problem solving with diagram

Problem-Solving Flowchart: A Visual Method to Find Perfect Solutions

Lucid Content

Reading time: about 7 min

“People ask me questions Lost in confusion Well, I tell them there's no problem Only solutions” —John Lennon, “Watching the Wheels”

Despite John Lennon’s lyrics, nobody is free from problems, and that’s especially true in business. Chances are that you encounter some kind of problem at work nearly every day, and maybe you’ve had to “put out a fire” before lunchtime once or twice in your career.

But perhaps what Lennon’s saying is that, no matter what comes our way, we can find solutions. How do you approach problems? Do you have a process in place to ensure that you and your co-workers come to the right solution?

In this article, we will give you some tips on how to find solutions visually through a problem-solving flowchart and other methods.

What is visual problem-solving?

If you are a literal thinker, you may think that visual problem-solving is something that your ophthalmologist does when your vision is blurry. For the rest of us, visual problem-solving involves executing the following steps in a visual way:

• Define the problem.
• Brainstorm solutions.
• Pick a solution.
• Implement solutions.
• Review the results.

How to make your problem-solving process more visual

Words pack a lot of power and are very important to how we communicate on a daily basis. Using words alone, you can brainstorm, organize data, identify problems, and come up with possible solutions. The way you write your ideas may make sense to you, but it may not be as easy for other team members to follow.

When you use flowcharts, diagrams, mind maps, and other visuals, the information is easier to digest. Your eyes dart around the page quickly gathering information, more fully engaging your brain to find patterns and make sense of the data.

Identify the problem with mind maps

So you know there is a problem that needs to be solved. Do you know what that problem is? Is there only one problem? Is the problem sum total of a bunch of smaller problems?

You need to ask these kinds of questions to be sure that you are working on the root of the issue. You don’t want to spend too much time and energy solving the wrong problem.

To help you identify the problem, use a mind map. Mind maps can help you visually brainstorm and collect ideas without a strict organization or structure. A mind map more closely aligns with the way a lot of our brains work—participants can bounce from one thought to the next defining the relationships as they go.

Mind mapping to solve a problem includes, but is not limited to, these relatively easy steps:

• In the center of the page, add your main idea or concept (in this case, the problem).
• Branch out from the center with possible root causes of the issue. Connect each cause to the central idea.
• Branch out from each of the subtopics with examples or additional details about the possible cause. As you add more information, make sure you are keeping the most important ideas closer to the main idea in the center.
• Use different colors, diagrams, and shapes to organize the different levels of thought.

Alternatively, you could use mind maps to brainstorm solutions once you discover the root cause. Search through Lucidchart’s mind maps template library or add the mind map shape library to quickly start your own mind map.

Create a problem-solving flowchart

A mind map is generally a good tool for non-linear thinkers. However, if you are a linear thinker—a person who thinks in terms of step-by-step progression making a flowchart may work better for your problem-solving strategy. A flowchart is a graphical representation of a workflow or process with various shapes connected by arrows representing each step.

Whether you are trying to solve a simple or complex problem, the steps you take to solve that problem with a flowchart are easy and straightforward. Using boxes and other shapes to represent steps, you connect the shapes with arrows that will take you down different paths until you find the logical solution at the end.

Flowcharts or decision trees are best used to solve problems or answer questions that are likely to come up multiple times. For example, Yoder Lumber , a family-owned hardwood manufacturer, built decision trees in Lucidchart to demonstrate what employees should do in the case of an injury.

To start your problem-solving flowchart, follow these steps:

• Draw a starting shape to state your problem.
• Draw a decision shape where you can ask questions that will give you yes-or-no answers.
• Based on the yes-or-no answers, draw arrows connecting the possible paths you can take to work through the steps and individual processes.
• Continue following paths and asking questions until you reach a logical solution to the stated problem.
• Try the solution. If it works, you’re done. If it doesn’t work, review the flowchart to analyze what may have gone wrong and rework the flowchart until you find the solution that works.

If your problem involves a process or workflow , you can also use flowcharts to visualize the current state of your process to find the bottleneck or problem that’s costing your company time and money.

Lucidchart has a large library of flowchart templates to help you analyze, design, and document problem-solving processes or any other type of procedure you can think of.

Draw a cause-and-effect diagram

A cause-and-effect diagram is used to analyze the relationship between an event or problem and the reason it happened. There is not always just one underlying cause of a problem, so this visual method can help you think through different potential causes and pinpoint the actual cause of a stated problem.

Cause-and-effect diagrams, created by Kaoru Ishikawa, are also known as Ishikawa diagrams, fishbone diagrams , or herringbone diagrams (because they resemble a fishbone when completed). By organizing causes and effects into smaller categories, these diagrams can be used to examine why things went wrong or might go wrong.

To perform a cause-and-effect analysis, follow these steps.

1. Start with a problem statement.

The problem statement is usually placed in a box or another shape at the far right of your page. Draw a horizontal line, called a “spine” or “backbone,” along the center of the page pointing to your problem statement.

2. Add the categories that represent possible causes.

For example, the category “Materials” may contain causes such as “poor quality,” “too expensive,” and “low inventory.” Draw angled lines (or “bones”) that branch out from the spine to these categories.

3. Add causes to each category.

Draw as many branches as you need to brainstorm the causes that belong in each category.

Like all visuals and diagrams, a cause-and-effect diagram can be as simple or as complex as you need it to be to help you analyze operations and other factors to identify causes related to undesired effects.

Collaborate with Lucidchart

You may have superior problem-solving skills, but that does not mean that you have to solve problems alone. The visual strategies above can help you engage the rest of your team. The more involved the team is in the creation of your visual problem-solving narrative, the more willing they will be to take ownership of the process and the more invested they will be in its outcome.

In Lucidchart, you can simply share the documents with the team members you want to be involved in the problem-solving process. It doesn’t matter where these people are located because Lucidchart documents can be accessed at any time from anywhere in the world.

Whatever method you decide to use to solve problems, work with Lucidchart to create the documents you need. Sign up for a free account today and start diagramming in minutes.

Lucidchart, a cloud-based intelligent diagramming application, is a core component of Lucid Software's Visual Collaboration Suite. This intuitive, cloud-based solution empowers teams to collaborate in real-time to build flowcharts, mockups, UML diagrams, customer journey maps, and more. Lucidchart propels teams forward to build the future faster. Lucid is proud to serve top businesses around the world, including customers such as Google, GE, and NBC Universal, and 99% of the Fortune 500. Lucid partners with industry leaders, including Google, Atlassian, and Microsoft. Since its founding, Lucid has received numerous awards for its products, business, and workplace culture. For more information, visit lucidchart.com.

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What is a Problem-Solving Flowchart & How to Make One

By Danesh Ramuthi , Aug 10, 2023

Problem-Solving Flowcharts, contrary to what many believe aren’t just aesthetic wonders — they’re almost like magical blueprints for troubleshooting those pesky problems that many of us face.

Flowcharts take business challenges and turn them into a navigable pathway. In this post, I will guide you on key aspects of problem-solving flowcharts such as what it is, the advantages of problem-solving flowcharts, how to create one and more.

Besides, you’ll also discover how to create problem-solving flowcharts with the help of Venngage’s Flowchart Maker.

And for those of you thinking, “I’m no designer, how can I create one?” worry not! I’ve got you covered. Just hop on Venggage’s Flowchart Templates and you’ll be charting your way to problem-solving glory in no time.

Click to jump ahead:

What are problem-solving flowcharts?

When to use problem-solving flowcharts, what are the advantages of flowcharts in problem-solving, what are the 7 steps of problem-solving flowcharts.

• 5 different types of problem-solving flowcharts

Best practices for designing effective problem-solving flowcharts

How to make a flowchart using venngage , problem-solving flowcharts faqs.

• Final Thoughts

Problem-Solving Flowcharts is a graphical representation used to break down problem or process into smaller, manageable parts, identify the root causes and outline a step-by-step solution. 

It helps in visually organizing information and showing the relationships between various parts of the problem.

This type of flowcharts consists of different symbols and arrows, each representing different components or steps in the problem-solving process. 

By following the flow of the chart, individuals or teams can methodically approach problem, analyze different aspects of it and come to a well-informed solution.

Problem-Solving Flowcharts is a versatile tool that can be used in various scenarios. Here’s when to consider utilizing one:

• Complex Problems: When faced with a multifaceted issue that involves multiple steps or variables, flowcharts can help break down the complexity into digestible parts.
• Team Collaboration: If you’re working with a team and need a common understanding of problem and its potential solutions then a flowchart provides a visual that everyone can refer to.
• Analyzing Processes: In a situation where you need to understand a particular process, whether it’s within a project or a part of regular operations then mapping it out in a flowchart can offer clarity.
• Decision Making: When various paths or decisions might be taken, a flowchart can outline the potential outcomes of each aiding in making an informed choice.
• Training and Onboarding: Flowcharts can be used in training materials to help new employees understand complex processes or procedures which makes the learning curve smoother.
• Identifying Root Causes: If you’re looking to identify the underlying causes of problem then a flowchart can facilitate a systematic approach to reaching the root of the issue.

Related: How to Use Fishbone Diagrams to Solve Complex Problems

Problem-solving flowcharts can offer several benefits to the users who are looking to solve a particular problem. Few advantages of flowcharts in problem solving are: 

Visual Clarity

When you’re dealing with multifaceted problems or processes, words alone can make the situation seem even more tangled. Flowcharts distill these complexities into easily understandable visual elements. 

By mapping out each phase or component of problem, flowcharts offer a bird’s eye view enabling individuals to grasp the bigger picture and the finer details simultaneously.

Sequential Representation

Flowcharts excel in laying out the sequence of events or actions. By indicating a clear starting point and illustrating each subsequent step, they guide users through a process or solution path methodically. 

This linear representation ensures that no step is overlooked and each is executed in the right order.  

Collaboration

Problem-solving often requires team effort and flowcharts are instrumental in fostering collaborative environments. 

When a team is discussing potential solutions or trying to understand problem’s intricacies, a flowchart serves as a collective reference point. 

It aids in synchronizing everyone’s understanding, minimizing miscommunications and promoting constructive discussions. 

Read more about: Flowcharts Symbols and Meaning

1. Define the Problem  

Before anything else, it’s essential to articulate the problem or task you want to solve clearly and accurately. By understanding exactly what needs to be addressed you can ensure that subsequent steps align with the core issue.

2. Identify the Inputs and Outputs  

Determine what inputs (such as data, information or resources) will be required to solve the problem and what the desired outputs or outcomes are. Identifying these factors will guide you in structuring the steps needed to reach the end goal and ensure that all necessary resources are at hand.

3. Identify the Main Steps  

Break down the problem-solving process into its main steps or subtasks. This involves pinpointing the essential actions or stages necessary to reach the solution. Create a roadmap that helps in understanding how to approach the problem methodically.

4. Use Decision Symbols  

In problem-solving, decisions often lead to different paths or outcomes. Using standard symbols to represent these decision points in the flowcharts allows for a clear understanding of these critical junctures. It helps visually present various scenarios and their consequences.

5. Add Descriptions and Details  

A well-designed flowcharts is concise but clear in its labeling. Using arrows and short, descriptive phrases to explain what happens at each step or decision point ensures that the flowcharts communicates the process without unnecessary complexity. 

6. Revise and Refine  

Creating a flowcharts is not always a one-and-done process. It may require revisions to improve its clarity, accuracy or comprehensiveness. Necessary refinement ensures that the flowcharts precisely reflects the problem-solving process and is free from errors or ambiguities.

7. Use Flowchart Tool  

While it’s possible to draw a flowcharts manually, using a flowcharts tool like Venngage’s Flowchart Maker and Venngage’s Flowchart Templates can make the process more efficient and flexible. These tools come with pre-designed templates and intuitive interfaces that make it easy to create, modify and share flowcharts. 

5 different types of problem-solving flowcharts 

Let’s have a look at 5 most common types of flowcharts that individuals and organizations often use. 

1. Process Flowchart s

A process flowcharts is a visual representation of the sequence of steps and decisions involved in executing a particular process or procedure. 

It serves as a blueprint that showcases how different stages or functions are interconnected in a systematic flow and it highlights the direction of the process from its beginning to its end.

Process flowcharts are instrumental in training and onboarding, sales process , process optimization, documentation, recruitment and in any scenario where clear communication of a process is crucial.

2. Flowcharts Infographic 

A flowcharts infographic is a great way to showcase the process or a series of steps using a combination of graphics, icons, symbols and concise text. It aims to communicate complex information in a clear and easy-to-understand manner, making it a popular tool for conveying information, data and instructions in a visually engaging way.

For example, you can use this flowchart to illustrate a health insurance process that visually explains the steps involved from finding a provider to paying for your healthcare provider. 

3. Circular Flowcharts

A circular flowcharts is used to illustrate the flow of information, goods, services or money within a closed system or process. It gets its name from its circular shape, which emphasizes the continuous and cyclical nature of the flow. 

Circular flowcharts are widely used in various fields such as economics, business, engineering and process management to help visualize and understand complex systems.

In a circular flowcharts , elements are represented using various shapes and connected with arrows to indicate the direction of flow. The circular arrangement indicates that the process is ongoing and repeats itself over time.

4. Swimlane flowcharts

Swimlane flowcharts , also known as cross-functional flowcharts are a specific type of flowchart that organizes the process flow into lanes or “swimlanes.” 

Each lane represents a different participant or functional area involved in the process and the flowchart shows how activities or information move between these participants. 

Swimlane flowcharts are particularly useful for illustrating complex processes that involve multiple stakeholders or departments.

In a swimlane flowcharts, the process is divided horizontally into lanes and each lane is labeled with the name of the department, person or role responsible for that part of the process. Vertically, the flowchart displays the sequence of steps or actions taken in the process.

5. Decision Flowchart s

Decision flowcharts, also known as decision trees or flow diagrams are graphical representations that illustrate the process of making decisions or solving problems. 

They are widely used in various fields such as computer science, business mapping , engineering and problem-solving scenarios. 

Decision flowcharts help break down complex decision-making processes into simple, sequential steps, making it easier to understand and follow.

A decision tree is a specialized flowchart used to visually represent the process of decision-making. 

Businesses and other individuals can employ a decision tree analysis as a tool to aid in evaluating different options and the possible consequences associated with each choice.

Decision trees Infographics can be used to create a more nuanced type of flowchart that is more informative and visually appealing by combining a decision flowchart and the flowchart infographic. 

Decision flowcharts are valuable tools for visualizing decision-making processes, analyzing complex problems and communicating them effectively to others.

Designing effective problem-solving flowcharts involves careful consideration of various factors to ensure clarity, accuracy and usability. Here are some best practices to create efficient and useful problem-solving flowcharts:

• Understand the problem first & clearly define it
• Keep it simple
• Use standard & recognizable symbols
• Ensure that the flowchart follows a logical and sequential order
• Clearly label each decision point, action and outcome
• Verify the flowchart’s accuracy by testing it
• Clearly state the decision criteria that lead to different branches
• Provide context when the flowchart is part of a larger process or system
• Review and revise the flowchart

Creating problem-solving flowchart on Venngage is incredibly simple. All you have to do is:

• Start by Signing Up and Creating an Account with Venngage
• Choose a flowchart template that best suits your needs from our library.
• Start editing your flowchart by choosing the desired shapes, labels and colors.
• You can also enhance your flowchart by incorporating icons, illustrations or backgrounds all of which are readily available in our library.
• Once done, you will have 2 options to choose from, either sharing it online for free or downloading your flowchart to your desktop by subscribing to the Premium or Business Plan. 

Is flowchart the representation of problem solutions?

Flowcharts are not the representation of problem solutions per se; rather, they are a visual representation of processes, decision-making steps and actions taken to arrive at a solution to problem.

What are the 3 basic structures of flowcharts?

3 Basic Structures of Flowcharts are:

• Sequence: Simplify Complexity
• Selection (Decision): Embrace Choices
• Repetition (Loop): Emphasize Iteration

What are the elements of a good flowchart?

A good flowchart should exhibit clarity and simplicity, using consistent symbols and labels to depict a logical sequence of steps. It should be readable, with appropriate white space to avoid clutter while eliminating ambiguity through well-defined decision criteria and paths.

Can flowcharts be used for both simple and complex problem-solving?

Yes, flowcharts can be used for both simple and complex problem-solving scenarios. Flowcharts are versatile visual tools that can effectively represent various processes, decision-making steps and problem-solving approaches regardless of their complexity.

In both cases, flowcharts offer a systematic and visual means of organizing information, identifying potential problems and facilitating collaboration among team members.

Can problem-solving flowcharts be used in any industry or domain?

Problem-solving flowcharts can be used in virtually any industry or domain. The versatility and effectiveness of flowcharts make them applicable to a wide range of fields such as Business and Management, Software Development and IT, Healthcare, Education, Finance, Marketing & Sales and a lot more other industries. 

Final thoughts

Problem-solving flowcharts are a valuable and versatile tool that empowers individuals and teams to tackle complex problems with clarity and efficiency.

By visually representing the step-by-step process of identifying, analyzing and resolving issues, flowcharts serve as navigational guides simplifying intricate challenges into digestible parts.

With the aid of modern tools like Venngage’s Flowchart Maker and Venngage’s Flowchart Templates , designing impactful flowcharts becomes accessible to all while revolutionizing the way problems are approached and solved.

Maths with David

Problem solving. draw diagram.

In mathematics, diagrams are often a useful way of organising information and help us to see relationships. A diagram can be a rough sketch, a number line, a tree diagram or two-way table, a Venn diagram, or any other drawing which helps us to tackle a problem.

Labels (e.g. letters for vertices of a polygon) are useful in a diagram to help us be able to refer to items of interest.

A diagram can be updated as we find out new information.

Examples of using a diagram to tackle a problem

First we will read all three examples and have a quick think about them and then we will look at how a diagram can help us with each one:

Restaurant Example

A restaurant offers a “business lunch” where people can choose either fish or chicken or vegetables for their main course, accompanied by a side portion of rice, chips, noodles or salad. How many different combined meals can they choose between?

