flow chart problem solving techniques

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.

About Lucidchart

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

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

Written 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.

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Flowchart Tutorial (with Symbols, Guide and Examples)

A flowchart is simply a graphical representation of steps. It shows steps in sequential order and is widely used in presenting the flow of algorithms, workflow or processes. Typically, a flowchart shows the steps as boxes of various kinds, and their order by connecting them with arrows.

What is a Flowchart?

A flowchart is a graphical representations of steps. It was originated from computer science as a tool for representing algorithms and programming logic but had extended to use in all other kinds of processes. Nowadays, flowcharts play an extremely important role in displaying information and assisting reasoning. They help us visualize complex processes, or make explicit the structure of problems and tasks. A flowchart can also be used to define a process or project to be implemented.

Flowchart Symbols

Different flowchart shapes have different conventional meanings. The meanings of some of the more common shapes are as follows:

The terminator symbol represents the starting or ending point of the system.

A box indicates some particular operation.

This represents a printout, such as a document or a report.

A diamond represents a decision or branching point. Lines coming out from the diamond indicates different possible situations, leading to different sub-processes.

It represents information entering or leaving the system. An input might be an order from a customer. Output can be a product to be delivered.

On-Page Reference

This symbol would contain a letter inside. It indicates that the flow continues on a matching symbol containing the same letter somewhere else on the same page.

Off-Page Reference

This symbol would contain a letter inside. It indicates that the flow continues on a matching symbol containing the same letter somewhere else on a different page.

Delay or Bottleneck

Identifies a delay or a bottleneck.

Lines represent the flow of the sequence and direction of a process.

When to Draw Flowchart?

Using a flowchart has a variety of benefits:

• It helps to clarify complex processes.
• It identifies steps that do not add value to the internal or external customer, including delays; needless storage and transportation; unnecessary work, duplication, and added expense; breakdowns in communication.
• It helps team members gain a shared understanding of the process and use this knowledge to collect data, identify problems, focus discussions, and identify resources.
• It serves as a basis for designing new processes.

Flowchart examples

Here are several flowchart examples. See how you can apply a flowchart practically.

Flowchart Example – Medical Service

This is a hospital flowchart example that shows how clinical cases shall be processed. This flowchart uses decision shapes intensively in representing alternative flows.

Flowchart Example – Simple Algorithms

A flowchart can also be used in visualizing algorithms, regardless of its complexity. Here is an example that shows how flowchart can be used in showing a simple summation process.

Flowchart Example – Calculate Profit and Loss

The flowchart example below shows how profit and loss can be calculated.

Creating a Flowchart in Visual Paradigm

Let’s see how to draw a flowchart in Visual Paradigm. We will use a very simple flowchart example here. You may expand the example when finished this tutorial.

• Select Diagram > New from the main menu.

• Enter the name of the flowchart and click OK .

• Enter Add items to Cart as the name of the process.

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Article • 9 min read

Flow Charts

Identify and communicate your optimal process.

By the Mind Tools Content Team

How often have you thought about streamlining a process in your organization but not been sure where to start? Or perhaps you've struggled to understand a process when it's described to you in detail.

Flow charts are a useful tool in these situations, as they make a process easy to understand at a glance. Using just a few words and some simple symbols, they show clearly what happens at each stage and how this affects other decisions and actions.

In this article and video, we look at how to create and use flow charts, and explore how they can help you to solve problems in your processes.

What Is a Flow Chart?

Flow charts are easy-to-understand diagrams that show how the steps of a process fit together. American engineer Frank Gilbreth is widely believed to be the first person to document a process flow, having introduced the concept of a "Process Chart" to the American Society of Mechanical Engineers in 1921.

Flow charts tend to consist of four main symbols, linked with arrows that show the direction of flow:

1. Elongated circles, which signify the start or end of a process.

2. Rectangles, which show instructions or actions.

3. Diamonds, which highlight where you must make a decision.

4. Parallelograms, which show input and output. This can include materials, services or people.

You can use many other symbols in a flow chart but remember that these diagrams are used for communication . If you use symbols that only a few people understand, you may fail to get your message across. So, be sure to keep things simple !

