its effectiveness over time. This may involve collecting feedback, analyzing performance metrics, and making adjustments as needed. Continuous monitoring and review allow for ongoing improvement and refinement of the problem-solving process.

How to Solve Problems in 5 Simple Steps?

Here's a breakdown of the 5 problem-solving steps for your understanding:

1. Define the Problem (Understand & Gather Information)

Identify the Issue: Clearly understand what the problem is. What isn't working, or what needs improvement?
Gather Information: Talk to people involved, collect data, and research relevant details to get a well-rounded picture of the situation.
Ask Why? Don't just focus on symptoms. Ask "why" several times to identify the root cause of the problem.

Example: Let's say customer complaints about slow website loading times have increased.

2. Brainstorm Solutions (Think Creatively & Be Open-Minded)

Think Outside the Box: Don't settle for the first solution that comes to mind. Brainstorm a variety of options, even seemingly unconventional ones.
Consider All Angles: Evaluate the problem from different perspectives. What are potential solutions from a technical standpoint? From a user experience point of view?
Build on Ideas: Don't shut down ideas prematurely. Encourage others to build upon and refine suggestions collaboratively.

Example: Potential solutions for slow website loading times could include optimizing images, upgrading server capacity, or implementing a content delivery network (CDN).

3. Evaluate & Choose a Solution (Consider Feasibility & Impact)

Weigh the Pros & Cons: Analyze the feasibility, resource requirements, and potential risks and benefits of each solution.
Align with Goals: Ensure the chosen solution directly addresses the root cause of the problem and aligns with your overall objectives.
Prioritize Impact: Choose the solution with the most significant potential to achieve a positive outcome and lasting improvement.

Example: Upgrading server capacity might be a very effective solution, but it could be expensive. Optimizing images is a more feasible solution that could yield significant improvement.

4. Implement the Solution (Take Action & Communicate Clearly)

Develop a Plan: Create a clear action plan outlining the steps involved in implementing the chosen solution. Assign tasks and set deadlines.
Communication is Key: Clearly communicate the plan to everyone involved, including stakeholders and team members.
Monitor Progress: Track the implementation process and make adjustments as needed based on the results.

Example: The website optimization plan might involve tasks like image resizing, code minification, and implementing caching mechanisms.

5. Evaluate the Outcome (Learn & Adapt)

Measure Success: Assess whether the implemented solution effectively resolved the problem. Did it meet your goals?
Lessons Learned: Reflect on what worked well and what could be improved during the problem-solving process.
Continuous Improvement: Use this experience to refine your problem-solving approach and enhance your skills for future challenges. Enroll in free online certification courses for professional development and skill enhancement.

Example: After website optimization, monitor website loading times and customer feedback to see if the issue has been resolved. If not, repeat the process, considering new solutions based on the learnings from this attempt.

Remember, problem-solving is an iterative process. Be prepared to adapt your approach as you gather more Information and evaluate the effectiveness of your solutions.

Essential Things to Consider in Each of the Problem-solving Steps

Creative problem solving requires careful consideration at each stage. Here are vital things to focus on:

1. Identifying & Defining the Problem

Gather Information: Consult stakeholders, review data, and gain insights from various perspectives.
Identify Root Cause: Address the underlying reason, not just symptoms.
Define Scope: Clearly outline the problem's boundaries to maintain focus.

2. Analyzing the Problem

Consider Multiple Perspectives: Explore diverse angles to uncover potential factors.
Brainstorm Freely: Foster creativity without judgment to generate innovative ideas.
Analyze Impact: Evaluate the severity and consequences of the problem if left unresolved.
Think Creatively: Explore unconventional solutions beyond initial ideas.
Consider Feasibility: Assess the practicality and resource requirements of each option.
Identify Potential Risks & Benefits: Weigh the pros and cons to select the most balanced approach.

4. Evaluating and Selecting a Solution

Align with Goals: Ensure the chosen solution addresses the core issue and aligns with objectives.
Consider Long-Term Impact: Choose solutions with lasting benefits beyond immediate results.
Team Input: Involve team members to gain diverse perspectives during evaluation.

5. Implementing the Solution

Develop a Clear Plan: Outline implementation steps with clear timelines and responsibilities.
Communication is Key: Ensure all stakeholders understand the plan to facilitate smooth execution.
Monitor Progress: Track implementation and adjust as needed based on results.

6. Evaluating the Outcome

Measure Effectiveness: Assess if the solution effectively resolves the problem or needs refinement.
Lessons Learned: Identify successes and areas for improvement to enhance future problem-solving efforts.

Problem Solving Examples

Let us look at problem solving example scenarios in a typical workplace: , example 1: project deadline challenge .

Situation: You're a project manager leading a team that is developing a new marketing campaign website. The launch date is approaching, but a critical developer is unexpectedly out sick for a week.
Action: You immediately assess the workload and delegate tasks among the remaining team members. You identify an opportunity to streamline a design element, reducing development time. You also reach out to a freelancer with a proven track record to fill in for the missing developer on specific tasks.
Result: The team successfully launches the website on time and within budget. The streamlined design element is praised by stakeholders for its user-friendliness.
Highlight: This example showcases your problem-solving skills, leadership, adaptability, and ability to manage resources effectively under pressure.

Example 2: Client Communication Breakdown

Situation: You're a Customer Service Representative for an e-commerce company. A regular customer expresses extreme dissatisfaction with a recent purchase due to a malfunctioning product and a negative experience with a previous representative.
Action: You actively listen to the customer's concerns, apologizing for the inconvenience. You then troubleshoot the product issue and offer a solution (replacement or refund). Additionally, you acknowledge the previous negative experience and offer to ensure better communication going forward.
Result: The customer is satisfied with the resolution and expresses appreciation for your attentiveness and problem-solving approach. They remain a loyal customer of the company.
Highlight: This example demonstrates your active listening skills, empathy, ability to de-escalate situations, and commitment to customer satisfaction.

By following these examples of problem-solving skills, you can effectively tackle challenges and achieve successful outcomes. Also, explore KnowledgeHut’ s best online courses for further skill enhancement.

Problem Solving Techniques

Effective problem-solving techniques are essential for tackling challenges and achieving desired outcomes. Here are some problem solving tools and techniques commonly used in problem-solving:

Brainstorming : Encourages the generation of a wide range of ideas and solutions in a non-judgmental environment. This technique promotes creativity and can uncover innovative approaches to problems.
Root Cause Analysis : Focuses on identifying the underlying causes of a problem rather than just addressing its symptoms. By pinpointing root causes, solutions can be targeted more effectively to prevent recurrence.
Fishbone Diagram (Ishikawa Diagram): Provides a visual representation of the various factors contributing to a problem, categorized into branches such as people, process, equipment, environment, and management. This technique helps analyze complex issues and identify potential causes.
SWOT Analysis : Evaluates the strengths, weaknesses, opportunities, and threats associated with a problem or situation. This technique helps assess the internal and external factors influencing the problem and guides decision-making.
Pareto Analysis: Focuses on identifying and prioritizing the most significant causes contributing to a problem. By allocating resources to address the vital few rather than the trivial many, this technique maximizes impact and efficiency.
5 Whys : Involves asking "why" repeatedly to trace the root cause of a problem. This iterative questioning technique helps uncover more profound layers of causation beyond surface-level symptoms.
Decision Matrix Analysis: Helps evaluate multiple options by systematically comparing their pros and cons against predetermined criteria. This technique facilitates objective decision-making by considering various factors and their relative importance.

By incorporating these problem-solving techniques in the workplace, you can approach problems systematically, generate creative solutions, and develop a well-rounded plan for achieving success.

Conquering challenges is a key to professional success, and practical problem-solving equips you to do just that. By following a structured approach, you can transform from a bystander to a solution-oriented individual. This involves gathering Information to clearly define the problem and identify its root cause. Analyzing the situation from various angles and brainstorming freely unlock creative solutions. Evaluating potential solutions ensures you choose the one that aligns with your goals and is feasible to implement. Clear communication and a well-defined plan are crucial for successful execution. Finally, reflecting on the outcome allows you to learn and continuously improve your problem-solving skills, making you an invaluable asset in any environment.

Frequently Asked Questions (FAQs)

The best method involves identifying the problem, brainstorming solutions, evaluating options, implementing the chosen solution, and assessing outcomes for improvement.

The principles include defining the problem, generating alternatives, evaluating options, implementing solutions, and reviewing outcomes for continuous improvement.

Different types include analytical problem-solving, creative problem-solving, critical thinking, decision-making, and systematic problem-solving.

The significant elements include understanding the problem, devising a plan, executing the plan, and evaluating the results.

The skills encompass critical thinking, decision-making, and analytical reasoning. These abilities aid in identifying, analyzing, and resolving problems effectively.

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Chapter 1: Solving Equations and Inequalities

Problem solving, learning objectives.

Translate words into algebraic expressions and equations
Define a process for solving word problems
Apply the steps for solving word problems to distance, rate, and time problems
Apply the steps for solving word problems to interest rate problems
Evaluate a formula using substitution
Rearrange formulas to isolate specific variables
Identify an unknown given a formula
Apply the steps for solving word problems to geometry problems
Use the formula for converting between Fahrenheit and Celsius

Define a Process for Problem Solving

Word problems can be tricky. Often it takes a bit of practice to convert an English sentence into a mathematical sentence, which is one of the first steps to solving word problems. In the table below, words or phrases commonly associated with mathematical operators are categorized. Word problems often contain these or similar words, so it’s good to see what mathematical operators are associated with them.

Some examples follow:

[latex]x\text{ is }5[/latex] becomes [latex]x=5[/latex]
Three more than a number becomes [latex]x+3[/latex]
Four less than a number becomes [latex]x-4[/latex]
Double the cost becomes [latex]2\cdot\text{ cost }[/latex]
Groceries and gas together for the week cost $250 means [latex]\text{ groceries }+\text{ gas }=250[/latex]
The difference of 9 and a number becomes [latex]9-x[/latex]. Notice how 9 is first in the sentence and the expression

Let’s practice translating a few more English phrases into algebraic expressions.