Rectangle Area Example

To the nearest centimetre, the length and width of a rectangle is 10cm and 8cm.

• What are the limits of accuracy for the area of the rectangle?
• the lengths of the sides?

Prime Numbers Example

Masha says that if she writes out numbers in rows of six then all of the prime numbers will either be in the column that has 1 at the top, or they will be in the column that has 5 at the top. How can you find out if she is correct?

Worked Solutions to Examples

One way to tackle this would be to write out a list, being systematic to ensure that all combinations are considered.

Another is to draw out a diagram like the one below. As shown, you actually don’t need to finish the diagram in order to conclude how many combinations there are:

You could also use a 2-way table as shown below:

Drawing a rough sketch of the rectangle labelled with the boundaries of its side lengths can really help us to visualise the situation here:

It can then be helpful to draw sketches of the smallest possible rectangle and the largest possible rectangle:

We can now answer the questions, so (a) the smallest possible area is 7.5 x 9.5 = 71.25cm 2 and the largest “possible” area is 8.5 x 10.5 = 89.25cm 2 . So the limits of accuracy are [71.25,89.25) cm 2 .

For (b), we can see from the sketches that the difference between the minimum and the maximum values is 1cm in the case of both the width and the lenght. For part (ii) we simply subtract the numbers above to give 89.25-71.25 = 18cm 2 .

Here, listing out numbers, especially for the first few is going to be helpful. We should list them as specified in the question, and we can highlight the prime numbers:

Because we know that no even numbers other than 2 are prime, we know that further prime numbers cannot be in the second, fourth or sixth column. The third column keeps adding 6s, so it is adding multiples of 3 to multiples of 3, so the numbers will always be divisible by 3, so further numbers in this column cannot be prime. So she is correct that the prime numbers must be in the first or the fifth column.

31 Questions of increasing difficulty

1.) In a cement factory, cement bags are placed on pallets made of planks of wood and bricks. The number of bricks needed to make a pallet is calculated as being one more than the length of the plank in metres (as shown below):

a.) What length of pallet uses five bricks?

b.) If the pallet is 7m long, how many bricks are used in it?

The factory needs pallets with a total length of 15m for the next batch of cement. It has planks of wood that are 4m long and 3m long.

c.) What combinations of planks can they have?

d.) How many bricks would be needed for each combination?

2.) Sonia wants to plant an apple tree in her garden. She needs to make sure that there is a circular area of lawn with diameter 3m around the base of the tree, so that all of the fruit will fall onto the lawn area.

Below is a (not to scale) sketch of Sonia’s garden:

Where could the tree be placed to meet her requirements?

3.) The diagram below represents towns A and B in a mountainous region:

The mountain rescue helicopters from both towns will always be sent to rescue any casualty within a 25km radius of town A or town B. The fire and rescue team from town B will travel to any accident scene closer to town B than town A.

Shade the region that the helicopters and town B’s fire an rescue team will both cover.

4.) A rectangle has length (2x+3) and width (x-1).

a.) Write an expression for the perimeter of the rectangle.

b.) Write an expression for the area of the rectangle.

The area of the rectangle is 250cm 2 .

c.) How long is the longest side?

d.) What is the perimeter of the rectangle?

5.) The probability that Hannah catches the 6.30am train to the city is 0.7.

If she misses the train, she will be late for work.

The probability that the train will be late is 0.15.

If the train is late, she will be late for work.

What is the probability that Hannah will be on time for work on a particular day?

Worked Solutions to Questions

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Free Editable Problem and Solution Graphic Organizer Examples

Problem and solution diagrams are useful tools that can be used in order to describe an issue or problem along with proposed steps for its elimination as well as a final solution at the end. If you are looking to understand more about problem and solution graphic organizers , keep on reading till the end. In this post, we are going to touch up some base concepts about these organizers while explaining some examples along the way.

1. What is a Problem and Solution Graphic Organizer

In summation, a problem and solution graphic organizer is defined as a graphical representation of a problem-solving process. The diagram involves writing the essence of the problem in the beginning, then suggesting steps for resolving it, and finally coming up with a solution. By using these diagrams, it becomes easy for a person or team to organize the relevant information into an easily perusable and understandable form.

The reason why problem and solution diagrams are so important is that they are easy to read and present. Should an organization face a problem or issue, the relevant team or department can come up with a simple and straightforward graphic organizer that depicts the best route forward while enumerating the steps necessary for taking that certain route.

If there is any modification that needs to be made with a certain aspect of the solution, it can be easily done so since every step will be separately and clearly mentioned.

2. The Problem and Solution Graphic Organizer Examples

Problem and solutions graphic organizers are used for depicting the steps needed for reconciliation when a certain problem arises. If two or more parties are involved in the resolution of any issue, it is important for them to be on the same level of understanding. Similarly, if there is a large organization and there are a lot of people who need to take part in solving the problem, it is essential that each one of them knows and understands what the issue is, what the steps are that are needed for the resolution and what the final solution will be. By using a problem and solution graphic organizer , you can delegate that knowledge and teach a large number of people the protocol that needs to be followed when solving a problem. The graphic organizer can be presented at a meeting or it can be individually given to each of the involved personnel.

Here are some examples of problem and solution diagrams:

Example 1: Problem and Solution Graphic Organizer

This graphic organizer depicts a simple problem and solution layout. In this example, the problem is shown at the top of the page and it is divided into three sections viz. ‘Who?’, ‘What?’ and ‘Why?’

The benefit of this segregation is that it not only helps the user to define the problem, but it also enables them to describe who the problem pertains to, what the problem actually is and why the problem surfaced. The simple method would be to mention the problem all in one go but dividing them like this gives greater clarity into the matter.

Then comes the ‘Possible Solutions’ section. This is where all possible solutions to the problem are discussed and brainstorming is done. After that, the selected/most suitable solution is delineated in the last section.

Example 2: Weekly Problem and Solution Graphic Organizer

In this example, the layout is a little different. This organizer depicts a problem-solving sheet for five days of a week viz. from Monday to Friday. Each day has three columns in front of it which are for "Rough Work/Drawing", "Sum/Number Sentence" and "Answer" respectively. Instead of focusing on a problem and giving a solution to it (as was the case in the previous example), this organizer features a set of columns and rows designed for students to help with their weekly problem-solving. This is namely an activity sheet for kids rather than an actual problem-solving diagram that can be officially used etc. This template can be useful to accomplish something similar to what it is made for i.e. learning and teaching, but it is not suitable for using to depict a certain problem and its solution.

Example 3: Problem & Solution Graphic Organizer

The Problem & Solution Graphic Organizer features a simple problem-solving structure. In this diagram, three boxes on the left are made for the problems while three boxes adjacent to them are for their respective solutions. This design does not have the sequence where the problem first appears followed by the steps of resolution and then the solution. Here, three problems are simultaneously listed with their solutions written directly beside them without any ‘Possible Solutions’ section or steps for resolution.

This sort of graphic organizer can be useful in circumstances where a multitude of problems have arisen at the same time and need to be dealt with swiftly. In such an instance, listing possible alternatives or steps can be arduous, and simply writing the solutions can be much easier.

Example 4: Problem Solution Graphic Organizer

This example features an unusual layout that can be used for problem-solving. Instead of listing the problem, the steps/possible solutions, and then lastly the solution, this example first mentions the problem and then three 'Goals' in the form of 'Event # 1, 2, and 3'. In the 'Event' spaces, you can put in the outcomes you require or the situations you need to find yourself in after resolving the problem. Hence, you would be enumerating the goals you need to achieve by solving the problem.

After the ‘Goals’, the ‘Resolution’ section is given. In this section, one could write the actual steps or procedure that needs to be followed to meet the above ‘Goals’. This template can be more suitable for intricate issues rather than simple problems that require a one-line solution.

Example 5: Problem and Solution Graphic Organizer Example

In this example, a very practical and useful approach is used. As we saw before, enumeration of possible solutions is useful for brainstorming and selecting the best one of the lot. This example makes it really easy and simple to compare alternative solutions. It first depicts the problem at the start of the page. Then, three choices are listed underneath the problem. For each choice, a ‘Pros/Cons’ list is given. Finally, in the end, there is a 'Solution' section where you can write the choice you selected and why it is the best one.

By listing the pros and cons of each choice, it can be established which route or plan of action is the most suited and beneficial. The choice which has the most pros and least number of cons can be easily selected.

Example 6: Problem and Solution Graphic Organizer PDF

This graphic organizer is labeled 'Compare and Contrast'. In this example, there are two different sets of problems and solutions. Each set starts off with the 'Text', succeeded by the 'Problem' and then the solution.

In each of the sets, the problem can be described along with the suggested solution. Being two, these problems and solutions can be compared with each other. This sort of graphic organizer can be suitable for specific situations which involve the comparison and matching of more than one problem/solution. This template can also be used to match the alternate solutions to a single problem but the problem part in both sections would have to be identical.

Example 7: Problem and Solution Worksheets

The next example on our list is the Problem and Solution Worksheet. The worksheet is an activity for students and is not exactly a template that can be used freely for any other situation, circumstance, or problem. In this worksheet, there are four sections, each of which contains a certain scenario. In each section, the problem is required and then the solution.

This activity is beneficial for teaching children about problem and solution organizers and the basics of problem-solving. Although the scenario in each section has been explicitly mentioned, it is still required of the students to point out which part is the problem and which part is the solution. This improves their identification skills.

Example 8: Problem and Solution Reading Comprehension Worksheet

This worksheet is also a suitable example to include in this list. The purpose of this worksheet is to tell students to find problems or issues in the story’s character and to list those issues along with their possible solutions.

Albeit with specific instruction, this worksheet also falls in the category of problem and solution graphic organizers. There are three different problems that need to be identified. Three solutions need to be given for each respective problem.

This example has a simple layout unlike some of the more complicated ones we have seen on this list. The worksheet simply requires the students to point out the problem and to suggest a solution. No alternatives are explored, nor are any pros and cons mentioned.

Example 9: Story Elements - Problem and Solution worksheet

This worksheet does not fall in the strict category of graphic organizers. This is a class activity that requires the student to match the problems to suitable solutions. In this example, the problems are given on the left hand and the solutions are given on the right. The solutions and problems are written all jumbled up and are not written adjacent to one another.

This sort of worksheet can be a useful tool in teaching kids the concept behind problem-solving. This example can be a stepping stone using which the students can, later on, realize how they have to present a solution to any problem that they face.

3. Online Problem and Solution Graphic Organizer Maker

Now that we have some idea of what these organizers are, let’s get to the part where we actually make one. If you are looking to make an organizer similar to the examples we saw above, simply head over to EdrawMax Online . At EdrawMax Online, there is a large variety of charts, drawings, and diagrams that you can make. The software is totally online, and it has a user-friendly interface. Shapes can be added from the library by simply dragging them over to the desired spot on the canvas. If you don’t want to make a layout from scratch, you can go to the template gallery and pick a pre-made organizer to edit as your own.

4. Key Takeaways

Problem and Solution Graphic Organizers are great tools that you can use for problem-solving. By mentioning the problem at hand, the steps needed for its resolution, and the selected solution, you can come up with a clear and concise representation of a problem-solving process. EdrawMax Online is your go-to place for making diagrams, drawings, and graphic organizers. The software is cloud-based and offline use available, free, and easy to use and it can convert your file into your desired format. You can find out more graphic organizer examples in the Template Gallery.

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Visual Problem Solving with Mind Maps and Flowcharts

Updated on: 25 July 2023

Everyone has problems, and we spend most of our working lives solving them. For those who find this quite negative, problems can be also termed as Issues, Challenges or Opportunities.

Some people are especially gifted at problem-solving while others struggle. Some are only good at solving some types of problems, while some other are simply great at finding viable solutions for any problem. Society generally calls the latter, smart.

What if I was to tell you that there’s a simple way to solve any problem you may encounter. In fact, it can be regarded as the smart way to solve problems.

Before we get into it, let’s see how people really fail at solving problems.

Problem-Solving   Fails

You Solve the Wrong Problem

Well, if you don’t know what the problem area is and don’t understand it very well, you’ll probably solve a problem that actually doesn’t exist while the actual problem remains as it is.

You Solve It Half Way

Again, this happens if you don’t know what the full problem is. Identifying and understanding the problem is so important before you start.

You Solve it but New Problems Show Up

This is typical when you don’t know much about the background about the problem area. If you know nothing about computers and you try to fix a broken computer, you probably won’t get very far and will likely make it worse.

You Don’t Know How

Well, obviously if you are trying to solve a problem that you have no clue about, this is going to be hard. When that’s the case, get the help of an expert in the domain the problem you are trying to solve belong to.

How to Solve Any Problem

As it’s quite clear the first step to solving any problem is understanding it thoroughly. Apart from getting a domain expert involved, the best trick I can bring you in is to draw it out. If you are a visual person this is the first thing you should do.

Different kinds of problems require different diagrams, but mind maps and flowcharts are common solutions to most problems.

Thinking Around the Problem

To get a background idea on what the problem and problem area is, mind maps can help greatly. Start with the core idea and branch out as you think about various aspects of the problem.

A mind map is a good place to start visual problem solving ( click on image to create your own mind map )

After thinking about wide aspects of the problem, it’s best to document what the immediate context of the issue is.

To do this, a concept map helps. A concept map is a diagram where you use various shapes to show areas of the problem and how they are connected.

Breaking It Down

Any big problem can be broken into a series of smaller problems. These are usually connected so a flowchart helps . Break the problem into smaller steps with a flowchart.

If you are analyzing an existing solution and trying to optimize it, a flowchart makes perfect sense as it also does the ‘defining’ part of the problem as well.

Analyze your problem further with a flowchart

Once you have broken down the problem into smaller easily solvable problems in a flow chart, you can start creating another chart for the solution as well.

Getting Help

You should always get help if it’s available when you are solving any problem. A second opinion or a second pair of eyes can help a lot in getting the optimal solution.

Tools to Aid Visual Problem Solving

While there is a myriad of tools to help you draw things, Creately is definitely one of the easiest ways to visualize your problem.

We support mind maps, flowcharts, concept maps and 50+ other diagram types which you can use for visual problem-solving.

Our professionally designed templates and productivity features  help you just focus on the drawing as it’s really easy to draw a beautiful diagram in it.

It also comes with built-in real-time collaboration so it helps when you want to get someone else to collaborate on your problem.

Other choices for drawing diagrams to solve problems include Dia, Google Draw or even Microsoft office packages.

Join over thousands of organizations that use Creately to brainstorm, plan, analyze, and execute their projects successfully.

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• What Is a Fishbone Diagram? | Templates & Examples

What Is a Fishbone Diagram? | Templates & Examples

Published on January 2, 2023 by Tegan George . Revised on January 29, 2024.

A fishbone diagram is a problem-solving approach that uses a fish-shaped diagram to model possible root causes of problems and troubleshoot possible solutions. It is also called an Ishikawa diagram, after its creator, Kaoru Ishikawa, as well as a herringbone diagram or cause-and-effect diagram.

Fishbone diagrams are often used in root cause analysis , to troubleshoot issues in quality management or product development. They are also used in the fields of nursing and healthcare, or as a brainstorming and mind-mapping technique many students find helpful.

Table of contents

How to make a fishbone diagram, fishbone diagram templates, fishbone diagram examples, advantages and disadvantages of fishbone diagrams, other interesting articles, frequently asked questions about fishbone diagrams.

A fishbone diagram is easy to draw, or you can use a template for an online version.

• Your fishbone diagram starts out with an issue or problem. This is the “head” of the fish, summarized in a few words or a small phrase.
• Next, draw a long arrow, which serves as the fish’s backbone.
• From here, you’ll draw the first “bones” directly from the backbone, in the shape of small diagonal lines going right-to-left. These represent the most likely or overarching causes of your problem.
• Branching off from each of these first bones, create smaller bones containing contributing information and necessary detail.
• When finished, your fishbone diagram should give you a wide-view idea of what the root causes of the issue you’re facing could be, allowing you to rank them or choose which could be most plausible.

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There are no built-in fishbone diagram templates in Microsoft programs, but we’ve made a few free ones for you to use that you can download below. Alternatively, you can make one yourself using the following steps:

• In a fresh document, go to Insert > Shapes
• Draw a long arrow from left to right, and add a text box on the right-hand side. These serve as the backbone and the head of the fish.
• Next, add lines jutting diagonally from the backbone. These serve as the ribs, or the contributing factors to the main problem.
• Next, add horizontal lines jutting from each central line. These serve as the potential causes of the problem.

Lastly, add text boxes to label each function.

You can try your hand at filling one in yourself using the various blank fishbone diagram templates below, in the following formats:

Fishbone diagram template Excel

Download our free Excel template below!

Fishbone diagram template Word

Download our free Word template below!

Fishbone diagram template PowerPoint

Download our free PowerPoint template below!

Fishbone diagrams are used in a variety of settings, both academic and professional. They are particularly popular in healthcare settings, particularly nursing, or in group brainstorm study sessions. In the business world, they are an often-used tool for quality assurance or human resources professionals.

Fishbone diagram example #1: Climate change

Let’s start with an everyday example: what are the main causes of climate change?

Fishbone diagram example #2: Healthcare and nursing

Fishbone diagrams are often used in nursing and healthcare to diagnose patients with unclear symptoms, or to streamline processes or fix ongoing problems. For example: why have surveys shown a decrease in patient satisfaction?

Fishbone diagram example #3: Quality assurance

QA professionals also use fishbone diagrams to troubleshoot usability issues, such as: why is the website down?

Fishbone diagram example #4: HR

Lastly, an HR example: why are employees leaving the company?

Fishbone diagrams come with advantages and disadvantages.

• Great tool for brainstorming and mind-mapping, either individually or in a group project.
• Can help identify causal relationships and clarify relationships between variables .
• Constant iteration of “why” questions really drills down to root problems and elegantly simplifies even complex issues.