When to Use a Flow Chart

All manner of organizations use flow charts to:

• Define a process.
• Standardize a process.
• Communicate a process.
• Identify bottlenecks or waste in a process.
• Solve a problem .
• Improve a process.

For example, software developers can use them to work out how the automated and manual parts of a process join up. Inexperienced team members might follow a flow chart to help them to complete activities in the right order. A manufacturer could ensure that it keeps to its values by applying a quality-control flow chart that presents questions and decision points. And an HR department might combine a flow chart with an organogram to show people who to contact about issues and when.

Why Use Flow Charts?

This tool's simplicity makes communicating and documenting a process quick and clear, so that the process will more likely be understood and applied correctly and consistently. It can also help you to estimate the timescale of the process, as you're better able to gauge the time needed for each task along the way. And you'll more likely identify who you should involve and at what stage, such as senior management or a compliance authority.

But you can also benefit from the process of creating a flow chart itself, as you build it step by step. You'll be able to focus on the detail of each individual stage, without feeling overwhelmed by the rest of the process, and then "zoom out" again to see the wider picture.

If your process or project involves several people or teams, you might find it more useful to use a Swim Lane Diagram rather than a flow chart – this helps you to show process flows between people and teams.

How to Create a Flow Chart

Follow these four steps:

Step 1: Identify Tasks

Begin by listing all of the tasks in a process in chronological order. Ask questions such as, "What happens next in the process?" or, "Do you need to make a decision before the next step?" or, "What approvals are required before you move on to the next task?"

Put yourself in the shoes of the person using the process, possibly for the first time. Talk to team members who work with the process directly, and get their opinions on where improvements could be made. Better yet, take a hands-on approach and go through the procedure yourself, and think about the practicalities of each stage. Use Customer Experience Mapping if your flow chart focuses on customer service, so that you can gain a better understanding of the process.

Step 2: Organize and Document Tasks

Next, start your flow chart by drawing the elongated circle shape and labeling it "Start."

Then, work through your whole process, and show the actions and decisions in the order that they happen. Link them with arrows to illustrate the flow of the process.

Where you need to make a decision, draw arrows from the decision diamond to each possible solution, and then label each arrow with the decision made. Remember to show the end of the process by using an elongated circle labeled "Finish."

Step 3: Double-Check the Process

When you've completed your flow chart, go back to the start and try it out to make sure that you haven't overlooked anything. Work through each step, and ask yourself whether you've represented the sequence of actions and the decisions involved correctly. Are there more decisions to be made at certain stages?

Then show your flow chart to other people, especially those who work directly with the process. Ask them to test that it works and to tell you if there are any problems or omissions.

Step 4: Challenge the Flow Chart

Finally, you might want to improve the process rather than just record it. So, see whether any of the steps that you've described are unnecessary or overly complicated. Identify any major bottlenecks , and deal with them to improve performance.

Are there any missing steps, no matter how small or seemingly insignificant, that you should add? And have you assigned tasks and decisions to the right people or automated them where it's most appropriate? Make any changes and then challenge the chart again.

As you challenge your flow chart, you might also be challenging your team members' tried and tested ways of working. So, take time to win support for your ideas, and don't expect to change people's habits overnight.

You may find that SIPOC diagrams will give you the detailed information that you need to introduce change in a controlled and effective way.

Flow Chart Software

You'll likely start with drawing flow charts by hand, but it's often more convenient to use a diagramming app to save, amend and share your charts.

Such apps vary from the simple and free, such as draw.io , creately and Pencil Project , to the more complex and paid-for, such as gliffy™ , Lucidchart , SmartDraw™ , and Visio® .

Flow charts can quickly become long and complicated, so that you can't represent them on a single piece of paper. This is where you can use "connectors" (shown as numbered circles) to link the flow when moving from one page to another. The user can follow the matching numbers to trace the flow of the process.