Translate the table into algebraic expressions:

In this example video, we show how to translate more words into mathematical expressions.

The power of algebra is how it can help you model real situations in order to answer questions about them.

Here are some steps to translate problem situations into algebraic equations you can solve. Not every word problem fits perfectly into these steps, but they will help you get started.

Read and understand the problem.
Determine the constants and variables in the problem.
Translate words into algebraic expressions and equations.
Write an equation to represent the problem.
Solve the equation.
Check and interpret your answer. Sometimes writing a sentence helps.

Twenty-eight less than five times a certain number is 232. What is the number?

Following the steps provided:

Read and understand: we are looking for a number.
Constants and variables: 28 and 232 are constants, “a certain number” is our variable because we don’t know its value, and we are asked to find it. We will call it x.
Translate: five times a certain number translates to [latex]5x[/latex] Twenty-eight less than five times a certain number translates to [latex]5x-28[/latex] because subtraction is built backward. is 232 translates to [latex]=232[/latex] because “is” is associated with equals.
Write an equation: [latex]5x-28=232[/latex]

[latex]\begin{array}{r}5x-28=232\\5x=260\\x=52\,\,\,\end{array}[/latex]

[latex]\begin{array}{r}5\left(52\right)-28=232\\5\left(52\right)=260\\260=260\end{array}[/latex].

In the video that follows, we show another example of how to translate a sentence into a mathematical expression using a problem solving method.

Another type of number problem involves consecutive numbers. Consecutive numbers are numbers that come one after the other, such as 3, 4, 5. If we are looking for several consecutive numbers it is important to first identify what they look like with variables before we set up the equation.

For example, let’s say I want to know the next consecutive integer after 4. In mathematical terms, we would add 1 to 4 to get 5. We can generalize this idea as follows: the consecutive integer of any number, x , is [latex]x+1[/latex]. If we continue this pattern we can define any number of consecutive integers from any starting point. The following table shows how to describe four consecutive integers using algebraic notation.

We apply the idea of consecutive integers to solving a word problem in the following example.

The sum of three consecutive integers is 93. What are the integers?

Read and understand: We are looking for three numbers, and we know they are consecutive integers.
Constants and Variables: 93 is a constant. The first integer we will call x . Second: [latex]x+1[/latex] Third: [latex]x+2[/latex]
Translate: The sum of three consecutive integers translates to [latex]x+\left(x+1\right)+\left(x+2\right)[/latex], based on how we defined the first, second, and third integers. Notice how we placed parentheses around the second and third integers. This is just to make each integer more distinct. is 93 translates to [latex]=93[/latex] because is is associated with equals.
Write an equation: [latex]x+\left(x+1\right)+\left(x+2\right)=93[/latex]

[latex]x+x+1+x+2=93[/latex]

Combine like terms, simplify, and solve.

[latex]\begin{array}{r}x+x+1+x+2=93\\3x+3 = 93\\\underline{-3\,\,\,\,\,-3}\\3x=90\\\frac{3x}{3}=\frac{90}{3}\\x=30\end{array}[/latex]

Check and Interpret: Okay, we have found a value for x . We were asked to find the value of three consecutive integers, so we need to do a couple more steps. Remember how we defined our variables: The first integer we will call [latex]x[/latex], [latex]x=30[/latex] Second: [latex]x+1[/latex] so [latex]30+1=31[/latex] Third: [latex]x+2[/latex] so [latex]30+2=32[/latex] The three consecutive integers whose sum is [latex]93[/latex] are [latex]30\text{, }31\text{, and }32[/latex]

There is often a well-known formula or relationship that applies to a word problem. For example, if you were to plan a road trip, you would want to know how long it would take you to reach your destination. [latex]d=rt[/latex] is a well-known relationship that associates distance traveled, the rate at which you travel, and how long the travel takes.

Distance, Rate, and Time

If you know two of the quantities in the relationship [latex]d=rt[/latex], you can easily find the third using methods for solving linear equations. For example, if you know that you will be traveling on a road with a speed limit of [latex]30\frac{\text{ miles }}{\text{ hour }}[/latex] for 2 hours, you can find the distance you would travel by multiplying rate times time or [latex]\left(30\frac{\text{ miles }}{\text{ hour }}\right)\left(2\text{ hours }\right)=60\text{ miles }[/latex].

We can generalize this idea depending on what information we are given and what we are looking for. For example, if we need to find time, we could solve the [latex]d=rt[/latex] equation for t using division:

[latex]d=rt\\\frac{d}{r}=t[/latex]

Likewise, if we want to find rate, we can isolate r using division:

[latex]d=rt\\\frac{d}{t}=r[/latex]

In the following examples you will see how this formula is applied to answer questions about ultra marathon running.

Ultra marathon running (defined as anything longer than 26.2 miles) is becoming very popular among women even though it remains a male-dominated niche sport. Ann Trason has broken twenty world records in her career. One such record was the American River 50-mile Endurance Run which begins in Sacramento, California, and ends in Auburn, California. [1] In 1993 Trason finished the run with a time of 6:09:08. The men’s record for the same course was set in 1994 by Tom Johnson who finished the course with a time of 5:33:21. [2]

In the next examples we will use the [latex]d=rt[/latex] formula to answer the following questions about the two runners.

What was each runner’s rate for their record-setting runs?

By the time Johnson had finished, how many more miles did Trason have to run?

How much further could Johnson have run if he had run as long as Trason?

What was each runner’s time for running one mile?

To make answering the questions easier, we will round the two runners’ times to 6 hours and 5.5 hours.

Read and Understand: We are looking for rate and we know distance and time, so we can use the idea: [latex]d=rt\\\frac{d}{t}=r[/latex]

Define and Translate: Because there are two runners, making a table to organize this information helps. Note how we keep units to help us keep track of what how all the terms are related to each other.

Write and Solve:

Trason’s rate:

[latex]\begin{array}{c}d=rt\\\\50\text{ miles }=\text{r}\left(6\text{ hours }\right)\\\frac{50\text{ miles }}{6\text{ hours }}=\frac{8.33\text{ miles }}{\text{ hour }}\end{array}[/latex].

(rounded to two decimal places)

Johnson’s rate:

[latex]\begin{array}{c}d=rt\\\\,\,\,\,\,\,\,50\text{ miles }=\text{r}\left(5.5\text{ hours }\right)\\\frac{50\text{ miles }}{6\text{ hours }}=\frac{9.1\text{ miles }}{\text{ hour }}\end{array}[/latex]

Check and Interpret:

We can fill in our table with this information.

Now that we know each runner’s rate we can answer the second question.

Here is the table we created for reference:

Read and Understand: We are looking for how many miles Trason still had on the trail when Johnson had finished after 5.5 hours. This is a distance, and we know rate and time.

Define and Translate: We can use the formula [latex]d=rt[/latex] again. This time the unknown is d , and the time Trason had run is 5.5 hours.

[latex]\begin{array}{l}d=rt\\\\d=8.33\frac{\text{ miles }}{\text{ hour }}\left(5.5\text{ hours }\right)\\\\d=45.82\text{ miles }\end{array}[/latex].

Have we answered the question? We were asked to find how many more miles she had to run after 5.5 hours. What we have found is how long she had run after 5.5 hours. We need to subtract [latex]d=45.82\text{ miles }[/latex] from the total distance of the course.

[latex]50\text{ miles }-45.82\text{ miles }=1.48\text{ miles }[/latex]

The third question is similar to the second. Now that we know each runner’s rate, we can answer questions about individual distances or times.

Read and Understand: The word further implies we are looking for a distance.

Define and Translate: We can use the formula [latex]d=rt[/latex] again. This time the unknown is d , the time is 6 hours, and Johnson’s rate is [latex]9.1\frac{\text{ miles }}{\text{ hour }}[/latex]

[latex]\begin{array}{l}d=rt\\\\d=9.1\frac{\text{ miles }}{\text{ hour }}\left(6\text{ hours }\right)\\\\d=54.6\text{ miles }\end{array}[/latex].

Have we answered the question? We were asked to find how many more miles Johnson would have run if he had run at his rate of [latex]9.1\frac{\text{ miles }}{\text{ hour }}[/latex] for 6 hours.

Johnson would have run 54.6 miles, so that’s 4.6 more miles than than he ran for the race.

Now we will tackle the last question where we are asked to find a time for each runner.

Read and Understand: we are looking for time, and this time our distance has changed from 50 miles to 1 mile, so we can use

Define and Translate: we can use the formula [latex]d=rt[/latex] again. This time the unknown is t , the distance is 1 mile, and we know each runner’s rate. It may help to create a new table:

We will need to divide to isolate time.

[latex]\begin{array}{c}d=rt\\\\1\text{ mile }=8.33\frac{\text{ miles }}{\text{ hour }}\left(t\text{ hours }\right)\\\\\frac{1\text{ mile }}{\frac{8.33\text{ miles }}{\text{ hour }}}=t\text{ hours }\\\\0.12\text{ hours }=t\end{array}[/latex].

0.12 hours is about 7.2 minutes, so Trason’s time for running one mile was about 7.2 minutes. WOW! She did that for 6 hours!

[latex]\begin{array}{c}d=rt\\\\1\text{ mile }=9.1\frac{\text{ miles }}{\text{ hour }}\left(t\text{ hours }\right)\\\\\frac{1\text{ mile }}{\frac{9.1\text{ miles }}{\text{ hour }}}=t\text{ hours }\\\\0.11\text{ hours }=t\end{array}[/latex].

0.11 hours is about 6.6 minutes, so Johnson’s time for running one mile was about 6.6 minutes. WOW! He did that for 5.5 hours!

Have we answered the question? We were asked to find how long it took each runner to run one mile given the rate at which they ran the whole 50-mile course. Yes, we answered our question.

Trason’s mile time was [latex]7.2\frac{\text{minutes}}{\text{mile}}[/latex] and Johnsons’ mile time was [latex]6.6\frac{\text{minutes}}{\text{mile}}[/latex]

In the following video, we show another example of answering many rate questions given distance and time.