Disadvantages

• Can lead to incorrect or inconsistent conclusions if the wrong assumptions are made about root causes or the wrong variables are prioritized.
• Fishbone diagrams are best suited to short phrases or simple ideas—they can get cluttered and confusing easily.
• Best used in the exploratory research phase, since they cannot provide true answers, only suggestions.

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If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

Methodology

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

Fishbone diagrams have a few different names that are used interchangeably, including herringbone diagram, cause-and-effect diagram, and Ishikawa diagram.

These are all ways to refer to the same thing– a problem-solving approach that uses a fish-shaped diagram to model possible root causes of problems and troubleshoot solutions.

Fishbone diagrams (also called herringbone diagrams, cause-and-effect diagrams, and Ishikawa diagrams) are most popular in fields of quality management. They are also commonly used in nursing and healthcare, or as a brainstorming technique for students.

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Nine essential problem solving tools: The ultimate guide to finding a solution

October 26, 2023 by MindManager Blog

Problem solving may unfold differently depending on the industry, or even the department you work in. However, most agree that before you can fix any issue, you need to be clear on what it is, why it’s happening, and what your ideal long-term solution will achieve.

Understanding both the nature and the cause of a problem is the only way to figure out which actions will help you resolve it.

Given that most problem-solving processes are part inspiration and part perspiration, you’ll be more successful if you can reach for a problem solving tool that facilitates collaboration, encourages creative thinking, and makes it easier to implement the fix you devise.

The problem solving tools include three unique categories: problem solving diagrams, problem solving mind maps, and problem solving software solutions.

They include:

• Fishbone diagrams
• Strategy maps
• Mental maps
• Concept maps
• Layered process audit software
• Charting software
• MindManager

In this article, we’ve put together a roundup of versatile problem solving tools and software to help you and your team map out and repair workplace issues as efficiently as possible.

Let’s get started!

Problem solving diagrams

Mapping your way out of a problem is the simplest way to see where you are, and where you need to end up.

Not only do visual problem maps let you plot the most efficient route from Point A (dysfunctional situation) to Point B (flawless process), problem mapping diagrams make it easier to see:

• The root cause of a dilemma.
• The steps, resources, and personnel associated with each possible solution.
• The least time-consuming, most cost-effective options.

A visual problem solving process help to solidify understanding. Furthermore, it’s a great way for you and your team to transform abstract ideas into a practical, reconstructive plan.

Here are three examples of common problem mapping diagrams you can try with your team:

1. Fishbone diagrams

Fishbone diagrams are a common problem solving tool so-named because, once complete, they resemble the skeleton of a fish.

With the possible root causes of an issue (the ribs) branching off from either side of a spine line attached to the head (the problem), dynamic fishbone diagrams let you:

• Lay out a related set of possible reasons for an existing problem
• Investigate each possibility by breaking it out into sub-causes
• See how contributing factors relate to one another

Fishbone diagrams are also known as cause and effect or Ishikawa diagrams.

2. Flowcharts

A flowchart is an easy-to-understand diagram with a variety of applications. But you can use it to outline and examine how the steps of a flawed process connect.

Made up of a few simple symbols linked with arrows indicating workflow direction, flowcharts clearly illustrate what happens at each stage of a process – and how each event impacts other events and decisions.

3. Strategy maps

Frequently used as a strategic planning tool, strategy maps also work well as problem mapping diagrams. Based on a hierarchal system, thoughts and ideas can be arranged on a single page to flesh out a potential resolution.

Once you’ve got a few tactics you feel are worth exploring as possible ways to overcome a challenge, a strategy map will help you establish the best route to your problem-solving goal.

Problem solving mind maps

Problem solving mind maps are especially valuable in visualization. Because they facilitate the brainstorming process that plays a key role in both root cause analysis and the identification of potential solutions, they help make problems more solvable.

Mind maps are diagrams that represent your thinking. Since many people struggle taking or working with hand-written or typed notes, mind maps were designed to let you lay out and structure your thoughts visually so you can play with ideas, concepts, and solutions the same way your brain does.

By starting with a single notion that branches out into greater detail, problem solving mind maps make it easy to:

• Explain unfamiliar problems or processes in less time
• Share and elaborate on novel ideas
• Achieve better group comprehension that can lead to more effective solutions

Mind maps are a valuable problem solving tool because they’re geared toward bringing out the flexible thinking that creative solutions require. Here are three types of problem solving mind maps you can use to facilitate the brainstorming process.

4. Mental maps

A mental map helps you get your thoughts about what might be causing a workplace issue out of your head and onto a shared digital space.

Because mental maps mirror the way our brains take in and analyze new information, using them to describe your theories visually will help you and your team work through and test those thought models.

5. Idea maps

Idea maps let you take advantage of a wide assortment of colors and images to lay down and organize your scattered thought process. Idea maps are ideal brainstorming tools because they allow you to present and explore ideas about the best way to solve a problem collaboratively, and with a shared sense of enthusiasm for outside-the-box thinking.

6. Concept maps

Concept maps are one of the best ways to shape your thoughts around a potential solution because they let you create interlinked, visual representations of intricate concepts.

By laying out your suggested problem-solving process digitally – and using lines to form and define relationship connections – your group will be able to see how each piece of the solution puzzle connects with another.

Problem solving software solutions

Problem solving software is the best way to take advantage of multiple problem solving tools in one platform. While some software programs are geared toward specific industries or processes – like manufacturing or customer relationship management, for example – others, like MindManager , are purpose-built to work across multiple trades, departments, and teams.

Here are three problem-solving software examples.

7. Layered process audit software

Layered process audits (LPAs) help companies oversee production processes and keep an eye on the cost and quality of the goods they create. Dedicated LPA software makes problem solving easier for manufacturers because it helps them see where costly leaks are occurring and allows all levels of management to get involved in repairing those leaks.

8. Charting software

Charting software comes in all shapes and sizes to fit a variety of business sectors. Pareto charts, for example, combine bar charts with line graphs so companies can compare different problems or contributing factors to determine their frequency, cost, and significance. Charting software is often used in marketing, where a variety of bar charts and X-Y axis diagrams make it possible to display and examine competitor profiles, customer segmentation, and sales trends.

9. MindManager

No matter where you work, or what your problem-solving role looks like, MindManager is a problem solving software that will make your team more productive in figuring out why a process, plan, or project isn’t working the way it should.

Once you know why an obstruction, shortfall, or difficulty exists, you can use MindManager’s wide range of brainstorming and problem mapping diagrams to:

• Find the most promising way to correct the situation
• Activate your chosen solution, and
• Conduct regular checks to make sure your repair work is sustainable

MindManager is the ultimate problem solving software.

Not only is it versatile enough to use as your go-to system for puzzling out all types of workplace problems, MindManager’s built-in forecasting tools, timeline charts, and warning indicators let you plan, implement, and monitor your solutions.

By allowing your group to work together more effectively to break down problems, uncover solutions, and rebuild processes and workflows, MindManager’s versatile collection of problem solving tools will help make everyone on your team a more efficient problem solver.

Download a free trial today to get started!

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MindManager® helps individuals, teams, and enterprises bring greater clarity and structure to plans, projects, and processes. It provides visual productivity tools and mind mapping software to help take you and your organization to where you want to be.

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35 problem-solving techniques and methods for solving complex problems

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

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

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

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

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

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

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

Problem-solving warm-up activities

Closing activities for a problem-solving process.

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

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

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

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

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

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

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

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

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

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

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

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

Tips for more effective problem solving

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

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

Clearly define the problem

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

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

Don’t jump to conclusions

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

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

Try different approaches  

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

Don’t take it personally 

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

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

Get the right people in the room

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

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

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

Document everything

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

Bring a facilitator 

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

Develop your problem-solving skills

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

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

Design a great agenda

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

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

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

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

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

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

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

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

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

2. Lightning Decision Jam

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

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

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

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

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

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

3. Problem Definition Process

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

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

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

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

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

4. The 5 Whys 

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

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

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

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

5. World Cafe

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

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

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

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

6. Discovery & Action Dialogue (DAD)

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

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

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

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

7. Design Sprint 2.0

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

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

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

8. Open space technology

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

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

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

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

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

Techniques to identify and analyze problems

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

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

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

Let’s take a look!

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

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

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

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

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

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

10. The Creativity Dice

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

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

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

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

11. Fishbone Analysis

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

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

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

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

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

12. Problem Tree 

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

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

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

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

13. SWOT Analysis

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

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

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

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

14. Agreement-Certainty Matrix

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

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

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

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

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

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

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

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

16. Speed Boat

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

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

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

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

17. The Journalistic Six

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

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

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

18. LEGO Challenge

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

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

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

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

19. What, So What, Now What?

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

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

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

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

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

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

20. Journalists  

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

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

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

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

Problem-solving techniques for developing solutions 

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

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

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

21. Mindspin  

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

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

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

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

22. Improved Solutions

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

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

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

23. Four Step Sketch

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

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

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

24. 15% Solutions

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

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

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

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

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

25. How-Now-Wow Matrix

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

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

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

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

26. Impact and Effort Matrix

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

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

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

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

27. Dotmocracy

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

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

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

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

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

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

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

28. Check-in / Check-out

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

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

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

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

29. Doodling Together  

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

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

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

30. Show and Tell

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

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

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

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

31. Constellations

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

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

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

32. Draw a Tree

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

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

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

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

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

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

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

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

How do I conclude a problem-solving process?

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

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

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

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

33. One Breath Feedback

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

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

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

34. Who What When Matrix 

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

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

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

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

35. Response cards

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

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

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

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

Save time and effort discovering the right solutions

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

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

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

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

Over to you

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

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

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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Affinity diagrams: Your key to more creative problem-solving

Reading time: about 5 min

Already know that you want to use an affinity diagram? Get started with our free template!

What is an affinity diagram?

Created in the 1960s by Japanese anthropologist Jiro Kawakita, affinity diagrams can also be referred to as affinity charts, affinity maps, or the KJ method. Affinity diagrams are ideal for sorting large amounts of data or long lists of ideas into related groups. You can use affinity diagrams to:

• Organize the results of a brainstorming session.
• Improve processes.
• Mediate professional conflict.
• Develop innovative solutions.
• Drive group consensus.

The theory of affinity diagrams is to harness natural creativity by facilitating an environment where everyone has a voice, conflict is minimized, and gut reactions are favored over analysis. Read on to discover how this happens.

How to create an affinity diagram

Affinity mapping is simple. Most people use sticky notes, markers, and a big blank wall, but all you really need is Lucidspark. Here’s how it works.

1. Open a new Lucidspark board and title it with your challenge.

The challenge should be written in the form of a question. For example, “How can we improve time management at the office?” Share your document with all participants and grant them editing access.

2. Have participants record their ideas on virtual sticky notes underneath the title question.

Multiple participants can edit the document in real time without overriding another participant’s changes. No ideas should be thrown out, and participants should not be limited to a certain number of ideas. This allows everyone to contribute openly without fear of being shut down. Also, because you are using Lucidspark, you don’t have to worry about running out of sticky notes.

3. Without speaking to each other, everyone moves the sticky notes so that similar items are grouped together.

This should be done in silence so that participants don’t bias each other and smother natural instincts. If one idea doesn’t fit with any of the others, it’s okay to leave it as a stand-alone. Also, if a participant doesn’t agree with the placement of an idea, they should feel free to move it. If an idea keeps being moved back and forth between multiple groupings, create multiple sticky notes with the same idea and put one in each of the contested groupings. This minimizes conflict. You should allow plenty of time for the process to occur. Several days may be ideal.

4. When everyone is finished grouping the sticky notes, gather all of the participants, and together, choose a label for each grouping that has emerged.

You can use one idea from the grouping that best represents all of the other ideas or choose a new title. If several groups seem related to each other, you may want to create a superheader that combines the groups.

You now have a completed affinity diagram that will help you to analyze your data, draw conclusions, and determine next steps.

Affinity diagramming in Lucidspark rather than with sticky notes makes it possible for anyone to participate, even those who are separated by distance. Participants can add ideas or create groupings at any convenient time, whether they are at home or the office. Additionally, Lucidcspark increases the level of anonymity in this process because co-workers aren’t watching as a participant goes to a physical wall and adds or moves a sticky note so contributions, can be made more openly.

A specific affinity diagram example

Let’s practice with an affinity mapping example. Say your content writing team is not producing as much content as you think they should be. You can use an affinity diagram to uncover any problems and come up with solutions to resolve them.

To start, you create a Lucidspark document with the title “What are the glitches in our content creation process?” After sharing the document with all of the relevant stakeholders, you give them time to record ideas at their leisure. The result looks something like this:

Now you ask everyone to organize their ideas into groups that are similar. Some of the sticky notes get moved back and forth, but after a few days, these are the results:

You schedule a meeting that all of the stakeholders attend, and you give titles to each of the groupings with more than one idea.

At this meeting, you also discuss ways to overcome these glitches. Because they are grouped into categories, it is easier to think about and determine root causes. Instead of solving 16 problems, you only need to solve five.

Affinity diagramming tips

Here are a few things to keep in mind as you make your first affinity diagram:

• Affinity diagramming works best when you limit your participants to smaller groups.
• The process of ideation and grouping should be silent. Don’t talk about it, or you'll inadvertently limit contributions for fear or rejection or judgment.
• If you have fewer than 15 data points, affinity diagramming may not be necessary.
• Don’t overthink groupings. Go with your first instinct.

Affinity diagram template

Because affinity diagramming is an organic process, you don’t want to restrict your team to a specific template. However, we have pre-populated this document with a title box and a few colorful sticky notes to get you started.

Click the image below to open this customizable template in Lucidspark.

Build your own affinity diagram in Lucidspark.

About Lucidspark

Lucidspark, a cloud-based virtual whiteboard, is a core component of Lucid Software's Visual Collaboration Suite. This cutting-edge digital canvas brings teams together to brainstorm, collaborate, and consolidate collective thinking into actionable next steps—all in real time. Lucid is proud to serve top businesses around the world, including customers such as Google, GE, and NBC Universal, and 99% of the Fortune 500. Lucid partners with industry leaders, including Google, Atlassian, and Microsoft. Since its founding, Lucid has received numerous awards for its products, business, and workplace culture. For more information, visit lucidspark.com.

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or continue with

Ishikawa Diagram

Ishikawa diagram is a great tool to help you solve problems by identifying their root causes. Sometimes called also cause-and-effect or fishbone diagram, it was created by Japanese professor Kaoru Ishikawa. It's especially effective for tackling complex problems.

How to use it

Building out this diagram consists of few simple steps. This can be done in a group as a workshop but also just as well on your own.

1) Define the problem

Start with defining the problem and then drawing a line to the left or right of it (that's up to your preference).

The line will be for adding factors in the next step.

2) Identify contributing factors or categories

List out the factors/categories that could be contributing to the problem you're solving. Plot them along the main line.

You can come up with your own factors or you might use generic categories: People, Equipments, Methods, Measurement, Material and Environment.

Categorising is very helpful for breaking down complex problems and looking at them from different perspectives.

3) Find possible root causes related to each factor

Ask "Why is this happening?" Write down each idea as a line under the factor it relates to. First principles thinking is useful here including the "Five whys" method.

Keep in mind that the problem might not have just one root cause but multiple. So it's important to capture everything that might explain the problem, even if just partially.

At this point, you should have a complete diagram but no definitive answer yet.

4) Analyse the diagram

The most important step is looking at all the possible root causes and analysing them. The diagram now provides a structure for your most important thinking and next steps.

There are many possibilities what you can do at this point. Perhaps you can gather more data/evidence for each root cause candidate or immediately identify the most likely one and quickly try to solve it. This will depend on your specific problems and identified possible causes. 

Now let's see how to apply this on a practical example.

Suppose you're a product manager and have to solve a trend of getting less and less new sign-ups. You start with this definition and then identify contributing factors.

In this example, you identified landing page issues, competition and marketing as factors.

Now let's find specific possible root causes under each factor:

With all of these written down, you can begin to analyse where the problem originates. In this example, you might first verify if the conversion rate is steady despite lower traffic. Then you might audit your sign-up flow to find any leaks and possibly streamline it.

This is a simplified example but this diagram can be definitely used for much more complex problems.

Ishikawa diagram offers a simple framework for finding root causes of problems:

• Define the problem
• Identify contributing factors or categories
• Find possible root causes related to each factor
• Analyse the diagram

You'll create the diagram with the first three steps. It will then provide a structure for your analysis.

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More problem solving tools

Iceberg Model

Uncover root causes of events by looking at hidden levels of abstractions.

Issue trees

Structure and solve problems in a systematic way.

How to Use Fishbone Diagram for Problem Solving

Fishbone diagram is a problem-solving tool, used in literal terms like a fishbone. It is also known as a cause and effect diagram. The mechanism is to specifically identify the cause and effect of any business or project problem.

A fishbone diagram can help define potential reasons for an issue. This article will dive into understanding the core principles of the fishbone diagram problem solving as a tool.

In 1943 at Tokyo University, Kaoru Ishikawa created the "Fishbone Diagram." Fishbone diagrams can also be called diagrams of "cause and effect." The fishbone diagram problem solving tool is a perfect tool to dig through an issue when we try to assess the root cause and find a solution effectively.

It offers a mechanism for explicitly identifying the "effect" and then brings you to think about the potential triggers, based on typical manufacturing problems. The fishbone diagram problem solving is a basic model that makes it easy to grasp swift and efficient root causes to implement corrective behavior.

It reflects the question or impact at the fish's head or mouth. Possible contributing factors under separate causal groups are identified on the smaller "bones." A fishbone diagram can help define potential reasons for an issue that would otherwise not be discussed by encouraging the team to look through the definitions and discuss alternate reasons.

Source: EdrawMind

1.1 Why Use Fishbone Diagram for Problem Solving

The fishbone diagram makes you consider more when solving specific problems. During a brainstorming activity, various groups inspire thoughts from different areas.