The image below shows part of a flow chart for how the receptionists in an example company should route incoming phone calls to the correct department:

Flow charts are simple diagrams that map out a process, so that you can easily communicate it to other people. You can also use them to define and analyze a process, build a step-by-step picture of it, and then standardize or improve it.

To draw a flow chart, identify the tasks and decisions that you make during a process, and write them down in order.

Then, arrange these steps in the flow chart format, using the appropriate symbols.

Finally, check and challenge your flow chart to make sure that it accurately represents the process, and that it shows the most efficient way of doing the job.

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How to create a problem-solving flow chart

Problem-solving is one of those topics that we’ve often discussed on this site (check out our Problem Solving guide ). We think it’s one of  THE  vital skills of business. Why? Because you’ll come across problems every day, and you need to arm yourself with the right tools to solve them.

A problem-solving flowchart is one of those tools. It’ll help you take a problem statement, break the problem down into likely causes helping you get to the bottom of what’s gone wrong.

In this post, we’ll cover

• What is a Problem Solving Flow Chart
• How to create a Problem Solving flow chart
• Example 1 of Problem Solving flow chart
• Example 2 of Problem Solving Flow chart
• What flow chart shapes to use
• When should you use a flow chart
• 7 tips on creating your Problem Solving chart

Key Benefits & Likely issues with the tool

Let’s get started!

What is a Problem Solving Flowchart

A Problem Solving flow chart is a diagram that uses shapes, arrows, and text to show a moving sequence of actions and/or activities that help solve a problem.  

How to create a Problem Solving flowchart

• Describe your problem.
• Pose Yes/No Questions that can help identify the cause of the problem
• Question each stage of the process until it is fully examined
• Repeat steps 2 & 3 until you have identified a solution
• Try the solution; if it is successful in addressing the root cause, then you’ve fixed your problem. If not, repeat the process until you have a solution that works.

A problem-solving flowchart attempts to identify a root cause/solution to the trigger that is causing the problem allowing you to change the process and prevent the problem from occurring. 

Let’s now demonstrate the effectiveness of a problem solving flowchart by showing some examples.

Example 1 Problem solving flow chart

In our first example, we’re going to start with something simple to show you the principle of the tool.

We have been given a cup of tea and we don’t like it!  

Let’s use a problem-solving flow chart to find out what’s gone wrong.

We’ve used Excel to capture this flow chart using flowchart shapes (insert –> shapes), you can, of course, use other applications to do this, you don’t’ have to have specialized flow chart software to do this. ( there’s a great flowchart in Excel video here ). Or you can simply use a pen and paper.

Use a rectangle and add your problem statement.

Remember to keep your problem statement unambiguous and straightforward. Here we’ve used “I don’t like my cup of tea.”

Now that we’ve got our problem statement, we’re going to start asking questions.

We’re going to examine the variables that go into a cup of tea in an attempt to find out what’s gone wrong.

** TIP** – Work through your process – rather than start from scratch, if you have a documented process, work through that examining each step to ascertain if there are issues. If not, you might find it useful to research and sketch out the process before starting with your flowchart.

We have a process for the cup of tea, which is:

1/ Boil Water

2/ Place Breakfast Tea teabag in the cup

3/ Add Water

4/ Leave to sit for 2 mins

4/ Remove teabag

5/ Add milk

6/ Add sugar

So our problem solving flow chart needs to examine each of those steps to determine where the failure has occurred. 

We’ll add a question shape (diamond), connect out problem statement to it using an arrow to check if we boiled the kettle. Our Diagram will now look like:

As a question, we want two possible routes – Yes and No.

Our process asks us to boil the kettle if we did, and the answer is Yes, then we can go to the next process step.

If the answer is No, then we have a problem. Our tea will be cold. 

Here we can do one of two things. We can terminate the flow chart, or we can add an activity to rectify the problem (this might be to remake the drink or to perhaps heat the drink up in the microwave).