Simple Interest

In order to entice customers to invest their money, many banks will offer interest-bearing accounts. The accounts work like this: a customer deposits a certain amount of money (called the Principal, or P ), which then grows slowly according to the interest rate ( R , measured in percent) and the length of time ( T , usually measured in months) that the money stays in the account. The amount earned over time is called the interest ( I ), which is then given to the customer.

The simplest way to calculate interest earned on an account is through the formula [latex]\displaystyle I=P\,\cdot \,R\,\cdot \,T[/latex].

If we know any of the three amounts related to this equation, we can find the fourth. For example, if we want to find the time it will take to accrue a specific amount of interest, we can solve for T using division:

[latex]\displaystyle\begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,I=P\,\cdot \,R\,\cdot \,T\\\\ \frac{I}{{P}\,\cdot \,R}=\frac{P\cdot\,R\,\cdot \,T}{\,P\,\cdot \,R}\\\\\,\,\,\,\,\,\,\,\,\,\,{T}=\frac{I}{\,R\,\cdot \,T}\end{array}[/latex]

Below is a table showing the result of solving for each individual variable in the formula.

In the next examples, we will show how to substitute given values into the simple interest formula, and decipher which variable to solve for.

If a customer deposits a principal of $2000 at a monthly rate of 0.7%, what is the total amount that she has after 24 months?

Substitute in the values given for the Principal, Rate, and Time.

[latex]\displaystyle\begin{array}{l}I=P\,\cdot \,R\,\cdot \,T\\I=2000\cdot 0.7\%\cdot 24\end{array}[/latex]

Rewrite 0.7% as the decimal 0.007, then multiply.

[latex]\begin{array}{l}I=2000\cdot 0.007\cdot 24\\I=336\end{array}[/latex]

Add the interest and the original principal amount to get the total amount in her account.

[latex] \displaystyle 2000+336=2336[/latex]

She has $2336 after 24 months.

The following video shows another example of finding an account balance after a given amount of time, principal invested, and a rate.

In the following example you will see why it is important to make sure the units of the interest rate match the units of time when using the simple interest formula.

Alex invests $600 at 3.25% monthly interest for 3 years. What amount of interest has Alex earned?

Read and Understand: The question asks for an amount, so we can substitute what we are given into the simple interest formula [latex]I=P\,\cdot \,R\,\cdot \,T[/latex]

Define and Translate: we know P, R, and T so we can use substitution. R = 0.0325, P = $600, and T = 3 years. We have to be careful! R is in months, and T is in years. We need to change T into months because we can’t change the rate—it is set by the bank.

[latex]{T}=3\text{ years }\cdot12\frac{\text{ months }}{ year }=36\text{ months }[/latex]

Substitute the given values into the formula.

[latex]\begin{array}{l} I=P\,\cdot \,R\,\cdot \,T\\\\I=600\,\cdot \,0.035\,\cdot \,36\\\\{I}=756\end{array}[/latex]

We were asked what amount Alex earned, which is the amount provided by the formula. In the previous example we were asked the total amount in the account, which included the principal and interest earned.

Alex has earned $756.

After 10 years, Jodi’s account balance has earned $1080 in interest. The rate on the account is 0.09% monthly. What was the original amount she invested in the account?

Read and Understand: The question asks for the original amount invested, the principal. We are given a length of time in years, and an interest rate in months, and the amount of interest earned.

Define and Translate: we know I = $1080, R = 0.009, and T = 10 years so we can use [latex]{P}=\frac{I}{{R}\,\cdot \,T}[/latex]

We also need to make sure the units on the interest rate and the length of time match, and they do not. We need to change time into months again.

[latex]{T}=10\text{ years }\cdot12\frac{\text{ months }}{ year }=120\text{ months }[/latex]

Substitute the given values into the formula

[latex]\begin{array}{l}{P}=\frac{I}{{R}\,\cdot \,T}\\\\{P}=\frac{1080}{{0.009}\,\cdot \,120}\\\\{P}=\frac{1080}{1.08}=1000\end{array}[/latex]

We were asked to find the principal given the amount of interest earned on an account. If we substitute P = $1000 into the formula [latex]I=P\,\cdot \,R\,\cdot \,T[/latex] we get

[latex]I=1000\,\cdot \,0.009\,\cdot \,120\\I=1080[/latex]

Our solution checks out. Jodi invested $1000.

Further Applications of Linear Equations

Formulas come up in many different areas of life. We have seen the formula that relates distance, rate, and time and the formula for simple interest on an investment. In this section we will look further at formulas and see examples of formulas for dimensions of geometric shapes as well as the formula for converting temperature between Fahrenheit and Celsius.

There are many geometric shapes that have been well studied over the years. We know quite a bit about circles, rectangles, and triangles. Mathematicians have proven many formulas that describe the dimensions of geometric shapes including area, perimeter, surface area, and volume.

Perimeter is the distance around an object. For example, consider a rectangle with a length of 8 and a width of 3. There are two lengths and two widths in a rectangle (opposite sides), so we add [latex]8+8+3+3=22[/latex]. Since there are two lengths and two widths in a rectangle, you may find the perimeter of a rectangle using the formula [latex]{P}=2\left({L}\right)+2\left({W}\right)[/latex] where

In the following example, we will use the problem-solving method we developed to find an unknown width using the formula for the perimeter of a rectangle. By substituting the dimensions we know into the formula, we will be able to isolate the unknown width and find our solution.

You want to make another garden box the same size as the one you already have. You write down the dimensions of the box and go to the lumber store to buy some boards. When you get there you realize you didn’t write down the width dimension—only the perimeter and length. You want the exact dimensions so you can have the store cut the lumber for you.

Here is what you have written down:

Perimeter = 16.4 feet Length = 4.7 feet

Can you find the dimensions you need to have your boards cut at the lumber store? If so, how many boards do you need and what lengths should they be?

Read and Understand: We know perimeter = 16.4 feet and length = 4.7 feet, and we want to find width.

Define and Translate:

Define the known and unknown dimensions:

First we will substitute the dimensions we know into the formula for perimeter:

[latex]\begin{array}{l}\,\,\,\,\,P=2{W}+2{L}\\\\16.4=2\left(w\right)+2\left(4.7\right)\end{array}[/latex]

Then we will isolate w to find the unknown width.

[latex]\begin{array}{l}16.4=2\left(w\right)+2\left(4.7\right)\\16.4=2{w}+9.4\\\underline{-9.4\,\,\,\,\,\,\,\,\,\,\,\,\,-9.4}\\\,\,\,\,\,\,\,7=2\left(w\right)\\\,\,\,\,\,\,\,\frac{7}{2}=\frac{2\left(w\right)}{2}\\\,\,\,\,3.5=w\end{array}[/latex]

Write the width as a decimal to make cutting the boards easier and replace the units on the measurement, or you won’t get the right size of board!

If we replace the width we found, [latex]w=3.5\text{ feet }[/latex] into the formula for perimeter with the dimensions we wrote down, we can check our work:

[latex]\begin{array}{l}\,\,\,\,\,{P}=2\left({L}\right)+2\left({W}\right)\\\\{16.4}=2\left({4.7}\right)+2\left({3.5}\right)\\\\{16.4}=9.4+7\\\\{16.4}=16.4\end{array}[/latex]

Our calculation for width checks out. We need to ask for 2 boards cut to 3.5 feet and 2 boards cut to 4.7 feet so we can make the new garden box.

This video shows a similar garden box problem.

We could have isolated the w in the formula for perimeter before we solved the equation, and if we were going to use the formula many times, it could save a lot of time. The next example shows how to isolate a variable in a formula before substituting known dimensions or values into the formula.

Isolate the term containing the variable, w, from the formula for the perimeter of a rectangle :

[latex]{P}=2\left({L}\right)+2\left({W}\right)[/latex].

First, isolate the term with w by subtracting 2 l from both sides of the equation.

[latex] \displaystyle \begin{array}{l}\,\,\,\,\,\,\,\,\,\,p\,=\,\,\,\,2l+2w\\\underline{\,\,\,\,\,-2l\,\,\,\,\,-2l\,\,\,\,\,\,\,\,\,\,\,}\\p-2l=\,\,\,\,\,\,\,\,\,\,\,\,\,2w\end{array}[/latex]

Next, clear the coefficient of w by dividing both sides of the equation by 2.

[latex]\displaystyle \begin{array}{l}\underline{p-2l}=\underline{2w}\\\,\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\\ \,\,\,\frac{p-2l}{2}\,\,=\,\,w\\\,\,\,\,\,\,\,\,\,\,\,w=\frac{p-2l}{2}\end{array}[/latex]

You can rewrite the equation so the isolated variable is on the left side.

[latex]w=\frac{p-2l}{2}[/latex]

The area of a triangle is given by [latex] A=\frac{1}{2}bh[/latex] where

A = area b = the length of the base h = the height of the triangle

Remember that when two variables or a number and a variable are sitting next to each other without a mathematical operator between them, you can assume they are being multiplied. This can seem frustrating, but you can think of it like mathematical slang. Over the years, people who use math frequently have just made that shortcut enough that it has been adopted as convention.

In the next example we will use the formula for area of a triangle to find a missing dimension, as well as use substitution to solve for the base of a triangle given the area and height.

Find the base ( b) of a triangle with an area ( A ) of 20 square feet and a height ( h) of 8 feet.

Use the formula for the area of a triangle, [latex] {A}=\frac{{1}}{{2}}{bh}[/latex] .

Substitute the given lengths into the formula and solve for b.

[latex]\displaystyle \begin{array}{l}\,\,A=\frac{1}{2}bh\\\\20=\frac{1}{2}b\cdot 8\\\\20=\frac{8}{2}b\\\\20=4b\\\\\frac{20}{4}=\frac{4b}{4}\\\\ \,\,\,5=b\end{array}[/latex]

The base of the triangle measures 5 feet.

We can rewrite the formula in terms of b or h as we did with perimeter previously. This probably seems abstract, but it can help you develop your equation-solving skills, as well as help you get more comfortable with working with all kinds of variables, not just x .