The fishbone diagram brings order to the process of cause and effect . It's easy for participants to understand the main problems or issues and focus on the question across different potential triggers.

The fishbone diagram helps distinguish the causes and reasons for a problem and lets people intuitively figure out the solutions.

1.2 The Usage of Fishbone Diagram

The fishbone diagram problem solving method can be used when trying to fix problems or discover the root cause of an issue or problem, which helps you to see below the surface, and dive deeper into the real problem.

Here are several typical fishbone diagram problem solving applications:

• Manufacturing: ,nbsp;Uncover the root cause of a manufacturing problem by brainstorming and rating the likelihood and effect of all factors affecting the manufacturing cycle;
• Marketing or Product Marketing: ,nbsp;Identify the possible factors that may impede your company's popularity in the marketplace by investigating all the places that affect your product acceptance;
• Service: ,nbsp;Uncover the root cause of a business issue by brainstorming, and rate the probability and effect of all factors impacting the service delivery process.

There are 7 steps lead you to use fishbone diagram for problem solving:

• Explain the agenda behind the diagram

Let your team members know that the diagram can help you see different fields or possible areas that might lead to a solution to your current business problem.

• Draw diagrams

Draw the pattern or shape on your whiteboard, or use a software diagramming tool to ease accessibility. If you need remote attendants to do this exercise, you can quickly build it in EdrawMind and display your computer.

• Determine a simple statement on an issue

Write down statements at the top of your page or above where you will build the diagram., which means everyone has the same idea of the issue you are concerned with.

• Select what categories to use

Categories are discussed in more detail below. For example, you can add Policies, Methods, Personnel, and Software categories.

• Identify potential causes within each category of your problem

Team members may trigger brainstorming or contribute factors that fall into this category. You can either go by category or only come up with ideas and determine which type they fit.

• Go a step deeper to define sub-causes for any cause in the category

If you decide whether something can or will break down to smaller points, build divisions from the critical point.

Team members study the diagram to determine the most relevant focus points. If you are trying to take this a step forward and fix the root cause, it helps define where you're trying to benefit your initiative. You can't solve all the root factors at once, and some can get more significant payoff than others. Check the diagram for an evaluation of where the concentration of the team is best.

• Record results

You bring the work in. Capture, and log your work. You will need to return to it later, so you don't want to miss the importance of the exercise that you got.

There are several tips that should be considered when using the fishbone diagram for solving problems:

• Using the fishbone diagram tool to keep the team focused not on signs, but the problem's causes;
• Make sure you leave ample room in the diagram between the main groups to add minor specific pointers later;
• Try making team members write every cause on sticky notes while you're brainstorming causes, moving around the community asking each person about a particular reason. Continue to go through the loops, have more pointers before all suggestions have been eliminated;
• Encourage each person to join in the brainstorming exercise and voice their own opinions;
• Remember that the strategy of "five-whys" is often used in combination with the fishbone diagram.

While it takes time to create a fishbone diagram , it will help you and your team define the real causes and encourage you to strengthen the process and make permanent improvements.

Regardless, whether you are using the graphical or indented fishbone hierarchy, this process optimization method will significantly help you understand the factors involved in a process. The root causes of the event are the underlying process and system issues, which allowed the contribution. Hence fishbone diagram , the problem-solving tool, is extremely crucial when discussing strategies to deal with problems.

EdrawMind is an easy-to-use, flexible mind mapping tool designed to help you generate modern, fresh visuals and mind maps. By combining the bullet points into a mind map on a project, EdrawMind lets you organize the thoughts or concepts and create essential strategies.

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• How to Use Ishikawa Diagrams to Solve Business Problems
• Learn Lean Sigma
• Root Cause Analysis

Do you want to solve business problems in an efficient manner? If this is the case, you should think about using Ishikawa Diagrams. Ishikawa Diagrams, also known as fishbone diagrams or cause-and-effect diagrams, are a visual tool that can help identify the root causes of a problem. As a result, they are an ideal solution for businesses looking to improve their processes and reduce errors.

We’ll look at how Ishikawa Diagrams can be used to solve business problems in this post. We’ll look at the anatomy of an Ishikawa Diagram and show you how to make one step by step. We’ll also look at real-world examples of business problems solved with Ishikawa Diagrams and the benefits gained by doing so. Finally, we’ll go over best practises for using Ishikawa Diagrams and how to avoid common pitfalls.

Whether you’re new to Ishikawa Diagrams or want to improve your problem-solving skills, this post will walk you through how to use this powerful tool to solve business problems.

Table of Contents

What is an ishikawa diagram.

Because of its appearance, the Ishikawa Diagram is also known as the fishbone diagram after its creator, Kaoru Ishikawa. The diagram is organised with a central spine and several branches that resemble fish bones. Each branch represents a possible cause category that contributes to the problem under consideration.

Because it is a versatile and widely used tool in problem solving and process improvement, an Ishikawa diagram is known by many different names. Here are some brief explanations for the various names:

Fishbone diagram: This name comes from the visual appearance of the diagram, which looks like a fish skeleton with the problem or effect at the head and the causes branching out like the bones of the fish.

Cause-and-effect diagram: This name reflects the diagram’s purpose, which is to aid in the identification of the root causes of a problem by mapping out the various factors that contribute to it. The diagram depicts the relationships between the causes and the effects, making it easier to determine where to focus improvement efforts.

Herringbone diagram: This is another name for the diagram’s appearance. The diagram’s branches resemble the bones of a herring, a type of fish.

While the names may be used interchangeably, they all refer to the same basic problem-solving and process-improvement tool.

An Ishikawa Diagram has six main branches, which are as follows:

• Personnel – This branch includes all human-related factors that may have an impact on the problem under consideration, such as training, communication, and teamwork.
• Process – This branch includes all of the steps and procedures involved in the process or activity, as well as the equipment, materials, and workflow.
• Machines – This branch includes all the physical equipment and machinery used in the process, including tools, machines, and technology.
• Materials – The raw materials and other inputs used in the process, such as supplies, ingredients, and components, are the focus of this branch.
• Environment – This branch includes all environmental factors that may affect the process, such as temperature, humidity, lighting, and noise.
• Measurement – This branch includes all metrics and measurements used to evaluate the process, such as quality standards, performance indicators, and statistical analysis.

Each of these branches is used to identify potential causes that may be contributing to the problem under investigation. For example, if a decrease in product quality is the issue, the Ishikawa Diagram can be used to identify the various factors that could be causing this problem, such as a lack of employee training, faulty equipment, or low-quality materials. The branches are used to identify as many potential causes as possible, which can then be further evaluated to determine the underlying cause of the problem.

The Ishikawa Diagram assists teams in gaining a better understanding of the problem being analysed and developing targeted solutions to address the root cause by identifying potential causes and organising them in a clear and concise manner.

How to Create an Ishikawa Diagram

Creating an Ishikawa Diagram is a simple process that begins with identifying the problem and breaking it down into its component parts. Here’s a step-by-step tutorial for making an Ishikawa Diagram:

• Step 1: Identify the problem and write it in a box at the top of the diagram.
• Step 2: To represent the main spine of the fishbone diagram, draw a horizontal arrow pointing to the problem box.
• Step 3: Draw a diagonal arrow for each of the diagram’s six main branches (People, Process, Equipment, Materials, Environment, and Measurement). Label each arrow with the name of the corresponding branch.
• Step 4: Determine the possible causes of the problem and document them on the appropriate branch. Create as many causes as you can and add them to the diagram.
• Step 5: If necessary, divide each cause into smaller sub-causes. Include these sub-causes in your diagram as well.
• Step 6: Determine the root cause of the problem by evaluating potential causes and sub-causes. The root cause is the underlying issue that is causing the problem being investigated.
• Step 7: Create and implement solutions to the root cause.

In addition to drawing an Ishikawa Diagram by hand, several software tools are available to help you create and collaborate on these diagrams. Among the most popular software tools are:

SmartDraw : This programme provides a variety of templates and tools for creating professional-looking Ishikawa Diagrams.

Lucidchart : This cloud-based software enables teams to work together in real-time to create Ishikawa Diagrams.

Creately : For creating Ishikawa Diagrams, this tool provides a variety of templates and customization options.

Creating Ishikawa Diagrams with software tools can save time and streamline the process of collaborating with team members. These tools also make it simple to share and export the diagram in a variety of formats, making it easier to include in presentations and reports.

Using Ishikawa Diagrams in Problem-Solving

Ishikawa Diagrams are a powerful problem-solving tool that can be used in root cause analysis. Teams can analyse the causes and develop solutions to address the root cause by identifying the various factors that contribute to a problem.

The process of determining the underlying cause of a problem rather than just addressing its symptoms is known as root cause analysis. This approach assists teams in developing more effective and long-term problem solutions.

To use an Ishikawa Diagram in root cause analysis, teams must first identify the problem and draw a fishbone diagram. The diagram’s six main branches (Personnel, Process, Machine, Materials, Environment, and Measurement) are used to identify potential problem causes. Teams can analyse the root cause by brainstorming and organizing these causes on the diagram.

Teams can use the “five whys” technique in addition to an Ishikawa Diagram to identify the root cause of a problem. The five whys technique is a method of drilling down into the root cause of a problem by asking “why” five times. The goal is for the team to keep asking “why” until they find the underlying root cause of the problem.

For example, if the issue is a product delivery delay, the five whys technique could be used as follows:

• Why was the product delivery delayed? – Because the shipment was sent to the wrong address.
• Why was it sent to the wrong address? – Because the shipping label was incorrect.
• Why was the label incorrect? – Because the person who prepared it didn’t check the address.
• Why didn’t they check the address? – Because they were in a rush to finish the task.
• Why were they in a rush? – Because they were given too many tasks to complete in a short amount of time.

In this example, the root cause of the product delivery delay is that the worker was assigned too many tasks to complete in a short period of time. By identifying the root cause, the team can develop solutions to the problem, such as allocating more time for tasks or more effectively delegating responsibilities.

To Summarize here is an overview of how Ishikawa Diagrams are used in root cause analysis follows:

Step 1: Brainstorm potential causes for each branch and write them on the diagram’s appropriate branch.

Step 2: Examine each possible cause to see if it is the root cause or a symptom of the problem.

Step 3: Use 5 Whys Analysis to ask “why” five times for each potential root cause identified to determine the underlying cause of the problem. Check out our 5 Whys Analysis Template to support this

Step 4: Once the root cause has been identified, develop and implement solutions to address it.

Here is an example of how a complete Ishikawa Diagram may look with potential problems identified on it.

To summarise, Ishikawa Diagrams are an effective problem-solving tool that can be combined with the five whys technique to identify the root cause of a problem. Teams can develop more effective and long-term solutions to improve their processes and operations by analysing potential causes and asking “why” to drill down into the underlying issue.

Examples of Business Problems Solved with Ishikawa Diagrams

Ishikawa Diagrams, also known as fishbone diagrams, have been used to solve a wide range of business problems. Here are some real-world examples of business problems solved with Ishikawa Diagrams:

Quality control issues in a manufacturing plant

A manufacturing plant was experiencing quality control issues with their products. The problem was identified using an Ishikawa Diagram, which helped the team to identify the potential causes of the problem. The diagram revealed that the issues were caused by a lack of training among the employees, poor machine maintenance, and inadequate raw materials. By addressing these issues, the plant was able to improve the quality of its products and reduce waste.

A call centre has a high employee turnover rate.

A call center’s ability to provide quality customer service was being hampered by high employee turnover. An Ishikawa Diagram was used to identify the problem, which assisted the team in determining the potential causes of the high turnover rate. According to the diagram, the problems were caused by low employee morale, insufficient training, and a lack of career development opportunities. The call centre was able to improve employee satisfaction and retention rates by addressing these issues.

Inventory management in a retail store is inefficient.

A retail store’s inventory management process was inefficient, resulting in excess inventory and stockouts. An Ishikawa Diagram was used to identify the problem, which assisted the team in determining the potential causes of the inefficiencies. According to the diagram, the problems were caused by inaccurate demand forecasting, insufficient inventory tracking, and poor communication among the store’s departments. The store was able to improve its inventory management process, reduce excess inventory, and prevent stockouts by addressing these issues.

The Ishikawa Diagram was used as a problem-solving tool in each of these examples to identify potential causes of the problem. The diagram enabled the teams to brainstorm and organise the various factors that could be contributing to the problem, allowing them to drill down to the root cause. The teams were able to implement more effective and long-term solutions to improve their processes and operations by addressing the root cause.

The advantages of using Ishikawa Diagrams in these scenarios include improved quality control, reduced waste, increased employee retention and satisfaction, and increased inventory management efficiency. The diagram enabled the teams to take a structured approach to problem-solving, allowing them to identify the root cause of the problem and develop more effective solutions.

Best Practice for Ishikawa Diagrams

Ishikawa Diagrams are a powerful problem-solving tool, but they must be used correctly to produce the desired results. Some best practises for using Ishikawa Diagrams in problem-solving processes are as follows:

• Clearly define the problem: Before you create an Ishikawa Diagram, you must first define the problem you are attempting to solve. This will aid your concentration and ensure that your diagram is relevant and effective.
• Involve a diverse team: Ishikawa Diagrams work best when used in a group setting. To ensure a well-rounded perspective, try to include a diverse group of people from various departments or areas of expertise.
• Brainstorm potential causes: Encourage team members to brainstorm all potential causes of the problem when creating the diagram. This will assist you in identifying all potential root causes and ensuring that your solutions are all-inclusive.
• Use clear and concise language: When labelling the branches of the diagram, use clear and concise language to ensure that everyone understands the meaning. Avoid using jargon or abbreviations that may be confusing to some team members.
• Prioritize potential causes: After identifying all potential causes, prioritise them based on their likelihood of contributing to the problem. This will allow you to concentrate your efforts on the most pressing root causes.
• Verify the root cause: Before implementing any solutions, test your hypothesis to determine the root cause of the problem. This will help you ensure that you are treating the underlying cause of the problem rather than just the symptoms.

Avoiding Common Mistakes When Using Ishikawa Diagrams

While Ishikawa Diagrams can be a useful problem-solving tool, there are some common errors that teams can make when creating and using them. Here are some errors to avoid:

• Jumping to conclusions: It is critical to avoid jumping to conclusions before identifying and evaluating all potential causes. Rushing to solutions without fully comprehending the underlying cause of the problem can result in ineffective and costly solutions.
• Excessive diagram complexity: Keep the diagram simple and focused on the problem at hand. Overcomplicating the diagram with too many branches or irrelevant information can make determining the true root cause of the problem difficult.
• Ignoring other sources of information: While Ishikawa Diagrams are a powerful tool, they should not be used as the sole source of information in problem-solving processes. Other data sources to consider include customer feedback, process data, and employee input.

Teams can effectively use Ishikawa Diagrams to identify and address the root causes of business problems by adhering to these best practises and avoiding common pitfalls.

Finally, Ishikawa Diagrams are a useful tool for solving business problems and determining the root causes of problems. Teams can effectively use Ishikawa Diagrams to find comprehensive solutions by following best practices such as clearly defining the problem, involving a diverse team, brainstorming potential causes, and prioritising root causes.

It’s critical to remember that Ishikawa diagrams should be used in conjunction with other sources of information to ensure a well-rounded approach to problem-solving. Teams can effectively leverage the power of Ishikawa diagrams in their problem-solving processes by avoiding common mistakes such as overcomplicating the diagram and jumping to conclusions.

Finally, using Ishikawa Diagrams to solve business problems can result in better processes, higher customer satisfaction, and a more efficient organisation. Teams can achieve greater success and propel their businesses forward by mastering this powerful tool.

• Ilie, G. and Ciocoiu, C.N., 2010. Application of fishbone diagram to determine the risk of an event with multiple causes .  Management research and practice ,  2 (1), pp.1-20.
• Radziwill, N., 2017. Creating ishikawa (fishbone) diagrams with R.   Software Quality Professional ,  20 (1), pp.47-48.

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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Problem Solving Stages Diagram

The  Problem Solving Stages Diagram is a concept diagram design. The template shows a linear process flow diagram containing up to ten individual process cycles. Although there are various problem-solving techniques depending on the complexity of issue or corporate structure. Because some problems are small and can be resolved quickly while others are complex and need more research. This diagram provides basic decision-making approach for solving a problem in hand. This diagram by default shows four main components of any problem-solving model , however you can easily add up to ten components with our diagram designer . These default components include Understanding, Brainstorming, Strategy, and Solution. This diagram could be used for personal, professional, and organizational difficulties. For example, threats, challenges, product quality, and risk management.

This diagram template is a useful tools for demonstrating problem-solving techniques and strategies as a learning experience. Further, it is suitable for organizations to outline their systematic approach to identify complications. And provide a visual roadmap to tackle them. The diagram of problem-solving model illustrates an intensive thought process. The users can copy this diagram template to another set of presentation and create waves in discussion.

Problem-solving – Flowchart example

The flowchart starts with identifying a problem. After the problem is identified, data is gathered and analyzed. Then, the solution is developed and the best solution is identified. If it isn’t successful, the solution development process starts again. If successful, the plan is implemented and is improved continuously.

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A flowchart, or flow chart, is a type of diagram that shows a step-by-step view of a process. Flowcharts document the tasks and decisions needed to achieve a specific goal. A basic flowchart is easy to make and understand. Businesses, engineers and software designers often use flowcharts to diagram their ideas.

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ORIGINAL RESEARCH article

Problem-appropriate diagram instruction for improving mathematical word problem solving.

• 1 Graduate School of Education, Kyoto University, Kyoto, Japan
• 2 Department of System Neuroscience, National Institute for Physiological Sciences, Okazaki, Japan
• 3 LaRAC, Univ. Grenoble Alpes, Grenoble, France

The use of diagrams can be effective in solving mathematical word problems solving. However, students worldwide do not construct diagrams unprompted or have trouble using them. In the present study, the effects of problem-appropriate diagram use instruction were investigated with an adaptation of the multiple baseline design method. The instruction for using line diagrams, tables, and graphs was provided to 67 junior high school students in a staggered manner and the effects on problem solving of three different types of problems was examined. The results showed that use of problem-appropriate diagrams increased and persisted over time. More importantly, the instruction led to increases in problem solving performance and to decreases in perceived cognitive load. These findings support the argument that effective diagram use depends on the acquisition not only of declarative knowledge, but also sufficient procedural and conditional knowledge.