Our flow chart now looks like this:

Step 2 in our Tea making process was to add a Breakfast-tea tea bag.

So, once again, we’ll ask a question about that step.

“Did we add an English Breakfast teabag.”

As before, we’ll use a question shape, using Yes or No answers. If we performed the process step correctly, we’d move on. If we didn’t, we’ll either end the problem solving (we’ve found the root cause), or we’ll add a corrective action.

Now we’ll repeat this process until we’ve reviewed the whole process.

Our finished flowchart looks like this.

However, we’re not finished.

What happens if we follow the flow chart, and we find we didn’t use boiled water. We remake the tea using boiled water, and we still don’t like it?  

We need to ask some further questions.

We need to update our flow chart to validate that we solved the problem and what to do if we didn’t.

So for each step of the process, our problem solving flowchart now looks like this.

Here’s our completed flow chart.

As you can see, we’ve identified the problem, and we’ve described a corrective action.

But there’s a problem here. With this flowchart, you can still follow it, validating the process, and still end up with a cup of tea that’s unsatisfactory. 

Why is that?

Well, it’s perfectly possible that we started out with a process that’s incorrect. What happens if the process called for using an incorrect tea bag from the start?

So we’ll simplify things by adding a block at the end that if you’re still not happy at the end of reviewing the steps, a full review of the process will be undertaken. This is a simple answer to this problem, and I would expect that you would expand this section in more detail if you were creating a flowchart yourself.

So what does a more complex process look like, how about we look at a business problem?

Example 2 Problem Solving flow chart

OK, so example 1 may have been a bit simple, and you are maybe looking for something in a business context.

So in Example 2, let’s look at a scenario that’s a little more complex.

Let’s assume that your organization has received a non-conforming part. You have been assigned to work with the Vendor to:

• Find out what went wrong
• Prevent recurrence

We’re going to use a problem solving flow chart to help us do that.

As with the first example, we’re going to state the problem.

“The part is non conforming.”

Using the production process from the Vendor, we’ll work through the stages to see if we can spot what’s gone wrong.

The diagram below shows an analysis of the first two steps of the production process using a problem-solving flow chart.

The first thing you’ll notice is that on one process step, there may be many questions to ascertain the potential issue.  

Some of these may be complex and require careful thought.

There may be multiple variables (systems, processes, tools, inputs, etc.) that may require attention.

You will need to analyze each process step, in full, to be sure you have caught all the possible causes of the fault.

Which Flow chart shapes should you use.

A problem solving flow chart usually utilizes only a small number of shapes. We show these in the table below.

When should you use a Problem Solving flow chart

There are many many problem tools available.

A flow chart lends itself to be used when:

• You are looking for a tool that is simple to use
• You are looking to use a tool that does not require complex software
• You want to validate a  process.
• You want something that facilitates collaboration
• You want something that you can use to communicate with others

7 Tips on creating great problem solving flow charts

1/ Use standard shapes!

2/ Make it easy to follow!

3/ Keep things on one page

4/ Don’t overload your boxes with text

5/ Go into enough detail. Don’t try and simplify activities as it might hide problems from being seen.

6/ Collaborate. Where you can utilize a team to help document the problem and the activities do so. The more knowledge of the process, the better chance you’ll have of locating the issue.

7/ Use a consistent direction to flow your process, moving things around the page can confuse people who might look at it.

A flow chart can provide you with a great advantage when looking to solve problems. Some of the key benefits include

• A visual aide that’s easy to understand
• Simple to use, does not require hours and hours of training
• A tool that facilitates collaboration
• Effective for aiding communication
• Provides an effective method of analysing a process

However, as with everything, there are some issues to look out for

• Flowchart fails to capture all process steps and therefore root cause analysis is hit and miss
• Lack of knowledge of the process by the individual compiling the flowchart results in inaccurate problem solving
• Inconsistent flow of process makes maps confusing
• Complex processes may be better suited to other tools (fishbone etc)
• Inconsistent formatting and/or use of shapes result in flowchart that is difficult to utilise.