Use the multiplication and division properties of equality to isolate the variable b .

[latex]\begin{array}{l}\,\,\,\,\,\,\,\,A=\frac{1}{2}bh\\\\\left(2\right)A=\left(2\right)\frac{1}{2}bh\\\\\,\,\,\,\,\,2A=bh\\\\\,\,\,\,\,\,\,\frac{2A}{h}=\frac{bh}{h}\\\\\,\,\,\,\,\,\,\,\frac{2A}{h}=\frac{b\cancel{h}}{\cancel{h}}\end{array}[/latex]

Write the equation with the desired variable on the left-hand side as a matter of convention:

Use the multiplication and division properties of equality to isolate the variable h .

[latex]\begin{array}{l}\,\,\,\,\,\,\,\,A=\frac{1}{2}bh\\\\\left(2\right)A=\left(2\right)\frac{1}{2}bh\\\\\,\,\,\,\,\,2A=bh\\\\\,\,\,\,\,\,\,\frac{2A}{b}=\frac{bh}{b}\\\\\,\,\,\,\,\,\,\,\frac{2A}{b}=\frac{h\cancel{b}}{\cancel{b}}\end{array}[/latex]

Temperature

Let’s look at another formula that includes parentheses and fractions, the formula for converting from the Fahrenheit temperature scale to the Celsius scale.

[latex]C=\left(F-32\right)\cdot \frac{5}{9}[/latex]

Given a temperature of [latex]12^{\circ}{C}[/latex], find the equivalent in [latex]{}^{\circ}{F}[/latex].

Substitute the given temperature in[latex]{}^{\circ}{C}[/latex] into the conversion formula:

[latex]12=\left(F-32\right)\cdot \frac{5}{9}[/latex]

Isolate the variable F to obtain the equivalent temperature.

[latex]\begin{array}{r}12=\left(F-32\right)\cdot \frac{5}{9}\\\\\left(\frac{9}{5}\right)12=F-32\,\,\,\,\,\,\,\,\,\,\,\,\,\\\\\left(\frac{108}{5}\right)12=F-32\,\,\,\,\,\,\,\,\,\,\,\,\,\\\\21.6=F-32\,\,\,\,\,\,\,\,\,\,\,\,\,\\\underline{+32\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+32}\,\,\,\,\,\,\,\,\,\,\,\,\\\\53.6={}^{\circ}{F}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{array}[/latex]

As with the other formulas we have worked with, we could have isolated the variable F first, then substituted in the given temperature in Celsius.

Solve the formula shown below for converting from the Fahrenheit scale to the Celsius scale for F.

To isolate the variable F, it would be best to clear the fraction involving F first. Multiply both sides of the equation by [latex] \displaystyle \frac{9}{5}[/latex].

[latex]\begin{array}{l}\\\,\,\,\,\left(\frac{9}{5}\right)C=\left(F-32\right)\left(\frac{5}{9}\right)\left(\frac{9}{5}\right)\\\\\,\,\,\,\,\,\,\,\,\,\,\,\frac{9}{5}C=F-32\end{array}[/latex]

Add 32 to both sides.

[latex]\begin{array}{l}\frac{9}{5}\,C+32=F-32+32\\\\\frac{9}{5}\,C+32=F\end{array}[/latex]

[latex]F=\frac{9}{5}C+32[/latex]

Think About It

Express the formula for the surface area of a cylinder, [latex]s=2\pi rh+2\pi r^{2}[/latex], in terms of the height, h .

In this example, the variable h is buried pretty deeply in the formula for surface area of a cylinder. Using the order of operations, it can be isolated. Before you look at the solution, use the box below to write down what you think is the best first step to take to isolate h .

[latex]\begin{array}{r}S\,\,=2\pi rh+2\pi r^{2} \\ \underline{-2\pi r^{2}\,\,\,\,\,\,\,\,\,\,\,\,\,-2\pi r^{2}}\\S-2\pi r^{2}\,\,\,\,=\,\,\,\,2\pi rh\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{array}[/latex]

Next, isolate the variable h by dividing both sides of the equation by [latex]2\pi r[/latex].

[latex]\begin{array}{r}\frac{S-2\pi r^{2}}{2\pi r}=\frac{2\pi rh}{2\pi r} \\\\ \frac{S-2\pi r^{2}}{2\pi r}=h\,\,\,\,\,\,\,\,\,\,\end{array}[/latex]

"Ann Trason." Wikipedia. Accessed May 05, 2016. https://en.wikipedia.org/wiki/Ann_Trason . ↵
"American River 50 Mile Endurance Run." Wikipedia. Accessed May 05, 2016. https://en.wikipedia.org/wiki/American_River_50_Mile_Endurance_Run . ↵
Writing Algebraic Expressions. Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/uD_V5t-6Kzs . License : CC BY: Attribution
Write and Solve a Linear Equations to Solve a Number Problem (1). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/izIIqOztUyI . License : CC BY: Attribution
Write and Solve a Linear Equations to Solve a Number Problem (Consecutive Integers). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/S5HZy3jKodg . License : CC BY: Attribution
Screenshot: Ann Trason Trail Running. Authored by : Lumen Learning. License : CC BY: Attribution
Problem Solving Using Distance, Rate, Time (Running). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/3WLp5mY1FhU . License : CC BY: Attribution
Simple Interest - Determine Account Balance (Monthly Interest). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/XkGgEEMR_00 . License : CC BY: Attribution
Simple Interest - Determine Interest Balance (Monthly Interest). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/mRV5ljj32Rg . License : CC BY: Attribution
Simple Interest - Determine Principal Balance (Monthly Interest). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/vbMqN6lVoOM . License : CC BY: Attribution
Find the Width of a Rectangle Given the Perimeter / Literal Equation. Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/jlxPgKQfhQs . License : CC BY: Attribution
Find the Base of a Triangle Given Area / Literal Equation. Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/VQZQvJ3rXYg . License : CC BY: Attribution
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Problem-Solving Method in Teaching

The problem-solving method is a highly effective teaching strategy that is designed to help students develop critical thinking skills and problem-solving abilities . It involves providing students with real-world problems and challenges that require them to apply their knowledge, skills, and creativity to find solutions. This method encourages active learning, promotes collaboration, and allows students to take ownership of their learning.

Definition of problem-solving method.

Problem-solving is a process of identifying, analyzing, and resolving problems. The problem-solving method in teaching involves providing students with real-world problems that they must solve through collaboration and critical thinking. This method encourages students to apply their knowledge and creativity to develop solutions that are effective and practical.

Meaning of Problem-Solving Method

The meaning and Definition of problem-solving are given by different Scholars. These are-

Woodworth and Marquis(1948) : Problem-solving behavior occurs in novel or difficult situations in which a solution is not obtainable by the habitual methods of applying concepts and principles derived from past experience in very similar situations.

Skinner (1968): Problem-solving is a process of overcoming difficulties that appear to interfere with the attainment of a goal. It is the procedure of making adjustments in spite of interference

Benefits of Problem-Solving Method

The problem-solving method has several benefits for both students and teachers. These benefits include:

Encourages active learning: The problem-solving method encourages students to actively participate in their own learning by engaging them in real-world problems that require critical thinking and collaboration
Promotes collaboration: Problem-solving requires students to work together to find solutions. This promotes teamwork, communication, and cooperation.
Builds critical thinking skills: The problem-solving method helps students develop critical thinking skills by providing them with opportunities to analyze and evaluate problems
Increases motivation: When students are engaged in solving real-world problems, they are more motivated to learn and apply their knowledge.
Enhances creativity: The problem-solving method encourages students to be creative in finding solutions to problems.

Steps in Problem-Solving Method

The problem-solving method involves several steps that teachers can use to guide their students. These steps include

Identifying the problem: The first step in problem-solving is identifying the problem that needs to be solved. Teachers can present students with a real-world problem or challenge that requires critical thinking and collaboration.
Analyzing the problem: Once the problem is identified, students should analyze it to determine its scope and underlying causes.
Generating solutions: After analyzing the problem, students should generate possible solutions. This step requires creativity and critical thinking.
Evaluating solutions: The next step is to evaluate each solution based on its effectiveness and practicality
Selecting the best solution: The final step is to select the best solution and implement it.

Verification of the concluded solution or Hypothesis

The solution arrived at or the conclusion drawn must be further verified by utilizing it in solving various other likewise problems. In case, the derived solution helps in solving these problems, then and only then if one is free to agree with his finding regarding the solution. The verified solution may then become a useful product of his problem-solving behavior that can be utilized in solving further problems. The above steps can be utilized in solving various problems thereby fostering creative thinking ability in an individual.

The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to succeed in school and in life.

Jonassen, D. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments. Routledge.
Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.
Mergendoller, J. R., Maxwell, N. L., & Bellisimo, Y. (2006). The effectiveness of problem-based instruction: A comparative study of instructional methods and student characteristics. Interdisciplinary Journal of Problem-based Learning, 1(2), 49-69.
Richey, R. C., Klein, J. D., & Tracey, M. W. (2011). The instructional design knowledge base: Theory, research, and practice. Routledge.
Savery, J. R., & Duffy, T. M. (2001). Problem-based learning: An instructional model and its constructivist framework. CRLT Technical Report No. 16-01, University of Michigan. Wojcikowski, J. (2013). Solving real-world problems through problem-based learning. College Teaching, 61(4), 153-156

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Comparison of problem-solving methods and techniques

Problem-solving is an essential skill in everyday life, in the professional world, and even in scientific research. However, with the multitude of approaches, methods, and techniques available, it can be challenging to navigate. Each problem is unique and may require a different approach. We will attempt to clarify the landscape of these approaches and methods by explaining their primary differences and when to use them, all summarized in the image above.

1 Comprehensive Problem-Solving approaches

This category encompasses complete and structured methods for tackling problem-solving in a systematic way. These approaches are designed to guide individuals or teams throughout the problem-solving process, providing clear and ordered steps to follow.