Introduction

In mathematics education, teachers draw on mathematical word problem solving to facilitate application of acquired knowledge and skills to real and hypothetical problems and situations ( Schoenfeld, 1985 ; Reed, 1999 ). Students, however, experience difficulties in solving word problems ( Mayer et al., 1992 ; Reed, 1999 ; Jitendra et al., 2007 ; Boonen et al., 2014 ) since it requires more than simple retention and recall of facts and procedural steps. An effective heuristic to alleviate these difficulties is the use of diagrams ( Hembree, 1992 ; Stylianou and Silver, 2004 ; Jitendra et al., 2007 ; Boonen et al., 2014 ). Diagrams facilitate self-explaining which in turn leads to deeper understanding ( Ainsworth and Th Loizou, 2003 ), promote the construction of mental models for drawing inferences, and provide guidance towards appropriate learning behaviour ( Butcher, 2006 ; van der Meij et al., 2017 ). More specifically in mathematics, diagrams enable the construction of accurate solutions by enhancing information and knowledge access ( Chu et al., 2017 ; Cooper et al., 2018 ). However, although these studies contribute to understanding the role of diagrams in learning, they provide only limited insights about constructing effective diagrams for oneself. In many situations, students need to construct their own diagrams for solving word problems in classroom exercises, homework, or tests. Previous research shows several obstacles when students are required to construct their own diagram, instead of just inspect and manipulate a given diagram. Indeed, students may omit constructing a diagram, fail to construct an appropriate diagram, or still draw incorrect inferences from their diagram ( Hegarty and Kozhevnikov, 1999 ; Uesaka and Manalo, 2006 ; Corter and Zahner, 2007 ; Uesaka et al., 2007 ; van Garderen et al., 2012 ). In the current study, we set out to study instruction as a way of improving students’ construction of appropriate diagrams in mathematical word problem solving.

The representational effect or the appropriateness of a diagram for a specific problem

Diagrams enhance understanding of a problem through the representation of its elements and their interrelations ( Hembree, 1992 ). In other words, they facilitate the construction of a schema or mental model of the problem text ( Zahner and Corter, 2010 ). Solving a mathematical word problem involves two steps: generation of a problem representation from the text and implementation or computation of the solution ( Kintsch and Greeno, 1985 ; Lewis and Mayer, 1987 ; Hegarty et al., 1995 ; Duval, 2006 ). The first step can be assimilated to a translation from one type of representation to another ( Ainsworth, 2006 ), also termed conversion from one semiotic register to another ( Duval, 2006 ). In Duval’s terminology, natural language, equations, and Cartesian graphs constitute different semiotic registers for representing abstract mathematical objects not directly available to the senses. For example, a problem stated in natural language can be converted into a line graph, but neither text nor graph can be equated with the mathematical object (e.g., a linear function) underlying the problem. Research shows the importance of this first step: when students construct an accurate visual-schematic representation of a problem situation, they are more likely to produce the correct answer ( Hegarty and Kozhevnikov, 1999 ; Boonen et al., 2014 ).

Diagrams may also facilitate the second step of implementing the solution to the problem. Different isomorphic representations of the same abstract structure or mathematical object differ in their potential for solving a problem, termed “the representational effect” ( Zhang and Norman, 1994 ; Zhang, 1997 ). Any problem can have multiple alternative forms of external representations ( Schnotz and Kürschner, 2008 ). Thus, different types of diagrams attract attention to different features and may give “representational guidance” ( Suthers, 2003 ). For example, tables attract attention to empty cells and may reveal patterns in a series of quantities in a problem. In mathematics, Duval spoke of “operational significance” ( Duval, 2006 ): a representation in a particular semiotic register is meaningful because of the operations that it affords. For example, tables and graphs do not give a visual-schematic representation of the problem situation, but instead provide a schema for how the problem can be solved ( Novick and Hurley, 2001 ; Zahner and Corter, 2010 ; Uesaka and Manalo, 2012 ). In effect, they facilitate what Duval (2006) described as transformations within the same semiotic register. For example, graphs allow visual inspection, which helps in identifying points of intersection of two or more trajectories.

There are a number of studies that have experimentally demonstrated the importance of matching problem requirements with representational affordances of diagrams. Hurley and Novick (2010) , for example, asked participants to solve problems using diagrams that did or did not match the problem requirements. Predictably, they found poorer performance (i.e., longer time to solve, inaccurate inferences) in mismatched cases. It is clear therefore that in solving mathematical word problems, not just any diagram will be efficient: the kind of diagram selected and constructed must match the requirements of the problem at hand. We will call this problem-appropriateness of a diagram. Ideally, students need to acquire the whole repertoire of diagrams because problem solving in mathematics requires “representational flexibility” ( Nistal et al., 2009 ) or “meta-representational competence” ( diSessa, 2004 ; Verschaffel et al., 2020 ). In order to achieve meta-representational competence, students first need to acquire knowledge of the different types of representations. Grawemeyer and Cox (2008) demonstrated that such knowledge is crucial when solving “representationally specific tasks” (those that can only be carried out effectively with the use of a very limited range of representations).

Three kinds of representational knowledge are a prerequisite for effective diagram construction and use: declarative (knowing that), procedural (knowing how), and conditional (knowing when; cf. Paris et al., 1983 ; Garner, 1990 ). In sum, students need to know that certain kinds of diagrams are helpful for solving certain kinds of problems (declarative knowledge). They need to know how to correctly construct the appropriate diagram based on relevant information in the problem description (procedural knowledge). Finally, they need to know when to use a diagram as well as when to use a specific kind of diagram (conditional knowledge). The question arises whether instruction about representational knowledge of different types of diagrams would increase unprompted diagram use per se , and problem-appropriate diagram use in particular. In investigating different types of diagram instruction, the current study addresses this question and thus goes one step further than previous studies on the interplay between different types of diagrams and different types of problems.

Cognitive load associated with constructing diagrams

One reason for the observed difficulties in constructing diagrams may lie in insufficient cognitive resources. From the perspective of cognitive load theory, problem solving tasks can only be successfully undertaken if the required or resulting cognitive load does not exceed the capacity of working memory ( Sweller, 1994 ; Sweller et al., 1998 ). The effort for visually representing concrete details explicitly described in a word problem is low (e.g., illustrating details). In contrast, the construction of an abstract diagram that does not visually resemble the represented entities, such as a table or a graph, requires more transformational steps. Thus, such a construction is more difficult and demands higher amounts of cognitive effort ( Uesaka and Manalo, 2012 ). Problem-appropriate diagram instruction may reduce cognitive load through schema construction ( Sweller et al., 1998 ; Schnotz and Kürschner, 2007 ). Schemas cluster elements of a problem and its solution together making them more manageable. Problem-appropriate instruction may draw attention to specific problem features that provide clues for selecting the most appropriate diagram ( Duval, 1999 , 2006 ), as well as the relevant declarative, procedural, and conditional knowledge for actually constructing and using that diagram (cf. Paris et al., 1983 ).

The present study

For developing knowledge about diagrams, appropriate instruction appears to be necessary ( van Meter and Garner, 2005 ; Jitendra et al., 2007 ; van Garderen, 2007 ; Uesaka et al., 2010 ; Manalo et al., 2019 ). Although instruction appears to promote spontaneity in diagram use, the role of cognitive load and the effect on the correctness in problem solving, particularly where more complex problems are involved, has not been established. Our main purpose therefore was to investigate whether diagram instruction results in increases in unprompted diagram construction. Moreover, we expect an increase of problem-appropriate diagrams following corresponding diagram-specific instruction. As a result, correctness in solving corresponding word problems should increase and persist over time. Finally, we expect to see corresponding decreases in levels of perceived cognitive load when working on mathematical word problems.

Three diagram-specific instructions for line diagrams, tables, and graphs were designed and tested on three corresponding types of problems “Compare quantities,” “Predict patterns,” and “Compare trajectories” respectively. These types of problems and diagrams for solving them are a very important part of the Japanese school curriculum ( Ayabe et al., 2021 ). An adaptation of the multiple baseline design method ( Baer et al., 1968 ; Morgan and Morgan, 2009 ) was used in order to compare the use of different kinds of diagrams and performance on different types of problems across time following different types of instruction. This design involves giving the three types of instruction in a staggered manner and observing the effect on all types of problems for the same participants. For example, an increase in the use of line diagrams specifically and corresponding improvement in problem solving performance should only occur after the line diagram instruction and exclusively for the targeted Compare quantities problems, not the Predict patterns and Compare trajectories problems. Thus, this design is more appropriate than a “no instruction” control group because it allows comparisons of (1) the same students (within-participant design) and (2) several kinds of instruction. Our specific hypotheses were as follows:

H1 : Diagram instruction leads to an overall increase in unprompted use of diagrams.

H2 : Diagram instruction leads to an increase in the use of problem-appropriate diagrams persisting in time.

H3 : Diagram instruction increases problem-solving performance (correct answer rates).

H4 : Diagram instruction reduces perceived cognitive load.

Materials and methods

A faculty ethics committee of Kyoto University approved the study. Participation was voluntary, and prior to the study, participants received verbal and written explanations. Informed consent was obtained from all participants and their parents.

Participants

Seventy junior high school students (aged approximately 14 years, all Japanese) from three regular classes of a junior high school in a small city in Japan participated in the study (ability grouping is not usually practiced in schools in Japan). Students in Japan perform well in mathematics by world standards (Japan ranked 5th in mathematics in PISA 2018; OECD, 2019 ). We used G*Power ( Faul et al., 2007 ) to estimate the minimum sample size for our within-participant design. This estimated that 46 participants would be required to detect a statistically significant difference for the assumed small to medium size effect (ƒ = 0.25, α-level p  = 0.05, power = 0.80). Considering class sizes in the school (≤ 25 students), and allowing for dropout, three classes were included to ensure minimal sample size. The experimental sessions were conducted during regular class sessions. All the students participated but three missed some sessions and their data were excluded. Data from 67 students (female = 36) were used in the analyses.

Problem-appropriate diagram instruction

Three dedicated instruction sessions covered the use of line, table, and graph diagrams. Instruction and practice sessions were held during regular class sessions (45 min duration). The instructions were given by the first author, assisted by a school mathematics teacher.

To ensure fidelity to plan and equivalence of the three instruction sessions, the authors discussed all contents and the instructional steps were determined in advance. PowerPoint slides were prepared and used to guide instruction. The instruction covered (1) the characteristics and functions of each kind of diagram (declarative knowledge), (2) the types and features of mathematics word problems that each diagram is useful for (conditional knowledge), and (3) the ways of constructing and the reasoning behind each diagram (procedural knowledge). During practice, the students solved example problems and constructed diagrams individually.

Line diagram instruction

Line diagrams, also known as “line numbers” or “tape diagrams” ( Murata, 2008 ), visually express quantities as line segments. Line diagrams allow inferring relationships between sums, differences, multiples, and proportions (declarative knowledge). Constructing a line diagram involves converting quantities to lines to enable easier visual comparisons of the lengths of the lines. Conditional knowledge included that line diagrams are helpful for solving complex problems about relationships between quantities. For developing procedural knowledge, students were asked to construct line diagrams in solving three word problems (isomorphic but different from those used in the tests).

Table instruction

The instructor explained and demonstrated how tables are effective for organizing numbers or quantities of two variables of interest. The students were told that creating an array for one variable and then arranging the second variable in a corresponding array would clarify the relationship between the two variables. Thus, a table makes it easier to find the rule that determines how the two variables change (declarative knowledge). The conditional knowledge conveyed was that tables are helpful for identifying a consistent pattern or rule of change in quantities to predict a future amount. For developing procedural knowledge, the students practiced constructing tables for use in solving three isomorphic word problems.

Graph instruction

The instructor explained that graphs (more specifically, cartesian graphs) are useful for visually representing complex variations or changes of quantities and gave a demonstration on how to represent two variables of a word problem as points with connecting lines on the x-and y-axes. The declarative knowledge included that graphs enable visual awareness of the change in quantities as they increase, decrease, or remain the same across space and time. It also included knowledge about how graphs can be used, such as extending two lines on graphs to find their intersection. The conditional knowledge conveyed was that a graph should be used for complicated processes of change that require projections of future events. Again, for developing procedural knowledge, the students practiced constructing graphs in solving three isomorphic problems.

Mathematical word problems

Five isomorphic problems (same problem structure but with different cover stories) for each of three problem types (Compare quantities, Predict patterns, and Compare trajectories) were used for three types of problem-appropriate diagrams (line, table, and graph diagrams respectively).

Compare quantities problems contained information about the magnitudes of lengths or distances. Solving these problems involved comparing these quantities. Line diagrams are appropriate because constructing a correct visual representation of the lengths not only provides a schematic layout of the problem situation, but also supports identification and working out of missing or unknown lengths (see example problems in Table 1 ).

Table 1 . Example problems (translated from Japanese) and student-constructed problem-appropriate diagrams.

Predict patterns problems contained information about quantities at multiple times or stages. Students were not informed of the rule-based character of the changes. Solving these problems required students to infer the rule and predict future quantities. Tables are appropriate because their structure makes patterns of changes visible, which leads to apprehending the underlying rule.

Compare trajectories problems contained information about actions from two or more entities (usually people). Solving these problems required students to compare trajectories of the different entities. Graphs are appropriate because they enable plotting distances (relative to a point of reference) across time, which in turn enables comparing trajectories.

Prior to the study, the 15 problems (5*3) were given to five mathematics teachers (female = 1; mean teaching experience = 9.2 years, SD  = 2.8 years) to check whether they were comparable and suitable for the intended grade level (14-year-olds at junior high school). Minor adjustments were made based on the teacher feedback. The revised problems were administered to 29 students from another school (female = 12; mean age = 13.2 years). Multiple comparisons using paired t-tests of the correct answer rates revealed no significant differences between the five problems of each type. Thus, they were considered equivalent and randomly used in the five test phases: Pre-test, Post-test after each of the three instruction sessions, and Delayed post-test.

Dependent measures

Unprompted and problem-appropriate diagram use.

An analysis grid was constructed for scoring the kind of diagram ( Table 2 ). Numbers, equations, formulas, or computations in columns were not considered as diagrams.

Table 2 . Analysis grid for scoring constructed diagrams.

Two teachers, with no vested interest in the study, rated all 1,005 answer sheets (5*3*67) in random order, blind to both test phase (5 phases) and type of problem (3 types). The teachers first rated 20% of the answer sheets, and compared and discussed their ratings with the first author. The teachers then independently scored the remaining answer sheets. Overall interrater agreement was high (Cohen’s kappa = 0.918). Unprompted diagram use was calculated as the presence of any kind of diagram. Problem-appropriate diagram use was calculated as the use of a specific kind of diagram for a specific type of problem (line diagram for Compare quantities, table for Predict patterns, and graph for Compare trajectories problems).

Correctness in problem solving

Correctness in problem solving was scored independently of diagram use. For each question (answer sheet), two answers were required for 0.5 points each. Correctness was scored 1 if both answers were correct, 0.5 if only one of them was correct, and 0 if both were incorrect or answers were missing.

Cognitive load

Cognitive load was measured using a short questionnaire for intrinsic cognitive load ( Leppink et al., 2014 ) translated to Japanese, with some minor adjustments. The questionnaire comprised four items, for example “I invested a very high mental effort in the complexity of this activity,” to be answered on a 10-point Likert-type scale (0 = “not at all the case” to 9 = “completely the case”). The reliability of the scale was confirmed on the 15 problems in the preliminary study (Cronbach’s alpha ranged from 0.67 to 0.93).

Design and procedure

Following the multiple baseline method, instruction in the use of line diagrams, tables, and graphs was provided in a staggered manner in three sessions, respectively, (see Table 3 ).

Table 3 . Summary of the multiple baseline design. All five test phases contained a Compare quantities, a Predict patterns, and a Compare trajectories problem.

The procedures used in administering the tests were identical across the five phases. Each test contained the three types of word problems in random order. Students were given 8 min to solve each problem. Students filled out the cognitive load questionnaire after solving each problem. All answer sheets were collected at the end of each session. No marks, grades, or feedback on the tests were given in between sessions.

Unprompted and problem-appropriate diagram use were dichotomous dependent variables (0 or 1). Therefore, Cochran’s Q, a non-parametric test, was used for analysis of main phase effects and McNemar’s test was used for pairwise comparisons. Correctness in problem solving had three possible scores (0, 0.5, 1) and perceived cognitive load ranged from 0 to 36. A repeated-measures analysis of variance was run on these variables as it is robust against violations of normal distribution assumptions ( Schmider et al., 2010 ). The Greenhouse–Geisser correction was used when the sphericity assumption was not met. We performed confirmatory analysis with the non-parametric Friedman test.

Did diagram instruction lead to an overall increase in unprompted use of diagrams?

Figure 1 shows diagram use (top row) as a function of problem type and test phase and allows comparing the percentage of answer sheets that included a diagram of any of the four kinds (cumulated shaded parts of the bars) against those that did not include any diagrams at all (white part of the bars). As expected, the unprompted use of any diagram seems to increase as a result of the instructions (white portion decreases over time) but only for the Predict patterns and Compare trajectories problems.

Figure 1 . Diagram use (top) , correctness in problem solving and perceived cognitive load (bottom) as a function of problem type and test phase. Cognitive load was normalized to range from 0 to 1.

The analysis showed no significant phase effect for Compare quantities problems [Cochran’s Q (4)  = 7.26, p  = 0.12]. Moreover, no significant difference was found in diagram use between the tests immediately before and after the line instruction [Pre-test versus Post line, McNemar’s χ 2 (1)  = 2.88, p  = 0.90, p values were multiplied by 10 as a Bonferroni correction]. Thus, the overall level of unprompted diagram use of any kind of diagram was high for Compare quantities problems (> 70%) from the beginning and stayed at such a high level throughout the five phases.

In the Predict patterns problems, a significant phase effect was found (Cochran’s Q (4)  = 48.35, p  < 0.001). However, no significant difference was found in unprompted use of any diagram between the tests immediately before and after the table instruction [Post line versus Post table McNemar’s χ 2 (1)  = 4.84, p  = 0.28]. A significant increase was observed only after graph instruction [Post line versus Post graph McNemar’s χ 2 (1)  = 22.09, p  < 0.001]. Moreover, unprompted use of any diagram for Predict patterns problems did not increase nor decrease from the Post graph to the Delayed test [Post graph versus Delayed McNemar’s χ 2 (1)  = 0.11, p  = 1.00]. Thus, unprompted use of any diagram increased following table instruction in the corresponding Predict patterns problems, but only towards the end of the procedure.

Finally, a significant phase effect was also found for Compare trajectories problems [ Q (4)  = 64.55, p  < 0.001]. The significant increase in unprompted use of any diagram followed graph instruction [Post table versus Post graph McNemar’s χ 2 (1)  = 13.44, p  < 0.01]. It seemed to still increase from the Post graph to the Delayed test, but this was not significant [Post graph versus Delayed McNemar’s χ 2 (1)  = 3.00, p  = 0.83]. Hence, following graph instruction, unprompted diagram use of any diagram for the corresponding Compare trajectories problems significantly increased and sustained.

Did diagram instruction lead to a persisting increase in problem-appropriate diagrams?

We expected an increase of problem-appropriate diagrams specifically. In other words, we expected increases in the use of line diagrams for comparing quantities, tables for predicting patterns, and graphs for comparing trajectories. Such problem-appropriate diagram use should occur directly following the corresponding instruction and persist in time even after alternative diagram instruction. Figure 1 does show this expected pattern of results. The use of each of the three types of diagrams increases after the corresponding instruction but only for the expected type of problem. Following line instruction, although some line diagrams were also used for comparing trajectories, the use of line diagrams increased for comparing quantities [phase effect in line diagram use, Cochran’s Q (4)  = 69.30, p  < 0.001], but not for the other two types of problems. Following table instruction, the use of tables increased for predicting patterns [phase effect in table use, Q (4)  = 121.39, p  < 0.001], not for the other two types of problems. And finally, following the graph instruction, the use of graphs increased for comparing trajectories [phase effect in graph use, Q (4)  = 105.86, p  < 0.001], again not for the other two types of problems.

Individual comparisons (again with Bonferroni corrections) confirmed the pattern of results. In the Compare quantities problems, the increase in line diagram use took place directly after the line instruction [between Pre-test and Post line test, McNemar’s χ 2 (1)  = 19.20, p  < 0.001]. It seemed to still increase in the Delayed test. Indeed, there was a significant difference between the Post line and Delayed test [ χ 2 (1)  = 10.71, p  < 0.01]. Thus, as Figure 1 shows, appropriate use of line diagrams for Compare quantities problems directly followed line instruction and still increased even after alternative table and graph instructions.

Similar results were obtained for the Predict patterns problems. Following table instruction, table use increased significantly for solving these problems [between Pre-test to Post table test, χ 2 (1)  = 27.00, p  < 0.001] and increased still further from Post table to the Delayed test [ χ 2 (1)  = 16.00, p  < 0.001]. Thus, appropriate use of tables for Predict pattern problems started directly after instruction, and even continued to increase, rather than decrease, after alternative diagram instruction.

Finally, in the Compare trajectories problems, graph use increased significantly just after the graph instruction [between Pre-test to Post graph test, χ 2 (1)  = 29.00, p  < 0.001]. However, unlike above, appropriate diagram use did not further increase in the Delayed test.

In all cases, the increase in problem-appropriate diagrams was observed directly after instruction but exclusively for the corresponding type of problem. Moreover, problem-appropriate diagram use tended to intensify, even despite the instruction on alternative diagrams. These results provide full support for the second hypothesis.

Did diagram instruction increase correctness in problem solving?

We expected an increase in correctness for each problem type directly following the corresponding diagram instruction and remaining stable over time. Such an improvement in problem solving can indeed be seen in Figure 1 (black bars in bottom bar graphs). Since the diagram-appropriate instruction took place in a staged fashion, the number of baseline data points differs for the three problem types, Comparing quantities, Predicting patterns, and Comparing trajectories (one, two, and three baseline data points, respectively). We therefore tested the pattern of results with three separate repeated-measurements analysis of variance, one for each problem type.

ANOVA revealed a significant phase effect for Compare quantities problems, F (4, 264)  = 9.24, p  < 0.001, η G 2  = 0.08. Comparing adjacent phases showed that only the first contrast, between Pre-test and Post line test, reached significance, t (66)  = 5.11, p  < 0.001, Cohen’s d  = 0.88, all p values were Bonferroni adjusted. Thus, correctness for Compare quantities problems significantly increased following line diagram instruction and the higher level of performance in problem solving persisted throughout the four subsequent test phases.

We also found a significant test phase effect for Predict patterns problems [ F (3.34, 220.12)  = 40.06, p  < 0.001, η G 2  = 0.26]. For this type of problem, Figure 1 shows that correctness increased directly after the appropriate table instruction. Indeed, in comparing adjacent test phases, the contrast for the comparison between Post line and Post table tests was significant, t (66)  = 8.95, p  < 0.001, d  = 1.55. Thus, correctness for Predict pattern problems augmented after the table instruction and the higher level maintained throughout the subsequent tests.

Finally, the test phase effect was significant for Compare trajectories problems, F (2.39, 157.56)  = 33.03, p  < 0.001, η G 2  = 0.26. Figure 1 clearly shows improved problem solving directly after the problem-appropriate graph instruction. This expected distinct increase in correctness after graph instruction was significant, t (66)  = 6.31, p  < 0.001, d  = 1.09. Improved correctness for Compare trajectories problems sustained at the obtained higher level in the Delayed test.

Friedman test results provided confirmation of these significant results in the Compare quantities problems [ χ 2 (4)  = 34.15, p  < 0.001], the Predict patterns problems [ χ 2 (4)  = 99.04, p  < 0.001], and the Compare trajectories problems [ χ 2 (4)  = 90.93, p  < 0.001]

Finally, we examined the relation between the use of problem-appropriate diagrams and correctness in problem solving in the Delayed test. Chi-square tests for contingency tables showed that the students who produced an appropriate diagram also obtained higher correctness in problem solving [Compare quantities, χ 2 (2)  = 7.16, p  < 0.05; Predict patterns, χ 2 (2)  = 19.30, p  < 0.001; Compare trajectories, χ 2 (2)  = 12.83, p  < 0.01]. These results show that the use of problem-appropriate diagrams is indeed concurrent with correctness in problem solving, providing full support for the third hypothesis.

Did diagram instruction reduce perceived cognitive load?

Finally, we expected that diagram instruction would decrease perceived cognitive load. Figure 1 shows that while the perceived cognitive load seems slightly decreasing over time (gray bars in bottom bar chart), the relation to diagram instruction is less marked. Again, we ran a separate analysis for each of the three problem types for the same reason given above.

The ANOVA showed a significant phase effect in the Compare quantities problems [ F (3.52, 232.01)  = 14.51, p  < 0.001, η G 2  = 0.08]. Unexpectedly, perceived cognitive load actually increased significantly following line diagram instruction [Pre-test versus Post line test, t (66)  = 2.81, p  < 0.05, d  = 0.49]. Subsequently, a significant decrease took place from the Post line to the Post table test, t (66)  = 4.14, p  < 0.001, d  = 0.72. Perceived cognitive load was lowest at Delayed test (significantly lower than at Pre-test, t (66)  = 4.13, p  < 0.001, d  = 0.71). In other words, line diagram instruction did not immediately lead to cognitive load reduction in solving the Compare quantities problems, but a delayed reduction could be observed.

A significant phase effect was also found for the Predict patterns problems, F (3.58, 236.09)  = 35.78, p  < 0.001, η G 2  = 0.19. In the Predict patterns problems, the pattern of perceived cognitive load variations fully supported the fourth hypothesis. No change in reported cognitive load was found prior to table instruction [Pre-test versus Post line test, t (66)  = 1.21, p  = 0.46 (ns), d  = 0.21], but a significant decrease followed table instruction [ t (66)  = 4.37, p  < 0.001, d  = 0.76, as well as a further decrease observed in the next Post graph test, t (66)  = 2.95, p  < 0.05, d  = 0.51. Cognitive load did not further decline in the Delayed test, t (66)  = 0.64, p  = 0.52 (ns), d  = 0.11]. Thus, evidence was found that table instruction reduced perceived cognitive load in solving the corresponding Predict patterns problems.

Finally, the analysis of perceived cognitive load showed a main effect of test phase for the Compare trajectories problems, F (3.41, 224.80)  = 22.77, p  < 0.001, η G 2  = 0.14. The contrasts showed that, while there was no change in perceived cognitive load between Pre-test and Post line test, there was an unexpected increase at Post table test [i.e., Post line test versus Post table test, t (66)  = 3.70, p  < 0.01, d  = 0.64]. Following graph instruction, the reported load then significantly decreased [i.e., Post table test versus Post graph test, t (66)  = 3.38, p  < 0.01, d  = 0.58]. A further decrease in perceived cognitive load was found at the Delayed test [Post graph test versus Delayed test, t (66)  = 5.50, p  < 0.001, d  = 0.95]. It is possible to interpret the decline in cognitive load from Post table test through to Delayed test as possibly stemming from practice effects. However, given that no decrease in perceived cognitive load actually occurred until after graph instruction was provided, we believe that on the whole these results can be taken as supporting the fourth hypothesis.

The results of the present study provide support for the hypotheses that we tested. Diagram instruction increased unprompted use of diagrams and, more importantly, it increased the use of problem-appropriate diagrams. These increases in use persisted in time. Furthermore, the instruction led to increases in student problem solving performance and to decreases in their perception of cognitive load associated with that problem solving. In this section, we consider the reasons for and meaning of these results, and discuss their theoretical, research, and practical implication.

Promoting unprompted and problem-appropriate diagram use

Two previously identified key challenges are that students generally lack spontaneity in diagram use and that, even when they construct diagrams, these are often not appropriate for the problem ( Hegarty and Kozhevnikov, 1999 ; Uesaka and Manalo, 2006 ; Corter and Zahner, 2007 ; Uesaka et al., 2007 ; van Garderen et al., 2012 ). The findings of the present study demonstrate that with instruction focusing on the correspondence between different types of problems and different kinds of diagrams both of these challenges can be resolved.

Previous research revealed that deficiencies in declarative knowledge is one important reason why students do not use diagrams when they should. Previous research also showed that instruction promotes greater spontaneity in the use of diagrams in mathematical word problem solving ( Uesaka et al., 2010 ). This was confirmed in the present study: there were significant increases in unprompted use of any diagrams in both the Predict patterns and Compare trajectories problems following diagram instruction. In the Compare quantities problems, increases in the unprompted use of any diagrams also followed instruction, but these were not significant. The most likely reason was that the level of diagram use in attempts at solving the Compare quantities problems was already high at the first baseline (Pre-test), and so the increases that followed were proportionally small. Note that in all three problem types, most of the diagrams that participants constructed prior to instruction were illustrations (see Figure 1 ), which would not have been helpful toward obtaining the correct solutions.

Instruction specifically should promote the construction of effective diagrams. Thus, in the present case, the goal of instruction was not for students to construct any diagram because not all diagrams are equal in helping toward generating the required answers. Different representations, even when they are isomorphic, vary in their potential for solving a problem ( Zhang and Norman, 1994 ; Zhang, 1997 ; Duval, 2006 ; Schnotz and Kürschner, 2008 ). Therefore, a crucial purpose of instruction is to enable students to determine and construct the most appropriate diagram to match the requirements of a problem. In the present study, for all three problem types, significant increases in problem-appropriate diagrams were evidenced following instruction, and those increases maintained. In the test phases following each instruction session, all three problem types were administered (in a random order) but, in each case, a significant increase was observed only in the problem type corresponding to the kind of diagram for which instruction had just been provided. This result suggests that, when given instruction, students are able to distinguish pertinent features of a problem and consequently select the most appropriate kind of diagram for solving it. They are able to develop both the necessary conditional and procedural knowledge.

Reducing cognitive load and improving word problem solving

A third important point is that, if students construct a problem-appropriate diagram, it should lead to a better problem solving performance. Again, this was demonstrated in the present study: the increases in appropriate diagram use coincided with significant improvements in problem solving performance. This outcome is understandable when we consider the representational effect mentioned earlier ( Zhang and Norman, 1994 ; Zhang, 1997 ) and the specific operations that representations can enable in mathematical problem solving ( Duval, 2006 ). More specifically, while some diagrams give an accurate visual-schematic representation for understanding a problem ( Hegarty and Kozhevnikov, 1999 ; Boonen et al., 2014 ), they may not help in actually solving it. Problem-appropriate diagrams, especially for more complex mathematical word problems, are not just visual or topographical representations. They are of a more abstract nature that enables drawing inferences or executing necessary operations. The execution of such operations is quite specific and systematic, requiring the connections between pertinent details in the problem text, the choice and construction of the diagram, and the derivation of the solution, to be explicitly explained – and practiced – in instruction sessions provided.

This brings up a fourth important point: that problem-appropriate instruction likely reduces the cognitive load experienced during problem solving, thereby facilitating the unprompted and appropriate use of diagrams, as well as freeing up cognitive resources that can be used in working out the answers. Evidence suggesting this was obtained in the current study: in all three problem types, instruction led to immediate or subsequent reductions in reported cognitive load, which coincided with increases in both appropriate diagram use and correct answer rates. According to cognitive load theory, the acquisition of knowledge and understanding relevant to a task leads to schema construction, which in turn leads to a reduction in intrinsic cognitive load and to freeing up of resources in working memory ( Sweller et al., 1998 ). In the case of problem solving and diagram use, prior to instruction the experience of cognitive load would likely be high, especially if the student is unsure about what to do. However, when problem-appropriate instruction is provided, the student would learn what to do and possess a schema to use for solving the problem. This means that the student’s experience of cognitive load would likely decrease ( Fuchs et al., 2020 ). Such decreases could have arisen because of practice effects ( Wesnes and Pincock, 2002 ), so it would be useful in future studies to obtain direct measurements of cognitive load (e.g., brain activity). In the present study, there is also evidence from the multiple baseline design that no significant decreases in cognitive load occurred prior to instruction, even in the Compare trajectories problems with three baseline points.

Theoretical implications

The findings of this research provide useful insights about the use of self-constructed diagrams in problem solving. They emphasize the importance of paying sufficient attention to the cultivation of procedural and conditional knowledge. In most Japanese mathematics classrooms, for example, teachers only demonstrate the use of diagrams, without any explicit explanation of how to select, construct, and use them ( Uesaka et al., 2007 ). Despite being familiar with the types of word problems and diagrams, students did not spontaneously use diagrams and failed to solve the problems at baseline. Thus, without proper explanations students have gaps in their procedural and conditional knowledge for diagram use, which not only explain the lack of spontaneous use, but also of inappropriate use and inability to draw the necessary inferences ( Hegarty and Kozhevnikov, 1999 ; Uesaka and Manalo, 2006 ; Corter and Zahner, 2007 ; Uesaka et al., 2007 ). The cultivation of the necessary (and presumably incomplete) procedural knowledge and conditional knowledge was addressed in this study through explicit instruction in problem-appropriate diagram use – which proved effective in improving problem solving behaviours.

The findings also indicate that an important consequence of such instruction is the reduction of cognitive load, specific to the problem type dealt with in the instruction. Our results suggest that cognitive load reduction is instrumental not only in promoting spontaneity in diagram use, but also in allowing sufficient cognitive resources to bear on the problem and hence to solve it successfully.

Furthermore, the findings draw attention to the distinction between two important functions that diagrams can serve in mathematical word problem solving: providing an accurate visual-schematic representation for understanding the problem and providing a schema or operational tool for solving it. Most students are aware of the first of these functions, which is why even prior to instruction many of the participants in the present study produced illustrations. However, such illustrations even when they portray an accurate schema of the problem situation, may not help in working out the solution to the problem. More complex problems often require the use of more abstract diagrams (tables, graphs) that do not visually portray the problem situation but instead directly facilitate obtaining the required solutions. In the research area of diagram use in mathematical word problem solving, little work has been undertaken on this second function ( Verschaffel et al., 2020 ). We believe it deserves more attention as, among other things, the transformational steps involved in their construction need to be better understood.

Research implications

In this research, the multiple baseline design allowed within-participant comparisons without requiring a control group. Multiple testing phases showed increases in performance only for the expected types of problems directly following the corresponding instruction. This design is more commonly used for evaluating individual behavioural change in response to an intervention, particularly when there is an expectation that the change would be irreversible ( Baer et al., 1968 ; Morgan and Morgan, 2009 ). Apart from across individuals (participants or clients), variations of the multiple baseline design include across settings, behaviours ( Morgan and Morgan, 2009 ), and populations ( Hawkins et al., 2007 ). The design has previously been used to evaluate the effect of providing instruction on mathematics skills to students. However, usually, instruction in a single mathematical operations using a particular teaching approach is evaluated across individual students ( Rivera and Smith, 1988 ). In the present study, we used the design to evaluate the effect of instruction on multiple aspects of participant responding (behaviour, performance, perception) across variations in types of problems, with the aim of demonstrating the need for problem-appropriate diagram instruction.