The DMAIC approach is a structured problem-solving method, divided into five main steps:

Define : Identify the problem, set objectives, and define the scope of analysis.
Measure : Gather data to assess the current performance of the process and measure variability.
Analyze : Dive deep into the data to identify the root causes of the problem.
Improve : Develop and implement solutions to eliminate the identified problem causes.
Control : Establish control mechanisms to monitor results and maintain long-term improvements.

Distinctiveness from other comprehensive problem-solving approaches:

The DMAIC approach stems from the Six-Sigma philosophy and places a greater emphasis than other global methods on quantified data, through measurement, and quantitative statistical analyses.

Preferred application

DMAIC is suitable for any type of recurring problem-solving, from medium to high complexity, occurring in an organization's processes or operations. Especially for problems that require quantitative data analyses.

1.2 8D Method

The 8D method is a structured problem-solving approach which stands for "eight disciplines" summarized as follows:

Form a multidisciplinary team : Create a problem-solving team composed of people with diverse skills.
Define the problem : Clearly identify the problem, its scope, and the resolution objectives.
Implement immediate measures : If necessary, take emergency actions to contain the problem.
Identify causes : Pinpoint the root causes of the problem.
Develop corrective actions : Design corrective actions to eliminate the immediate causes.
Implement corrective actions : Execute the corrective actions and monitor their effectiveness.
Prevent recurrence : Validate that corrective actions are effective and prevent the problem's recurrence.
Acknowledge the involved individuals : Document the resolution process and recognize the team's contributions.

It explicitly introduces a step to implement immediate actions before identifying the root causes.

Even though the method applies to recurring problem-solving, from medium to high complexity, it tends to be mainly used for medium complexity problems that require urgent actions.

1.3 The A3 method

The A3 method originates from the Toyota Production System (TPS). At Toyota, the A3 paper format was adopted to document, visualize, and share problems, analyses, and solutions concisely. This format has become a principle for reporting, and particularly applied in problem solving. It is more a principle than a method. The steps in the A3 method are not specified, but often follow the example below:

Describe the current situation
Define the objective
Identify the root causes
Define the corrective actions
Define the implementation plan
Track the results
Learn from the experience

It emphasizes clarity of communication through a simple, visual document containing concise information.

Although the method applies to recurring problem-solving, from medium to high complexity, it tends to be primarily used for medium complexity problems.

1.4 The Change or Transformation project

The Transformation, or Change approach, is a comprehensive method for solving complex problems related to an organization and its operational methods (organization, governance, management methods, processes, staff skills, and motivations...). It involves conducting an in-depth diagnostic of the organization to identify its strengths, weaknesses, opportunities, and threats, then using this information to draft a transformation or improvement plan which will involve a significant part of change management. This approach relies on a holistic analysis of the current company situation, followed by designing and implementing a project aiming to achieve specific change or improvement goals.

There isn't truly a Change/Transformation approach that has established its "brand", acronyms, and standard structure like DMAIC, 8D, etc. However, all Transformation projects apply similar approaches, and they are frequent enough that this approach deserves to be on our list. It places a more particular emphasis on organizational, managerial, and human aspects, even though process improvement is also part of its scope.

This method mainly applies to solving recurring problems of high complexity of organizational and human nature (organization, governance, management, skills, and motivation...) especially across multiple departments or services of the organization.

1.5 The PDCA method

The PDCA (Plan, Do, Check, Act) is a continuous improvement cycle used to solve problems, enhance processes, and achieve goals. Here's a brief description of each step:

Plan: Identify the problem or the objective, set goals, design an action plan, and choose methods to achieve them.
Do: Implement the action plan by executing the planned activities.
Check: Evaluate the results obtained against the set objectives, by collecting data and checking performance.
Act: Take measures to adjust, correct, and improve the plan based on the results of the evaluation. Repeat the cycle to continue improvement.

Distinguishing feature compared to other global problem-solving approaches:

PDCA is more of a continuous improvement principle based on a cycle that continually repeats to solve problems, enhance processes, or achieve objectives. It is more generic and can be applied to various situations.

PDCA is often used for incremental improvements and regular adjustments in a process or activity. It is less used to solve complex, identified, or chronic problems and to bring about significant improvements.

The Kaizen event, often referred to as "Kaizen Blitz" or simply "Kaizen," stemming from Toyota's production philosophy, is a targeted and intensive approach aimed at rapidly improving a process, product, or service within an organization.

It typically lasts from a few days to a week, brings together a multidisciplinary team, and follows a procedure of analysis, ideation, rapid implementation, and review.

Although Kaizen covers the entire problem-solving process, it is more focused, both in terms of duration (a few days) and scope compared to broader approaches.

It is particularly suitable for low or medium complexity problems, aiming to achieve immediate and visible improvements, often focused on process efficiency and waste reduction, within a continuous improvement context.

1.7 Conclusion on global problem-solving approaches

Except for Kaizen, which is more targeted than the others, the differences lie mainly in certain aspects more or less highlighted by one method or another.

The effectiveness of the method used will probably depend more on the way (rigor, demand, flexibility, commitment of individuals, etc.) it is implemented than the method itself.

2 Specific methods used within the problem-solving process

2.1 5w2h method.

The method is a management and organization tool used to ask essential questions in order to gather specific and relevant information on a given subject. The letters 5W2H represent the initials of each question as follows:

What? : This question aims to clearly define the object or subject under examination. It's the first step to ensure everyone understands what's being discussed.
Who? : This pertains to determining who is involved or affected by the subject. This could include individuals, teams, departments, or other stakeholders.
Where? : This question seeks to identify places or locations related to the subject. This could mean physical locations, specific departments in an organization, or even geographical areas.
When? : It's essential to determine the timeline or time frame associated with the subject. This can include deadlines, due dates, specific moments, and so on.
Why? : The "Why?" question seeks to comprehend the motivations, reasons, or objectives behind the subject. It helps explore the reasons leading to a particular situation or decision.
How? : This question delves into the methods, processes, or means used concerning the subject. It aids in understanding the steps or actions required to achieve a goal.
How much? : This involves quantifying elements related to the subject. This can comprise figures, measurements, financial resources, quantities, and more.

The most appropriate use of the 5W2H method is typically in the Problem Definition phase for the following reasons:

Clarifying the subject: The "What?" question helps to precisely define what the project is about, avoiding ambiguity.
Identifying stakeholders: By answering the "Who?" question, the team can determine who's involved in the process or problem to be solved, which is vital for stakeholder management.
Location: The "Where?" question helps identify the physical places or areas of the organization affected by the project.
Scheduling: By answering the "When?" question, timelines and deadlines for the project can be set.
Understanding methods and resources: The "How?" and "How much?" questions help understand existing processes, available resources, and measurements related to the problem.
Understanding motivations: Finally, the "Why?" question can assist in grasping why the problem is crucial to solve.

2.2 Ishikawa method for identifying root causes

The Ishikawa diagram , also known as the fishbone diagram, is a problem-solving technique used to identify and analyze the root causes of a specific issue. It was developed by Japanese statistician Kaoru Ishikawa. Here's how it works:

Problem identification: The team clearly identifies the problem or adverse effect that needs resolving. This issue is typically written at the far right of a fish-shaped diagram.
Diagram creation: A fish-shaped diagram is drawn with a horizontal line representing the problem to solve. This line resembles a fish's spine.
Cause categories: On the diagram, "spines" are drawn perpendicular to the central spine of the fish. These represent different cause categories that might contribute to the problem. Common categories include the "5 M's" (Material, Manpower, Methods, Environment, Machines) or the "4 P's" (Product, Processes, People, Partners).
Identifying potential causes: The team then contemplates potential causes for each category and notes them along the corresponding spines. These causes are often identified through brainstorming sessions.
Analyze and identify root causes: Once all potential causes are recognized, the team analyzes each to determine if it's genuinely linked to the problem and if there are deeper underlying reasons, in order to pinpoint the root causes. Techniques like Pareto charts, data analysis, or the "5 whys" can be employed to identify and prioritize causes based on their significance.

One can argue that the essence of the Ishikawa method lies mainly within stages 1 to 4, up to the identification of potential causes.

Step 5 is more an extension of the Ishikawa method involving the use of other data analysis methods, such as Pareto charts, statistical analyses, or other in-depth investigative techniques.

The Ishikawa method is suitable for two phases of the problem-solving process:

Problem Definition: The "core" of the Ishikawa method is apt as it allows for the identification of potential causes to clarify the problem's scope and the extent of subsequent analyses. Indeed, the analysis and identification of root causes stage is lengthier and more resource-intensive and will thus be more suitable for the next phase.
Identifying causes: Both the core of the method and its extension to other methods are used here. The strength of the Ishikawa method is its ability to identify and structure analysis axes using complementary approaches. It's also common to undertake the "core" of the method in the problem definition phase and continue it in this stage (after validating the continuation of the problem-solving process).

2.3 Process mapping and critique

If problem solving is oriented towards improving a process, then the method of process mapping is suitable. This method aims to understand, analyze, and improve a process by visualizing it in detail and identifying optimization opportunities. Within this framework, this method can be applied at two stages of the problem-solving process:

Problem definition: At this stage, a high-level map will be preferred, for example, a simplified flow diagram, such as a SIPOC . This is generally sufficient to identify the main opportunities to explore later and to clarify the problem definition.
Cause identification: In this case, and especially for complex problems or significant processes, a detailed mapping that includes all steps, subprocesses, tasks, and interactions will be favored. This can be complemented by a SIPOC map if major issues are identified concerning the documents used (inputs, outputs) and the providers or customers of these documents.

2.4 Structured questionnaires

Questionnaires are generally categorized under general techniques of the following chapter. However, since we are referring here to two very specific types of questionnaires designed for problem-solving, we place them in this category.

Scoping - Survey: A structured but simple questionnaire (some open questions and performance perception scores) is answered by a selection of organization leaders (scoping) or by a large number of employees (survey).
Assessment against a benchmark: A very precise questionnaire answered by a selection of leaders or experts to assess how certain practices are conducted and if they match the state of the art (the benchmark).

These two types of questionnaires are used in two different phases:

Scoping - survey is appropriate in the problem definition phase
Assessment against a benchmark is used in the root cause identification phase

2.5 Benefit/Ease Matrix

The Benefit/Ease matrix is a tool that allows for the evaluation and ranking of potential actions based on two key criteria:

Benefit: Benefits, whether qualitative or quantitative, expected from the implementation of each action.
Ease: This represents the ease with which the proposed actions can be implemented or carried out. Ease depends on various factors such as available resources, required skills, legal constraints, or local conditions.

3 General techniques used in problem-solving

This category includes methods that are not specifically designed for use in problem-solving, but can be. They can also be more of techniques or principles rather than actual methods. Therefore, they can be integrated or used with more specific methods. For example, the "5 whys" can be used in the Ishikawa method to delve deeper into the causes indicated on each fishbone.

3.1 Brainstorming

Brainstorming is a technique for generating ideas creatively and collaboratively. It aims to gather a group of people to explore ideas, solutions, or concepts by encouraging free thought, creativity, and diversity of perspectives.

It is mainly used in the phases of:

Problem definition: Brainstorming can be used to gather initial ideas about areas that deserve particular attention, identify problems or opportunities requiring improvement.
Action definition: Brainstorming is particularly useful in this phase as it promotes the generation of a wide range of potential solutions to identified problems. It allows the team to think creatively about process changes, improvements, and innovations that could effectively solve the problems.

3.2 The 5 whys

The "5 Whys" is more of a technique than a method. It involves repeatedly asking the question "Why?" typically until the root cause of a problem is reached. The goal is to move beyond the obvious symptoms of a problem to identify underlying factors contributing to its occurrence.

3.3 Affinity diagram

The affinity diagram method, also known as the KJ method, is a group management technique used to organize and group ideas, information, or problems into logical categories. It consists of collecting items related to a subject, displaying them randomly, and then grouping them based on similarities or relations.

3.4 Quantitative data analysis

Data analysis is an essential element of problem-solving. However, the level of analysis, especially when it comes to quantitative analysis, varies greatly. Thus, we propose a categorization of analysis methods by complexity level to better indicate which analyses to use and when.

3.4.1 Categorization of analyses

Here is a categorization from the simplest to the most complex, with illustrations for each type, for quantitative analyses:

Basic statistics (mean, median, mode, variance, standard deviation)
Graphs (bar charts, histograms, pie charts)
Pareto charts
Scatter plots
Correlation analyses
Hypothesis tests (t-test, ANOVA)
Confidence intervals
Linear and logistic regression
Decision trees and random forests
Simple simulation
Optimization (linear programming, network optimization)
Neural networks
Clustering (like K-means)
Deep learning techniques

3.4.2 When to use them during problem-solving?

It depends both on the stage and on the complexity of identifying the real root causes, especially through a quantitative analysis.

Problem definition phase: Generally, descriptive analyses are sufficient at this stage.
Cause identification phase: Descriptive analyses are naturally used. Exploratory analyses, and even inferential/predictive analyses, are often used for specific causes. For instance, when calculating the capability of a process and verifying that it meets requirements (such as the defect rate, non-quality rate, etc.). This is even the basis of the approach and the term "six sigma", which requires less than 3.4 defects per million. For very specific and complex problems, advanced methods (simulations, AI) may be used.
Action definition phase: The main data analysis performed here is estimating the impacts of the actions, which is usually a descriptive analysis. However, it may happen that you simulate and compare several scenarios by performing sensitivity analyses, exploratory, or even predictive types. It is also likely that with the maturation of AI-based techniques, these tools will be used more and more to make action recommendations.

3.5 The Business Case

In the context of problem-solving, the "Business Case" identifies the gains, costs, investments, and financial risks associated with solving the problem. It supports several actions, such as deciding to continue the problem-solving process, prioritizing causes and actions, or tracking results:

Problem definition: At this stage, the Business Case is used to decide whether to proceed with the analysis and action definition phases. The Business Case is generally vague at this stage due to a lack of many data.
Cause identification: An estimated quantitative impact of the different causes can help focus on the causes generating the greatest financial losses.
Action definition: The Business Case is established at the end of the phase to decide whether or not to implement the actions. This time it is more precise because all the necessary data could be collected in the previous phases.
Measuring results: The Business Case is then used to verify that the impact of the solutions not only brings operational benefits but also translates into the organization's accounts.

The Business Case is used more the more complex the problem is, and therefore costly to solve. It will then be necessary to justify the investment in human and financial resources to solve the problem. It will be used less for simple problems, or in a very simplified way, for example, when the "Kaizen" method is used.

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A3 is a principle, not a problem-solving method !!

The pdca cycle or deming wheel: how and why to use it, the 5 whys method: how and when to use it, 5w2h or 5w1h methods: how and when to use them, 8d method (8 disciplines), ishikawa diagram and root cause analysis, continuous improvement process : a challenge for significant benefits, dmaic process: a methodology to implement six sigma, what is an operational audit of the organisation, improvement and innovation excellence.

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2: Problem Solving as a Process

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Peter L. Moore
Iowa State University

2.1 What is a problem?

Let’s establish this right away: a problem is an intellectual challenge. Solving a problem is then a process of undertaking and overcoming the challenge.

As we have indicated elsewhere, authentic problems are often poorly-structured and vague. They are not carefully-crafted to yield whole-number answers with a few minutes of symbolic manipulation, like those you typically encounter in school. Authentic problems could take hours, days, or even longer to solve, and you may not al- ways know with confidence that you have succeeded because the answers aren’t in the back of the book. Problems don’t require only the application of a recently-learned method or algorithm; indeed, you may not know at the outset which methods are appropriate for solving the problem. You may not be given all the information needed to achieve a complete solution, or information you are given may be uncertain or incomplete. In short, authentic problems are hard, and that can be frustrating.

Problems/exercises/answers

Many mathematics teachers and scholars distinguish between problems and exercises . An exercise prompts you to practice a method that you recently learned or for which you recently studied examples. Exercises usually have answers that can be compared with an answer key. A problem is more challenging because there may be fewer cues to the appropriate solution methods and there may be no explicit relationship between these methods and the instruction received.

But wait! Don’t close your book (or laptop) and walk away just yet! Having just explained the difficulties, consider the flip side of the problem-solving coin: problems that are authentic are also inherently interesting, particularly when they address contemporary issues or puzzles in your chosen area of study. Solutions and solution methods for such problems are therefore not just an academic dead-end, but can lend themselves to practical applications in the real world. The rewards of achieving a clever and well-justified solution to a practical and interesting problem should outweigh by far the moments of uncertainty, frustration, or disappointment encountered along the way.

Most of the problems discussed in this book are designed to mimic authentic problems, and in many cases are drawn from or inspired by encounters with local researchers and practitioners. As we endeavor to address these problems, we’ll often find it helpful to explore sim- pler problems and exercises to help with sense-making. Thus, our time will be spent moving back and forth from focus problems to auxiliary problems and exercises. Read on through the end of this chapter to understand how this approach can lead to more successful problem-solving.

Problem solving cannot be reduced to a simple recipe or fast and easy method, but in the past 70 years, much has been learned about how successful construction of solutions differs from unsuccessful attempts. A key component is the use of heuristics , or habits of mind that are useful in solving problems. The modern idea of heuristics has its origin in the work of Hungarian mathematician George Pólya in the mid 20$^{th}$ century. Heuristics help guide us in decisions about how to approach a problem. With the help of heuristics and the benefit of experience, we may develop problem-solving strategies that lead to successful solutions. We’ll begin our study of problem-solving with a brief look at Pólya’s method and some of his heuristics and then consider how they might apply to problem-solving in the natural science and natural resource management contexts.

Definition: Strategy

A strategy is a definite sequence of steps or operations that leads to a solution.

2.2 Pólya’s method and beyond

A credentialed mathematician and academic, Pólya was no stranger to the struggles of solving difficult problems. But he was also a teacher and concerned himself with the development of problem-solving skill and intuition in students. He studied his own problem- solving process and that of his professional colleagues and distilled his observations into four essential principles. These principles are general that is, their use needn’t be limited to mathematical problem- solving. The method can be summarized as follows:

Polya's Method, Condensed And Slightly Revised

1. Understand the problem . What is the unknown or target quantity? Is there enough information to find a solution? How is the information that is available relevant to the un- known?

2. Plan a solution strategy . How can you proceed from the information available to the unknown? What steps are necessary, and how will the given information be used?

3. Execute the solution plan . If the solution plan is chosen well, the implementation of the plan should yield the sought-after result. If unsurmountable difficulty arises, an alternative plan may need to be formulated.

4. Check the result . Does the result satisfy the conditions stated in the problem? Is it consistent with expectations or within reasonable bounds? Can you arrive at the same result using a different approach?

If it helps to have a mnemonic to remember these, how about UPEC for Understand, Plan, Execute, and Check.

These principles may seem obvious, but when the time comes to actually solve a problem it is easy to overlook one or more of them or to lose track of what we are after. Employing this method as a general framework for approaching problem-solving will yield more consistent success and more reliable results.

Consider the most common words out of a typical college student’s mouth when confronted with a novel problem: “I don’t know where to start” . Perhaps the student really means “you haven’t yet told me exactly what to do to get the answer”. But if the instructor were to point the student toward a solution method every time she was confronted with a challenging problem, she would learn only two things: 1) how to implement algorithms and compute numerical results as instructed; and 2) to relinquish all control of choosing how to approach and solve a problem to somebody else.

$^{1}$If I had a nickel for everytime I’ve heard that...

$^{2}$Though the memory of how to use mathematical algorithms certainly degrades with time unless used or reviewed frequently

Sadly, this is of- ten the best outcome of the standard school mathematics curriculum. The worst outcome is that students dismiss math as boring, difficult, or irrelevant. In some cases, a diligent student develops some facility$^{2}$ with basic manipulations of mathematical symbols and numbers, but little or no ability to create the frame of mind and methodological structure needed to begin and confidently proceed trying solutions.