Like in previous studies, we expected resulting changes to be irreversible, and thus to maintain in post-instruction test phases. But we also expected the effects to be problem type-specific, with limited or no transfer across the problem types. Our results confirmed these expectations. In fact, the multiple baseline design has proven crucial in demonstrating not only the problem type-specific effects of the instructions, but also the co-occurrence of pertinent changes in behaviour, performance, and perception (increases in appropriate diagram use and correct answer rates, along with decreases in cognitive load). Therefore, from a research design perspective, we have been able to demonstrate a useful variation of the multiple baseline design that may have potential further applications in classroom educational research.

Practical implications

The results of the present study indicate that teachers need to explicitly provide instruction on diagram use if their students are to use them effectively in mathematical word problem solving. Many students will not likely construct a diagram if they lack adequate knowledge and skills: it may seem too demanding, and any effort in constructing a diagram may not pay off. Necessary problem-appropriate diagram instruction largely depends on teachers possessing the corresponding knowledge and skills. However, some teachers may be proficient in using diagrams in mathematical word problem solving, but may not have considered how to articulate such knowledge to convey it effectively to their students. It is therefore important to incorporate training in this area both for pre-service teachers in mathematics education, as well as for in-service teachers who may need upskilling through professional development courses.

Limitations and directions for future research

In the present study, we tested our hypotheses on the use of only three kinds of diagrams to solve three kinds of mathematical word problems. This is an important limitation to note as there are other kinds of diagrams that can be used to solve other types of problems, and it would be imperative to examine those in future research. Furthermore, our student participants all came from the same grade level in one school. We acknowledge that student capabilities in both mathematical word problem solving and diagram use would vary according to their age and grade level, as well as other aspects of their educational experiences. Thus it would also be useful to evaluate the effectiveness of problem-appropriate instruction on diagram use on students at other grade levels and from different educational backgrounds.

The instructions were also provided by the first author and an assisting teacher rather than the students’ real classroom teachers. An important step to take in future research would be to develop and evaluate instruction that real classroom teachers could use in cultivating diagram use capabilities in their own students.

The results of this study indicate that instruction on diagram use enables the construction and use of appropriate diagrams, improves ability to correctly solve problems, and reduces perception of the cognitive load associated with mathematical word problem solving. The instruction needs to be problem-appropriate, meaning that students need to learn specific details about the construction and use of different kinds of diagrams relevant to solving specific types of problems. As mathematical word problem solving is one crucial means by which understanding of the relevance of mathematics in the real world is cultivated, and diagram use is arguably one of the most effective heuristics for solving them, the effect of instruction indicated by our findings warrants serious consideration – especially as the extent to which such instruction is currently provided in most classrooms may be too general and thus inadequate.

Data availability statement

The datasets presented in this article are not readily available because the datasets generated during and/or analyzed during the current study are not publicly available because we did not obtain consent for secondary use from the participants but have a possibility to be available from the corresponding author on reasonable request. Requests to access the datasets should be directed to [email protected] .

Ethics statement

The studies involving human participants were reviewed and approved by Psychology Research Ethics Review Board, Graduate School of Education, Kyoto University. Written informed consent to participate in this study was provided by the participants’ legal guardian/next of kin.

Author contributions

HA and EM conceived the idea of the study. HA conducted experiments (including preliminary experiments) and drafted the original manuscript. EV developed a data scoring plan, and HA scored. EV and EM oversaw the rigor of the scoring process and its results. All authors developed the statistical analysis plan. HA conducted the analysis and EV additionally checked the results. All authors contributed to the interpretation of the results. EM supervised the conduct of this study. All authors reviewed the manuscript draft and revised it critically on intellectual content. All authors contributed to the article and approved the submitted version.

Acknowledgments

HA’s work on this study was supported by research grants received from the Future Education Research Institute, and the Japan Society for the Promotion of Science (JSPS: Grant for Young Scientists, 20J23507). EM’s work on this research was supported by a grant-in-aid (20K20516) received from JSPS. The authors express their gratitude to the students and teachers of Gifu Shotoku Gakuen University Junior High School, Japan (especially Yukio Fuwa, the Head Teacher) and the staff of Achieve Academy, Japan (especially Noriko Hanaki, the School Manager) for their assistance in the collection and analysis of the data.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Ainsworth, S. (2006). DeFT: a conceptual framework for considering learning with multiple representations. Learn. Instr. 16, 183–198. doi: 10.1016/j.learninstruc.2006.03.001

CrossRef Full Text | Google Scholar

Ainsworth, S., and Th Loizou, A. (2003). The effects of self-explaining when learning with text or diagrams. Cogn. Sci. 27, 669–681. doi: 10.1016/S0364-0213(03)00033-8

Ayabe, H., Manalo, E., Fukuda, M., and Sadato, N. (2021). “What diagrams are considered useful for solving mathematical word problems in Japan?” in Diagrammatic representation and inference. Diagrams 2021. Lecture notes in artificial intelligence . eds. A. Basu, G. Stapleton, S. Linker, C. Legg, E. Manalo, and P. Viana (Cham: Springer), 12909, 79–12983.

Google Scholar

Baer, D. M., Wolf, M. M., and Risley, T. R. (1968). Some current dimensions of applied behaviour analysis. J. Appl. Behav. Anal. 1, 91–97. doi: 10.1901/jaba.1968.1-91

PubMed Abstract | CrossRef Full Text | Google Scholar

Boonen, A. J. H., van Wesel, F., and Jolles, J., & van der Schoot (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: an item-level analysis in elementary school children. Int. J. Educ. Res. , 68, 15–26. doi: 10.1016/j.ijer.2014.08.001

Butcher, K. R. (2006). Learning from text with diagrams: promoting mental model development and inference generation. J. Educ. Psychol. 98, 182–197. doi: 10.1037/0022-0663.98.1.182

Chu, J., Rittle-Johnson, B., and Fyfe, E. R. (2017). Diagrams benefit symbolic problem-solving. Br. J. Educ. Psychol. 87, 273–287. doi: 10.1111/bjep.12149

Cooper, J. L., Sidney, P. G., and Alibali, M. W. (2018). Who benefits from diagrams and illustrations in math problems? Ability and attitudes matter. Appl. Cogn. Psychol. 32, 24–38. doi: 10.1002/acp.3371

Corter, J. E., and Zahner, D. C. (2007). Use of external visual representations in probability problem solving. Stat. Educ. Res. J. 6, 22–50. doi: 10.52041/serj.v6i1.492

DiSessa, A. A. (2004). Metarepresentation: native competence and targets for instruction. Cogn. Instr. 22, 293–331. doi: 10.1207/s1532690xci2203_2

Duval, R. (1999). “Representation, vision and visualization: cognitive functions in mathematical thinking. Basic issues for learning.” in Twenty First Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1, 3–26 . Available at: http://eric.ed.gov/ERICWebPortal/recordDetail?accno=ED466379%5Cnhttp://informahealthcare.com/doi/abs/10.1076/noph.25.1.3.7140

Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educ. Stud. Math. 61, 103–131. doi: 10.1007/s10649-006-0400-z

Faul, F., Erdfelder, E., Lang, A.-G., and Buchner, A. (2007). G*power 3: a flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behav. Res. Methods 39, 175–191. doi: 10.3758/BF03193146

Fuchs, L., Fuchs, D., Seethaler, P. M., and Barnes, M. A. (2020). Addressing the role of working memory in mathematical word-problem solving when designing intervention for struggling learners. ZDM-Math. Edu. 52, 87–96. doi: 10.1007/s11858-019-01070-8

Garner, R. (1990). When children and adults do not use learning strategies: toward a theory of settings. Rev. Educ. Res. 60, 517–529. doi: 10.3102/00346543060004517

Grawemeyer, B., and Cox, R. (2008). “The effects of users’ background diagram knowledge and task characteristics upon information display selection,” in Diagrams 2008, lecture notes in artificial intelligence . eds. G. Stapleton, J. Howse, and J. Lee, vol. 5223 (Berlin: Springer), 321–334.

Hawkins, N. G., Sanson-Fisher, R. W., Shakeshaft, A., D’Este, C., and Green, L. W. (2007). The multiple baseline design for evaluating population-based research. Am. J. Prev. Med. 33, 162–168. doi: 10.1016/j.amepre.2007.03.020

Hegarty, M., and Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. J. Educ. Psychol. 91, 684–689. doi: 10.1037/0022-0663.91.4.684

Hegarty, M., Mayer, R. E., and Monk, C. A. (1995). Comprehension of arithmetic word problems: a comparison of successful and unsuccessful problem solvers. J. Educ. Psychol. 87, 18–32. doi: 10.1037/0022-0663.87.1.18

Hembree, R. (1992). Experiments and relational studies in problem solving: a meta-analysis. J. Res. Math. Educ. 23, 242–273. doi: 10.2307/749120

Hurley, S. M., and Novick, L. R. (2010). Solving problems using matrix, network, and hierarchy diagrams: the consequences of violating construction conventions. Q. J. Exp. Psychol. 63, 275–290. doi: 10.1080/17470210902888908

Jitendra, A. K., Griffin, C. C., Haria, P., Leh, J., Adams, A., and Kaduvettoor, A. (2007). A comparison of single and multiple strategy instruction on third-grade students’ mathematical problem solving. J. Educ. Psychol. 99, 115–127. doi: 10.1037/0022-0663.99.1.115

Kintsch, W., and Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychol. Rev. 92, 109–129. doi: 10.1037/0033-295X.92.1.109

Leppink, J., Paas, F., van Gog, T., van der Vleuten, C. P. M., and van Merriënboer, J. J. G. (2014). Effects of pairs of problems and examples on task performance and different types of cognitive load. Learn. Instr. 30, 32–42. doi: 10.1016/j.learninstruc.2013.12.001

Lewis, A. B., and Mayer, R. E. (1987). Students’ miscomprehension of relational statements in arithmetic word problems. J. Educ. Psychol. 79, 363–371. doi: 10.1037/0022-0663.79.4.363

Manalo, E., Uesaka, Y., Chen, O., and Ayabe, H. (2019). “Showing what it looks like: teaching students how to use diagrams in problem solving, communication, and thinking,” in Deeper learning, dialogic learning, and critical thinking: Research-based strategies for the classroom . ed. E. Manalo (London: Routledge), 231–246.

Mayer, R. E., Lewis, A. B., and Hegarty, M. (1992). “Mathematical misunderstandings: qualitative reasoning about quantitative problems,” in The nature and origins of mathematical skills . ed. J. I. D. Campbell (Amsterdam: Elsevier), 137–154.

Morgan, D. L., and Morgan, R. K. (2009). Single-case research methods for the behavioral and health sciences. Thousand Oaks, CA: Sage.

Murata, A. (2008). Mathematics teaching and learning as a mediating process: the case of tape diagrams. Math. Think. Learn. 10, 374–406. doi: 10.1080/10986060802291642

Nistal, A. A., van Dooren, W., Clarebout, G., Elen, J., and Verschaffel, L. (2009). Conceptualising, investigating and stimulating representational flexibility in mathematical problem solving and learning: a critical review. ZDM - Int. J. Math. Educ. 41, 627–636. doi: 10.1007/s11858-009-0189-1

Novick, L. R., and Hurley, S. M. (2001). To matrix, network, or hierarchy: that is the question. Cogn. Psychol. 42, 158–216. doi: 10.1006/cogp.2000.0746

OECD (2019). Programme for international student assessment (PISA): results from PISA 2018, country note: Japan. Avalailbe at: https://www.oecd.org/pisa/publications/PISA2018_CN_JPN.pdf (Accessed February 12, 2021).

Paris, S. G., Lipson, M. Y., and Wixson, K. K. (1983). Becoming a strategic reader. Cont. Edu. Psychol. 8, 293–316. doi: 10.1016/0361-476X(83)90018-8

Reed, S. K. (1999). Word problems: Research and curriculum reform. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.

Rivera, D., and Smith, D. D. (1988). Using a demonstration strategy to teach midschool students with learning disabilities how to compute long division. J. Learn. Disabil. 21, 77–81. doi: 10.1177/002221948802100203

Schmider, E., Ziegler, M., Danay, E., Beyer, L., and Bühner, M. (2010). Is it really robust?: reinvestigating the robustness of ANOVA against violations of the normal distribution assumption. Methodology 6, 147–151. doi: 10.1027/1614-2241/a000016

Schnotz, W., and Kürschner, C. (2007). A reconsideration of cognitive load theory. Educ. Psychol. Rev. 19, 469–508. doi: 10.1007/s10648-007-9053-4

Schnotz, W., and Kürschner, C. (2008). External and internal representations in the acquisition and use of knowledge: visualization effects on mental model construction. Instr. Sci. 36, 175–190. doi: 10.1007/s11251-007-9029-2

Schoenfeld, A. H. (1985). Mathematical problem solving. Cambridge, MA: Academic Press.

Stylianou, D. A., and Silver, E. A. (2004). The role of visual representations in advanced mathematical problem solving: an examination of expert-novice similarities and differences. Math. Think. Learn. 6, 353–387. doi: 10.1207/s15327833mtl0604_1

Suthers, D. D. (2003). Representational guidance for collaborative inquiry. Arg. Learn 1994, 27–46. doi: 10.1007/978-94-017-0781-7_2

Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learn. Instr. 4, 295–312. doi: 10.1016/0959-4752(94)90003-5

Sweller, J., van Merrienboer, J. J. G., and Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educ. Psychol. Rev. 10, 251–296. doi: 10.1023/A:1022193728205

Uesaka, Y., and Manalo, E. (2006). “Active comparison as a means of promoting the development of abstract conditional knowledge and appropriate choice of diagrams in math word problem solving” in Diagrams 2006. Lecture notes in artificial intelligence 4045 . eds. D. Barker-Plummer, R. Cox, and N. Swoboda (Berlin: Springer), 181–195.

Uesaka, Y., and Manalo, E. (2012). Task-related factors that influence the spontaneous use of diagrams in math word problems. Appl. Cogn. Psychol. 26, 251–260. doi: 10.1002/acp.1816

Uesaka, Y., Manalo, E., and Ichikawa, S. (2007). What kinds of perceptions and daily learning behaviors promote students’ use of diagrams in mathematics problem solving? Learn. Instr. 17, 322–335. doi: 10.1016/j.learninstruc.2007.02

Uesaka, Y., Manalo, E., and Ichikawa, S. (2010). “The effects of perception of efficacy and diagram construction skills on students' spontaneous use of diagrams when solving math word problems” in Diagrams 2010. Lecture notes in artificial intelligence 6170 . eds. A. K. Goel, M. Jamnik, and N. H. Narayanan (Berlin Springer), 197–211.

van der Meij, J., van Amelsvoort, M., and Anjewierden, A. (2017). How design guides learning from matrix diagrams. Instr. Sci. 45, 751–767. doi: 10.1007/s11251-017-9425-1

van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. J. Learn. Disabil. 40, 540–553. doi: 10.1177/00222194070400060501

van Garderen, D., Scheuermann, A., and Jackson, C. (2012). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learn. Disabil. Q. 36, 145–160. doi: 10.1177/0731948712438558

van Meter, P., and Garner, J. K. (2005). The promise and practice of learner-generated drawing: literature review and synthesis. Educ. Psychol. Rev. 17, 285–325. doi: 10.1007/s10648-005-8136-3

Verschaffel, L., Schukajlow, S., Star, J., and Van Dooren, W. (2020). Word problems in mathematics education: a survey. ZDM-Math. Edu. 52, 1–16. doi: 10.1007/s11858-020-01130-4

Wesnes, K., and Pincock, C. (2002). Practice effects on cognitive tasks: a major problem? Lancet Neurol. 1:473. doi: 10.1016/S1474-4422(02)00236-3

Zahner, D., and Corter, J. E. (2010). The process of probability problem solving: use of external visual representations. Math. Think. Learn. 12, 177–204. doi: 10.1080/10986061003654240

Zhang, J. (1997). The nature of external representations in problem solving. Cogn. Sci. 21, 179–217. doi: 10.1016/S0364-0213(99)80022-6

Zhang, J., and Norman, D. A. (1994). Representations in distributed cognitive tasks. Cogn. Sci. 18, 87–122. doi: 10.1207/s15516709cog1801_3

Keywords: self-constructed diagrams, instructional methods, mathematical word problem solving, cognitive load, representational effect, multiple baseline design, Japanese students, visual representation

Citation: Ayabe H, Manalo E and de Vries E (2022) Problem-appropriate diagram instruction for improving mathematical word problem solving. Front. Psychol . 13:992625. doi: 10.3389/fpsyg.2022.992625

Received: 12 July 2022; Accepted: 12 September 2022; Published: 03 October 2022.

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Copyright © 2022 Ayabe, Manalo and de Vries. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Hiroaki Ayabe, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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Do You Understand the Problem You’re Trying to Solve?

To solve tough problems at work, first ask these questions.

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Problem solving skills are invaluable in any job. But all too often, we jump to find solutions to a problem without taking time to really understand the dilemma we face, according to Thomas Wedell-Wedellsborg , an expert in innovation and the author of the book, What’s Your Problem?: 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 contribute to the situation. You’ll also learn why searching for just one root cause can be misleading.

Key episode topics include: leadership, decision making and problem solving, power and influence, business management.

HBR On Leadership curates the best case studies and conversations with the world’s top business and management experts, to help you unlock the best in those around you. New episodes every week.

• Listen to the original HBR IdeaCast episode: The Secret to Better Problem Solving (2016)
• Find more episodes of HBR IdeaCast
• Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org .

HANNAH BATES: Welcome to HBR on Leadership , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock the best in those around you.

Problem solving skills are invaluable in any job. But even the most experienced among us can fall into the trap of solving the wrong problem.

Thomas Wedell-Wedellsborg says that all too often, we jump to find solutions to a problem – without taking time to really understand what we’re facing.

He’s an expert in innovation, and he’s the author of the book, What’s Your Problem?: 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 contribute to the situation. You’ll also learn why searching for one root cause can be misleading. And you’ll learn how to use experimentation and rapid prototyping as problem-solving tools.

This episode originally aired on HBR IdeaCast in December 2016. Here it is.

SARAH GREEN CARMICHAEL: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Sarah Green Carmichael.

Problem solving is popular. People put it on their resumes. Managers believe they excel at it. Companies count it as a key proficiency. We solve customers’ problems.

The problem is we often solve the wrong problems. Albert Einstein and Peter Drucker alike have discussed the difficulty of effective diagnosis. There are great frameworks for getting teams to attack true problems, but they’re often hard to do daily and on the fly. That’s where our guest comes in.

Thomas Wedell-Wedellsborg is a consultant who helps companies and managers reframe their problems so they can come up with an effective solution faster. He asks the question “Are You Solving The Right Problems?” in the January-February 2017 issue of Harvard Business Review. Thomas, thank you so much for coming on the HBR IdeaCast .

THOMAS WEDELL-WEDELLSBORG: Thanks for inviting me.

SARAH GREEN CARMICHAEL: So, I thought maybe we could start by talking about the problem of talking about problem reframing. What is that exactly?

THOMAS WEDELL-WEDELLSBORG: Basically, when people face a problem, they tend to jump into solution mode to rapidly, and very often that means that they don’t really understand, necessarily, the problem they’re trying to solve. And so, reframing is really a– at heart, it’s a method that helps you avoid that by taking a second to go in and ask two questions, basically saying, first of all, wait. What is the problem we’re trying to solve? And then crucially asking, is there a different way to think about what the problem actually is?

SARAH GREEN CARMICHAEL: So, I feel like so often when this comes up in meetings, you know, someone says that, and maybe they throw out the Einstein quote about you spend an hour of problem solving, you spend 55 minutes to find the problem. And then everyone else in the room kind of gets irritated. So, maybe just give us an example of maybe how this would work in practice in a way that would not, sort of, set people’s teeth on edge, like oh, here Sarah goes again, reframing the whole problem instead of just solving it.

THOMAS WEDELL-WEDELLSBORG: I mean, you’re bringing up something that’s, I think is crucial, which is to create legitimacy for the method. So, one of the reasons why I put out the article is to give people a tool to say actually, this thing is still important, and we need to do it. But I think the really critical thing in order to make this work in a meeting is actually to learn how to do it fast, because if you have the idea that you need to spend 30 minutes in a meeting delving deeply into the problem, I mean, that’s going to be uphill for most problems. So, the critical thing here is really to try to make it a practice you can implement very, very rapidly.

There’s an example that I would suggest memorizing. This is the example that I use to explain very rapidly what it is. And it’s basically, I call it the slow elevator problem. You imagine that you are the owner of an office building, and that your tenants are complaining that the elevator’s slow.

Now, if you take that problem framing for granted, you’re going to start thinking creatively around how do we make the elevator faster. Do we install a new motor? Do we have to buy a new lift somewhere?

The thing is, though, if you ask people who actually work with facilities management, well, they’re going to have a different solution for you, which is put up a mirror next to the elevator. That’s what happens is, of course, that people go oh, I’m busy. I’m busy. I’m– oh, a mirror. Oh, that’s beautiful.

And then they forget time. What’s interesting about that example is that the idea with a mirror is actually a solution to a different problem than the one you first proposed. And so, the whole idea here is once you get good at using reframing, you can quickly identify other aspects of the problem that might be much better to try to solve than the original one you found. It’s not necessarily that the first one is wrong. It’s just that there might be better problems out there to attack that we can, means we can do things much faster, cheaper, or better.

SARAH GREEN CARMICHAEL: So, in that example, I can understand how A, it’s probably expensive to make the elevator faster, so it’s much cheaper just to put up a mirror. And B, maybe the real problem people are actually feeling, even though they’re not articulating it right, is like, I hate waiting for the elevator. But if you let them sort of fix their hair or check their teeth, they’re suddenly distracted and don’t notice.

But if you have, this is sort of a pedestrian example, but say you have a roommate or a spouse who doesn’t clean up the kitchen. Facing that problem and not having your elegant solution already there to highlight the contrast between the perceived problem and the real problem, how would you take a problem like that and attack it using this method so that you can see what some of the other options might be?

THOMAS WEDELL-WEDELLSBORG: Right. So, I mean, let’s say it’s you who have that problem. I would go in and say, first of all, what would you say the problem is? Like, if you were to describe your view of the problem, what would that be?

SARAH GREEN CARMICHAEL: I hate cleaning the kitchen, and I want someone else to clean it up.

THOMAS WEDELL-WEDELLSBORG: OK. So, my first observation, you know, that somebody else might not necessarily be your spouse. So, already there, there’s an inbuilt assumption in your question around oh, it has to be my husband who does the cleaning. So, it might actually be worth, already there to say, is that really the only problem you have? That you hate cleaning the kitchen, and you want to avoid it? Or might there be something around, as well, getting a better relationship in terms of how you solve problems in general or establishing a better way to handle small problems when dealing with your spouse?

SARAH GREEN CARMICHAEL: Or maybe, now that I’m thinking that, maybe the problem is that you just can’t find the stuff in the kitchen when you need to find it.

THOMAS WEDELL-WEDELLSBORG: Right, and so that’s an example of a reframing, that actually why is it a problem that the kitchen is not clean? Is it only because you hate the act of cleaning, or does it actually mean that it just takes you a lot longer and gets a lot messier to actually use the kitchen, which is a different problem. The way you describe this problem now, is there anything that’s missing from that description?

SARAH GREEN CARMICHAEL: That is a really good question.

THOMAS WEDELL-WEDELLSBORG: Other, basically asking other factors that we are not talking about right now, and I say those because people tend to, when given a problem, they tend to delve deeper into the detail. What often is missing is actually an element outside of the initial description of the problem that might be really relevant to what’s going on. Like, why does the kitchen get messy in the first place? Is it something about the way you use it or your cooking habits? Is it because the neighbor’s kids, kind of, use it all the time?

There might, very often, there might be issues that you’re not really thinking about when you first describe the problem that actually has a big effect on it.

SARAH GREEN CARMICHAEL: I think at this point it would be helpful to maybe get another business example, and I’m wondering if you could tell us the story of the dog adoption problem.

THOMAS WEDELL-WEDELLSBORG: Yeah. This is a big problem in the US. If you work in the shelter industry, basically because dogs are so popular, more than 3 million dogs every year enter a shelter, and currently only about half of those actually find a new home and get adopted. And so, this is a problem that has persisted. It’s been, like, a structural problem for decades in this space. In the last three years, where people found new ways to address it.

So a woman called Lori Weise who runs a rescue organization in South LA, and she actually went in and challenged the very idea of what we were trying to do. She said, no, no. The problem we’re trying to solve is not about how to get more people to adopt dogs. It is about keeping the dogs with their first family so they never enter the shelter system in the first place.

In 2013, she started what’s called a Shelter Intervention Program that basically works like this. If a family comes and wants to hand over their dog, these are called owner surrenders. It’s about 30% of all dogs that come into a shelter. All they would do is go up and ask, if you could, would you like to keep your animal? And if they said yes, they would try to fix whatever helped them fix the problem, but that made them turn over this.

And sometimes that might be that they moved into a new building. The landlord required a deposit, and they simply didn’t have the money to put down a deposit. Or the dog might need a $10 rabies shot, but they didn’t know how to get access to a vet.

And so, by instigating that program, just in the first year, she took her, basically the amount of dollars they spent per animal they helped went from something like $85 down to around $60. Just an immediate impact, and her program now is being rolled out, is being supported by the ASPCA, which is one of the big animal welfare stations, and it’s being rolled out to various other places.

And I think what really struck me with that example was this was not dependent on having the internet. This was not, oh, we needed to have everybody mobile before we could come up with this. This, conceivably, we could have done 20 years ago. Only, it only happened when somebody, like in this case Lori, went in and actually rethought what the problem they were trying to solve was in the first place.

SARAH GREEN CARMICHAEL: So, what I also think is so interesting about that example is that when you talk about it, it doesn’t sound like the kind of thing that would have been thought of through other kinds of problem solving methods. There wasn’t necessarily an After Action Review or a 5 Whys exercise or a Six Sigma type intervention. I don’t want to throw those other methods under the bus, but how can you get such powerful results with such a very simple way of thinking about something?

THOMAS WEDELL-WEDELLSBORG: That was something that struck me as well. This, in a way, reframing and the idea of the problem diagnosis is important is something we’ve known for a long, long time. And we’ve actually have built some tools to help out. If you worked with us professionally, you are familiar with, like, Six Sigma, TRIZ, and so on. You mentioned 5 Whys. A root cause analysis is another one that a lot of people are familiar with.

Those are our good tools, and they’re definitely better than nothing. But what I notice when I work with the companies applying those was those tools tend to make you dig deeper into the first understanding of the problem we have. If it’s the elevator example, people start asking, well, is that the cable strength, or is the capacity of the elevator? That they kind of get caught by the details.

That, in a way, is a bad way to work on problems because it really assumes that there’s like a, you can almost hear it, a root cause. That you have to dig down and find the one true problem, and everything else was just symptoms. That’s a bad way to think about problems because problems tend to be multicausal.

There tend to be lots of causes or levers you can potentially press to address a problem. And if you think there’s only one, if that’s the right problem, that’s actually a dangerous way. And so I think that’s why, that this is a method I’ve worked with over the last five years, trying to basically refine how to make people better at this, and the key tends to be this thing about shifting out and saying, is there a totally different way of thinking about the problem versus getting too caught up in the mechanistic details of what happens.

SARAH GREEN CARMICHAEL: What about experimentation? Because that’s another method that’s become really popular with the rise of Lean Startup and lots of other innovation methodologies. Why wouldn’t it have worked to, say, experiment with many different types of fixing the dog adoption problem, and then just pick the one that works the best?

THOMAS WEDELL-WEDELLSBORG: You could say in the dog space, that’s what’s been going on. I mean, there is, in this industry and a lot of, it’s largely volunteer driven. People have experimented, and they found different ways of trying to cope. And that has definitely made the problem better. So, I wouldn’t say that experimentation is bad, quite the contrary. Rapid prototyping, quickly putting something out into the world and learning from it, that’s a fantastic way to learn more and to move forward.

My point is, though, that I feel we’ve come to rely too much on that. There’s like, if you look at the start up space, the wisdom is now just to put something quickly into the market, and then if it doesn’t work, pivot and just do more stuff. What reframing really is, I think of it as the cognitive counterpoint to prototyping. So, this is really a way of seeing very quickly, like not just working on the solution, but also working on our understanding of the problem and trying to see is there a different way to think about that.

If you only stick with experimentation, again, you tend to sometimes stay too much in the same space trying minute variations of something instead of taking a step back and saying, wait a minute. What is this telling us about what the real issue is?

SARAH GREEN CARMICHAEL: So, to go back to something that we touched on earlier, when we were talking about the completely hypothetical example of a spouse who does not clean the kitchen–

THOMAS WEDELL-WEDELLSBORG: Completely, completely hypothetical.

SARAH GREEN CARMICHAEL: Yes. For the record, my husband is a great kitchen cleaner.

You started asking me some questions that I could see immediately were helping me rethink that problem. Is that kind of the key, just having a checklist of questions to ask yourself? How do you really start to put this into practice?

THOMAS WEDELL-WEDELLSBORG: I think there are two steps in that. The first one is just to make yourself better at the method. Yes, you should kind of work with a checklist. In the article, I kind of outlined seven practices that you can use to do this.

But importantly, I would say you have to consider that as, basically, a set of training wheels. I think there’s a big, big danger in getting caught in a checklist. This is something I work with.

My co-author Paddy Miller, it’s one of his insights. That if you start giving people a checklist for things like this, they start following it. And that’s actually a problem, because what you really want them to do is start challenging their thinking.

So the way to handle this is to get some practice using it. Do use the checklist initially, but then try to step away from it and try to see if you can organically make– it’s almost a habit of mind. When you run into a colleague in the hallway and she has a problem and you have five minutes, like, delving in and just starting asking some of those questions and using your intuition to say, wait, how is she talking about this problem? And is there a question or two I can ask her about the problem that can help her rethink it?

SARAH GREEN CARMICHAEL: Well, that is also just a very different approach, because I think in that situation, most of us can’t go 30 seconds without jumping in and offering solutions.

THOMAS WEDELL-WEDELLSBORG: Very true. The drive toward solutions is very strong. And to be clear, I mean, there’s nothing wrong with that if the solutions work. So, many problems are just solved by oh, you know, oh, here’s the way to do that. Great.

But this is really a powerful method for those problems where either it’s something we’ve been banging our heads against tons of times without making progress, or when you need to come up with a really creative solution. When you’re facing a competitor with a much bigger budget, and you know, if you solve the same problem later, you’re not going to win. So, that basic idea of taking that approach to problems can often help you move forward in a different way than just like, oh, I have a solution.

I would say there’s also, there’s some interesting psychological stuff going on, right? Where you may have tried this, but if somebody tries to serve up a solution to a problem I have, I’m often resistant towards them. Kind if like, no, no, no, no, no, no. That solution is not going to work in my world. Whereas if you get them to discuss and analyze what the problem really is, you might actually dig something up.

Let’s go back to the kitchen example. One powerful question is just to say, what’s your own part in creating this problem? It’s very often, like, people, they describe problems as if it’s something that’s inflicted upon them from the external world, and they are innocent bystanders in that.

SARAH GREEN CARMICHAEL: Right, or crazy customers with unreasonable demands.

THOMAS WEDELL-WEDELLSBORG: Exactly, right. I don’t think I’ve ever met an agency or consultancy that didn’t, like, gossip about their customers. Oh, my god, they’re horrible. That, you know, classic thing, why don’t they want to take more risk? Well, risk is bad.

It’s their business that’s on the line, not the consultancy’s, right? So, absolutely, that’s one of the things when you step into a different mindset and kind of, wait. Oh yeah, maybe I actually am part of creating this problem in a sense, as well. That tends to open some new doors for you to move forward, in a way, with stuff that you may have been struggling with for years.

SARAH GREEN CARMICHAEL: So, we’ve surfaced a couple of questions that are useful. I’m curious to know, what are some of the other questions that you find yourself asking in these situations, given that you have made this sort of mental habit that you do? What are the questions that people seem to find really useful?

THOMAS WEDELL-WEDELLSBORG: One easy one is just to ask if there are any positive exceptions to the problem. So, was there day where your kitchen was actually spotlessly clean? And then asking, what was different about that day? Like, what happened there that didn’t happen the other days? That can very often point people towards a factor that they hadn’t considered previously.

SARAH GREEN CARMICHAEL: We got take-out.

THOMAS WEDELL-WEDELLSBORG: S,o that is your solution. Take-out from [INAUDIBLE]. That might have other problems.

Another good question, and this is a little bit more high level. It’s actually more making an observation about labeling how that person thinks about the problem. And what I mean with that is, we have problem categories in our head. So, if I say, let’s say that you describe a problem to me and say, well, we have a really great product and are, it’s much better than our previous product, but people aren’t buying it. I think we need to put more marketing dollars into this.

Now you can go in and say, that’s interesting. This sounds like you’re thinking of this as a communications problem. Is there a different way of thinking about that? Because you can almost tell how, when the second you say communications, there are some ideas about how do you solve a communications problem. Typically with more communication.

And what you might do is go in and suggest, well, have you considered that it might be, say, an incentive problem? Are there incentives on behalf of the purchasing manager at your clients that are obstructing you? Might there be incentive issues with your own sales force that makes them want to sell the old product instead of the new one?

So literally, just identifying what type of problem does this person think about, and is there different potential way of thinking about it? Might it be an emotional problem, a timing problem, an expectations management problem? Thinking about what label of what type of problem that person is kind of thinking as it of.

SARAH GREEN CARMICHAEL: That’s really interesting, too, because I think so many of us get requests for advice that we’re really not qualified to give. So, maybe the next time that happens, instead of muddying my way through, I will just ask some of those questions that we talked about instead.

THOMAS WEDELL-WEDELLSBORG: That sounds like a good idea.

SARAH GREEN CARMICHAEL: So, Thomas, this has really helped me reframe the way I think about a couple of problems in my own life, and I’m just wondering. I know you do this professionally, but is there a problem in your life that thinking this way has helped you solve?

THOMAS WEDELL-WEDELLSBORG: I’ve, of course, I’ve been swallowing my own medicine on this, too, and I think I have, well, maybe two different examples, and in one case somebody else did the reframing for me. But in one case, when I was younger, I often kind of struggled a little bit. I mean, this is my teenage years, kind of hanging out with my parents. I thought they were pretty annoying people. That’s not really fair, because they’re quite wonderful, but that’s what life is when you’re a teenager.

And one of the things that struck me, suddenly, and this was kind of the positive exception was, there was actually an evening where we really had a good time, and there wasn’t a conflict. And the core thing was, I wasn’t just seeing them in their old house where I grew up. It was, actually, we were at a restaurant. And it suddenly struck me that so much of the sometimes, kind of, a little bit, you love them but they’re annoying kind of dynamic, is tied to the place, is tied to the setting you are in.

And of course, if– you know, I live abroad now, if I visit my parents and I stay in my old bedroom, you know, my mother comes in and wants to wake me up in the morning. Stuff like that, right? And it just struck me so, so clearly that it’s– when I change this setting, if I go out and have dinner with them at a different place, that the dynamic, just that dynamic disappears.

SARAH GREEN CARMICHAEL: Well, Thomas, this has been really, really helpful. Thank you for talking with me today.

THOMAS WEDELL-WEDELLSBORG: Thank you, Sarah.  

HANNAH BATES: That was Thomas Wedell-Wedellsborg in conversation with Sarah Green Carmichael on the HBR IdeaCast. He’s an expert in problem solving and innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

We’ll be back next Wednesday with another hand-picked conversation about leadership from the Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

We’re a production of Harvard Business Review. If you want more podcasts, articles, case studies, books, and videos like this, find it all at HBR dot org.

This episode was produced by Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Music by Coma Media. Special thanks to Maureen Hoch, Adi Ignatius, Karen Player, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener.

See you next week.

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