For the challenge of getting started, Pólya’s framework offers Understand . What is the problem really asking, and what exactly do you want to end up with as a result? Take, for instance, the pheasant count problem that we introduced in the first chapter: what is Heuristic: Narrow the options Use the known properties of the unknown quantity to identify strategies appropriate to the problem.

the unknown in that problem? Essentially, the question we posed there was how many pheasants we should expect to be living in Iowa in the next few years. In some ways, this is a specific reinterpretation of the problem statement, but the simple act of making that re- interpretation not only helps us understand what we are looking for concretely, but our formal statement of it might clarify to colleagues or readers what our solution is driving at.

Since Pólya’s framework was developed from the perspective of a mathematician, some of the questions and suggestions pertain mostly to abstract problems. The framework doesn’t take advantage of the fact that most of our problems are situated in real-world contexts and involve quantities whose properties can be used as an asset in identifying, constructing, and evaluating solutions. If you’re not exactly clear on what I mean by that, go ahead and peak at the next chapter where we discuss the definition and properties of quantities.

On the next page, I have expanded and elaborated upon Pólya’s framework and adapted some of the details for problem-solving in natural sciences. Pólya’s framework, and our elaboration of it for problems in the natural sciences, may help us be better organized, but when it comes to applying the quantitative skills we spent years developing in math and statistics classes, we still have little guidance. In Pólya’s How to Solve It , this is the point where the idea and utility of heuristics was introduced. In the next section, we will introduce and review some generic heuristics that can aid with understanding the problem and inspiring a solution plan.

2.3 A Few Versatile Heuristics

The heuristics we consider here are just a snapshot of the generic methods we might employ in many problems, and some of these are further elaborated in subsequent chapters. These should be some of your most frequent go-to tools for the initial understanding and planning phases, and can be interpreted differently according to the constraints or conditions of each problem. In selecting optimal strategies, the field of options may be narrowed by examining the nature of the unknown. Think about the unknown and what it represents, not only for the focus problem but for any sub-problems or for any goals identified as necessary to solving the focus problem. Could the problem be stated in the form “how much...?”, “how many...?”, or “is...or not?”. If so, the problem might require arithmetic and/or algebraic reasoning. If data is available or supplied and the problem can be stated in the form “what relationship...?” or “how

Definition: Heuristic

Heuristic : Narrow the options Use the known properties of the unknown quantity to identify strategies appropriate to the problem.

Solving ILL-Structured Problems

1. Understand the problem

Do you understand the problem as it is stated?

Can you restate the problem in your own words?

What is the unknown or desired quantity or output (be specific)? Is it a number? A function? A procedure?

Can you make a drawing or diagram to illustrate how the unknown relates to any known quanti- ties or to the broader problem-space?

Do you already know approximately what the value should be? Can you guess a ballpark or range of reasonable values?

How accurate does your solution need to be? What are the consequences of errors?

What information do you already have?

Is the information that you already have sufficient to solve the problem?

If appropriate, can you write the problem as an algebraic equation with suitable notation?

2. Plan a solution .

Consider multiple approaches if possible

Have you successfully solved a problem like this before?

Has somebody else documented a solution method to this or a similar problem?

If the problem can be written explicitly as a mathematical statement, do you recognize an algo- rithm or heuristic that can yield the desired unknown?

If a solution method is apparent, can you assemble all the needed quantities?

If the problem is not immediately solvable, or a solution method not yet apparent...

Can you break the problem into smaller sub-problems that may be easier to solve?

Can you approximate uncertain or unknown quantities?

Could you solve a related auxiliary problem to gain insight?

If data are given, what exploratory analyses could be done to spark ideas?

3. Execute the plan

At each step, check to see if the incremental result matches expectations. Double-check all formulae and algebraic manipulations.

If appropriate, is unit/dimensional homogeneity satisfied?

If you encounter difficulties, revisit the plan and alternatives.

4. Check the solution

Is the result reasonable?

Is it consistent with ballpark estimates or benchmarks?

If appropriate, can you substitute the result into the original problem and satisfy the assumptions and conditions?

Double-check algebraic manipulations.

Double-check numerical compuations.

Could you document your full solution with a concise but complete summary of steps, justification of assumptions and methods?

Could a colleague reproduce your approach and find the same solution?

does...change as you vary...?”, graphical and statistical reasoning are probably appropriate. If the problem can be stated in the form “how big...?”, “what distance...?” or “where...?”, then geometric or spatial reasoning could be necessary . There are certainly problems that won’t be easily stated in any of these terms, and all options should then remain open. Nevertheless, recognizing common properties in the nature of problems can sometimes narrow down your choices of strategies and make promising solution methods or approaches more apparent.

$^{3}$Each of these types of reasoning and the context-specific strategies that are particularly helpful for them are reviewed in separate chapters in this book.

Break the problem into sub-problems. Complex problems often require multiple steps that can be divided into discrete sub-goals. For example, determining the value of an unknown quantity that is required to solve the focus problem can be considered distinct from solving the focus problem itself. Therefore mapping out the solution in terms of incremental sub-goals can clarify the pathway to a solution.
Express conditions algebraically. Assign symbols to relevant quantities and express the relationship, if known, as an equation relating the quantities. If relationships are not known beforehand, use dimensional analysis to suggest them.
Guess the correct answer or solution. Usually a guess or ball- park estimate is not sufficient if the issue is truly a problem , but estimates can still be used to help you recognize if you are on the right track in later computations. If you know approximately what the solution is or what range it should lie within, use this value to check your work. If the solution is not known beforehand but algebraic or practical constraints are available on related quantities, use those quantities to get a ballpark estimate. At this stage, back-of-the-envelope calculations in scientific notation can make quick work of it.
Try a few values. Where some values are unknown but are not
the desired quantity, try to solve the problem with a few supposed numerical values. Sometimes the outcome of algebraic relation- ships is relatively insensitive to the precise value of the quantities included in the relationship. When the relationship is strongly sensitive to unknown or poorly-constrained quantities, identify those quantities as important intermediate goals or sub-problems.
Draw a picture or diagram. When the problem is inherently spatial, such as in the case of habitat or landscape ecology problems, make a map or schematic drawing of the geometric or spatial relationships between known and unknown quantities. To the extent that it is possible, scale distances or spatial dimensions accurately.
List all possible cases. If you’re confronted with a logic or simple probabilistic puzzle, make a list or matrix containing possible permutations or combinations.
Work backwards. Where the desired ending condition is known or can be approximated but the steps to reach it are not known, use the end result to help “back out” the steps.
Visualize the data. If data or input values are given and a relationship or summary-statistic is desired, make a graph or diagram from the data. In some cases, visual representation of the data can suggest or substantiate approximate values for the unknowns or can illustrate the form of functional relationships.
Solve a simpler problem. Sometimes a condition or relationship is too complex to solve easily in its full form. In these cases, it may be possible and helpful to simplify the condition to make the problem tractable. You can do this by assuming that an unknown value is known (as in Try a few values ), by eliminating one or more terms in sums and differences, or by using a simpler statement of the original condition.

The heuristics above are by no means a recipe for success in every situation, but they should be available to you in your repertoire of things to consider. In the chapters that follow, we will elaborate on some of these strategies and add more context-specific tools that can be applied in practical problems.

2.4 Stepping back

Before we set you loose on solving problems, it is important to ad- dress the mind-set of problem solving. If you have ever uttered the words “I suck at math” or something similar, this section is particularly for you. But as far as I’m concerned, realizing how the mind constructs knowledge and understanding in a problem-solving task is an empowering notion. Alan Schoenfeld, mathematician and math- education specialist, has identified four aspects of the mental process of problem-solving that are essential: Resources, Heuristics, Control, and Belief. Each is necessary and problem-solving cannot or will not proceed without them. First, let’s look at what each means, and then we’ll consider how they contribute to our problem-solving success.

These are the things you know or understand about the prob- lem domain, constraints on quantities and their representation in the problem domain, and the skills you possess in perform- ing algorithmic procedures.
The decision-making tools used to make sense of challenging problems that allow you to make progress or develop insight. Most of the chapters of this booklet are devoted to developing strategies useful in natural science or resource management domains.
Control is the management and self-awareness of the problem-solving process. It includes planning, execution and evaluation decisions and and the selection of resources and heuristics for the problem.
Belief includes the set of notions one has about the problem domain as well as one’s own abilities or challenges in ap- plying math and statistics to the problem domain; this also includes preconceptions and (mis)understandings that could lead to the use of (in)correct resources and heuristics in a given problem.

Your mathematics and statistics education up to this point has almost certainly stressed resources. Thus, the quantitative resources you bring to a problem consist of all the algorithms and methods you know how to use and your understanding of what they do or mean. Unless you’ve followed a curriculum through school and college that has deliberately made use of these resources, you’ve probably forgot- ten many of them, but re-learning them may not be as challenging as learning them naively. Control and belief are gained from experience, and can build from any foundation of resources and heuristics. The heuristics and strategies themselves can be a bit of a problem though.

You may have been instructed some in the development solution strategies in school, but there’s an important distinction between learning what to use and learning when to use it. Some people may argue that it is not a mathematician’s prerogative to instruct students in their service courses in more than resources, since heuristics vary from one discipline to another and control and belief grow with experience. This argument is fair, but as non-mathematicians we’re left with training in how to implement algorithms, but little idea about how to use those algorithms unless presented with problems that aren’t really problems but exercises.

As a result, when the going gets tough,...we get stuck. That’s where this course comes in (hopefully to the rescue??). This is your opportunity to work with resources you already have at your disposal, perhaps learn a few more, and to be introduced to strategies for using them in problems that you might encounter in other natural resource courses, in internships, or in your career. By working through these problems in a systematic manner, you’ll learn how to control your problem-solving process while building your experience base. I sincerely hope that your belief system evolves in such a way that you become confident that you can solve quantitative problems too !

Exercise 1.

Think of a challenging problem that you needed help to solve in one of your high school or college courses. It could be a mathematical problem, but doesn’t have to be. Describe the problem and reflect on what assistance you needed to arrive at a solution. Were you unable to get started? Did you need help with recognizing and implementing the appropriate algorithms? What was the nature of the assistance that helped you solve the problem? Was it satisfying to arrive at the correct solution?

Exercise 2.

Now reflect on a challenging problem that you were able to solve correctly without assistance. Why were you successful? Were you able to overcome any difficulties or hurdles along the way? Was it more or less satisfying to solve this problem on your own than to solve a problem with help? Why?

Exercise 3.

What resources do you think a person needs to be able to make good predictions of pheasant population over the coming 5 years?

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Transformations That Work

Michael Mankins
Patrick Litre

More than a third of large organizations have some type of transformation program underway at any given time, and many launch one major change initiative after another. Though they kick off with a lot of fanfare, most of these efforts fail to deliver. Only 12% produce lasting results, and that figure hasn’t budged in the past two decades, despite everything we’ve learned over the years about how to lead change.

Clearly, businesses need a new model for transformation. In this article the authors present one based on research with dozens of leading companies that have defied the odds, such as Ford, Dell, Amgen, T-Mobile, Adobe, and Virgin Australia. The successful programs, the authors found, employed six critical practices: treating transformation as a continuous process; building it into the company’s operating rhythm; explicitly managing organizational energy; using aspirations, not benchmarks, to set goals; driving change from the middle of the organization out; and tapping significant external capital to fund the effort from the start.

Lessons from companies that are defying the odds

Idea in Brief

The problem.

Although companies frequently engage in transformation initiatives, few are actually transformative. Research indicates that only 12% of major change programs produce lasting results.

Why It Happens

Leaders are increasingly content with incremental improvements. As a result, they experience fewer outright failures but equally fewer real transformations.

The Solution

To deliver, change programs must treat transformation as a continuous process, build it into the company’s operating rhythm, explicitly manage organizational energy, state aspirations rather than set targets, drive change from the middle out, and be funded by serious capital investments.

Nearly every major corporation has embarked on some sort of transformation in recent years. By our estimates, at any given time more than a third of large organizations have a transformation program underway. When asked, roughly 50% of CEOs we’ve interviewed report that their company has undertaken two or more major change efforts within the past five years, with nearly 20% reporting three or more.

Michael Mankins is a leader in Bain’s Organization and Strategy practices and is a partner based in Austin, Texas. He is a coauthor of Time, Talent, Energy: Overcome Organizational Drag and Unleash Your Team’s Productive Power (Harvard Business Review Press, 2017).
PL Patrick Litre leads Bain’s Global Transformation and Change practice and is a partner based in Atlanta.

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What is Problem Solving? Steps, Process & Techniques
Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below. Step. Characteristics. 1. Define the problem. Differentiate fact from opinion. Specify underlying causes. Consult each faction involved for information. State the problem specifically.
35 problem-solving techniques and methods for solving complex problems
6. Discovery & Action Dialogue (DAD) One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions. With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so.
The Problem-Solving Process
Overview of the Problem-Solving Mental Process. 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.
The Art of Effective Problem Solving: A Step-by-Step Guide
Table of Contents. 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. Conclusion.
Problem solving
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. ... with aim of finding the best solution for a given challenge. Modern information ...
36 Problem-solving techniques, methods and tools
18. Open Space Technology. Open Space Technology is a method for large groups to create a problem-solving agenda around a central theme. It works best when your group is comprised of subject-matter experts and experienced individuals with a sufficient stake in the problem.
The Problem-Solving Process
The Problem-Solving Process. Problem-solving is an important part of planning and decision-making. The process has much in common with the decision-making process, and in the case of complex decisions, can form part of the process itself. We face and solve problems every day, in a variety of guises and of differing complexity.
Problem-Solving Strategies: Definition and 5 Techniques to Try
In general, effective problem-solving strategies include the following steps: Define the problem. Come up with alternative solutions. Decide on a solution. Implement the solution. Problem-solving ...
How to improve your problem solving skills and strategies
6. Solution implementation. This is what we were waiting for! All problem solving strategies have the end goal of implementing a solution and solving a problem in mind. Remember that in order for any solution to be successful, you need to help your group through all of the previous problem solving steps thoughtfully.
Problem Solving
Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to ...
Problem-Solving Strategies and Obstacles
Problem-solving is a vital skill for coping with various challenges in life. This webpage explains the different strategies and obstacles that can affect how you solve problems, and offers tips on how to improve your problem-solving skills. Learn how to identify, analyze, and overcome problems with Verywell Mind.
What is Problem Solving? (Steps, Techniques, Examples)
The problem-solving process typically includes the following steps: Identify the issue: Recognize the problem that needs to be solved. Analyze the situation: Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present. Generate potential solutions: Brainstorm a list of possible ...
PDF THIRTEEN PROBLEM-SOLVING MODELS
The Six-Step method provides a focused procedure for the problem solving (PS) group. It ensures consistency, as everyone understands the approach to be used. By using data, it helps eliminate bias and preconceptions, leading to greater objectivity. It helps to remove divisions and encourages collaborative working.
Problem Solving
Cognitive—Problem solving occurs within the problem solver's cognitive system and can only be inferred indirectly from the problem solver's behavior (including biological changes, introspections, and actions during problem solving).. Process—Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of ...
1.3: Problem Solving Strategies
In 1945, Pólya published the short book How to Solve It, which gave a four-step method for solving mathematical problems: First, you have to understand the problem. ... and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric, like this one ...
35 problem-solving techniques and methods for solving complex problems
Every effective problem solving process begins with an agenda. A well-structured workshop is one of the best methods by successfully guiding a select from exploring a problem to implementing an solution. ... we hope we've given you the tools to find the best solve as simply and lightweight as possible.
What Is Problem-Solving? How to Use Problem-Solving Skills to Resolve
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.
What is Problem Solving? Process, Techniques, Examples
Here's a breakdown of a common problem-solving process, presented in a pointwise manner: 1. Identifying the Problem. The first step in the problem-solving process is clearly defining the issue. This involves gathering relevant Information, observing patterns or trends, and understanding the impact of the problem on stakeholders.
14 Effective Problem-Solving Strategies
14 types of problem-solving strategies. Here are some examples of problem-solving strategies you can practice using to see which works best for you in different situations: 1. Define the problem. Taking the time to define a potential challenge can help you identify certain elements to create a plan to resolve them.
Problem Solving
L = Length. W = Width. In the following example, we will use the problem-solving method we developed to find an unknown width using the formula for the perimeter of a rectangle. By substituting the dimensions we know into the formula, we will be able to isolate the unknown width and find our solution.
Problem-Solving Method In Teaching
The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to ...
Comparison of problem-solving methods and techniques
This category encompasses complete and structured methods for tackling problem-solving in a systematic way. These approaches are designed to guide individuals or teams throughout the problem-solving process, providing clear and ordered steps to follow. 1.1 DMAIC. The DMAIC approach is a structured problem-solving method, divided into five main ...
2: Problem Solving as a Process
Problems don't require only the application of a recently-learned method or algorithm; indeed, you may not know at the outset which methods are appropriate for solving the problem. You may not be given all the information needed to achieve a complete solution, or information you are given may be uncertain or incomplete.
Do You Understand the Problem You're Trying to Solve?
To Solve Your Toughest Problems, Change the Problems You Solve. In this episode, you'll learn how to reframe tough problems by asking questions that reveal all the factors and assumptions that ...
Transformations That Work
Michael Mankins is a leader in Bain's Organization and Strategy practices and is a partner based in Austin, Texas. He is a coauthor of Time, Talent, Energy: Overcome Organizational Drag and ...
Answered: The initial tableau of a linear…
The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem. Z $1 1 3 1 0 15 5 1 0 10 45 1 1 0 1 0 5 -3 0 0 0 1 0 The maximum is when x₁ = x2 = s₁ = $2 and $3 - (Type integers or simplified fractions.) =. Transcribed Image Text: The initial tableau of a linear programming problem is given.
How to solve Champions Cup's South African problem
The issues thrown up by this season's campaign should bring everyone back to the table and introduce a new format that would see 18 clubs split into three pools of six, with each club playing ...

Table of Contents

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

Daniel Croft

Free Lean Six Sigma Templates

5S Floor Marking Best Practices

How to Measure the ROI of Continuous Improvement Initiatives

8D Problem-Solving: Common Mistakes to Avoid

The Evolution of 8D Problem-Solving: From Basics to Excellence

8D: Tools and Techniques

How to Select the Right Lean Six Sigma Projects: A Comprehensive Guide

36 Problem-solving techniques, methods and tools

11 Problem-solving techniques for clarity and confidence

1. Take a moment, take a breath

2. Ask questions to understand the full extent of the issue

3. Consider alternative perspectives

4. Make your office space conducive to problem-solving

5. Use problem-solving methodologies to guide the process

6. Use analogies to solve complex problems

7. Establish clear constraints

8. Dislodge preconceived ideas

9. Level the playing field

10. Take a break from the problem

11. Limit feedback sessions

16 Tried and tested problem-solving methodologies

12. Six Thinking Hats

13. Lightning Decision Jam (LDJ)

14. The 5 Why’s

15. World Café

16. Discovery and Action Dialogue (DAD)

17. Design Sprint 2.0

18. Open Space Technology

19. Round-Robin Brainstorming Technique

20. Failure Modes and Effects Analysis (FMEA)

21. Flip It!

22. The Creativity Dice

23. SWOT Analysis

24. The Journalistic Six

25. Gamestorming

26. Four-Step Sketch

27. 15% Solutions

9 Problem-solving tools for gathering and selecting ideas

28. Fishbone Diagram

29. The Problem Tree

30. SQUID Diagram

31. The Speed Boat

32. The LEGO Challenge

33. The Three W’s: What? So What? Now What?

34. Now-How-Wow Matrix

35. Impact-Effort Matrix

36. Dot Voting

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The Problem-Solving Process

1. Define the Problem

2. Analyze the Problem

3. Generate Potential Solutions

4. Select Best Solution

5. Take Action

6. Monitor and Review

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