There are a great many tools out there for problem-solving, and flow charts can be used either as a stand-alone tool or conjunction with one of these other tools.

Flowcharts can make for a great problem-solving tool.  

They’re simple to use, effective, and facilitate collaboration.

We hope you’ve found our article useful, in particular the example walkthroughs.

If you’re looking to use the tool, we’d love some feedback from you and hearing how you’ve got on. Why not fire us a message on twitter or use the comments section below.

This article is part of our Problem Solving Guide.   

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Visual problem solving with flowcharts and mind maps

What’s life without problems? Probably a little boring, if we’re being honest. If everything were perfect all the time, there would be no challenges, and things would get pretty monotonous. This is a rather optimistic view on what many believe to be an aggravating part of life. No matter how you feel about problems, one thing is true: problems are inevitable . You can’t always control how many problems you encounter in your life, but you can learn better ways to solve them. So, what can we do for those really complex issues that aren’t easily solved? Visual problem solving is the perfect way to see solutions and break down complex issues.

Make your own flowchart with Gleek .

What is visual problem solving?

Visual problem solving is the process of using aids like charts or diagrams to display all the aspects of a problem in order to find viable solutions. When problem solving, sometimes it’s hard to see what’s causing the problem, or other relationships and correlations that are affecting whatever it is you’re working on. Two common methods for problem solving include mind maps and flowcharts . A mind map is a non-linear diagram, used for making new ideas or breaking down complex issues. A flowchart is a linear diagram, used for making action plans and describing processes.

5 steps to solve problems

Identify the true problem

Maybe you know what the issue is in clear terms, or perhaps it’s still a little confusing. A good way to get a concrete vision of the problem you need to solve is to pose it as a question, or a short statement. You might come up with something like ‘our sales have dropped’, or, as a question ‘what can we do to increase sales?’.

Get information

Now that you have a clear objective to solve, the next step is to gather all the relevant information that pertains to the issue. This can look like statistics, comments from customers, employee feedback, and more. Once you’ve collected the data, you’ll need to analyze it from all angles to get a clear view on the topic.

Brainstorming session

Get any and all potential solution ideas out on the table. Doesn’t matter how silly an idea seems, just put anything that comes to mind on the drawing board. This is where your visual aids will really come in handy, especially mind maps. You might need more than one chart, depending on how complicated the issue is.

Choose the best idea(s)

Whether on your own or with a team, you’ll have to eliminate the potential solutions that just won’t work. To find the solution that’ll work best, it’s good to analyze it in the same way you did the problem – by looking at potential outcomes, and all facets involved.

Make an action plan

So you think you’ve found the perfect solution! Now what? If your problem is complicated, usually the solution will be too. Here is where another visual aid, like a flowchart, will be helpful. Map out the specific steps you need in order to implement your solution. Then, it’s time to put your plan into action.

These are just the basic steps you can use to start problem solving. You may find that other actions are needed during your own journey.

Common mistakes when problem solving

Mistakes? We all make them from time to time. Here are some common mistakes we are prone to when trying to fix problems.

Undefined problem – When identifying the problem, it’s possible that the problem is too big, multi-faceted, or too complex to tackle all at once. A way to avoid this is to break the problem down into chunks, following common themes.

More problems arise – This isn’t always a direct result of anything we do, but it can happen nonetheless. The best way to deal with more problems that arise when you’re trying to solve the original one is to think of the possible things that could go wrong during the solution stage. When you’re prepared for any situation, you’ll rarely have any setbacks.

No action plan – Finding a way to solve your problem doesn’t mean that the planning is over. On the contrary, you need to create a strategy to properly execute your solution so you won’t end up with a half-solved problem and even more issues than you started with.

When to use flowcharts

One way to chart your problems and progress is through flowcharts. For those who like to think in a step-by-step or linear fashion, flowcharts are the best way to visualize things. Let’s have a look at some situations that are best suited to flowcharts.

Big problems – Flowcharts can help break down a large problem or solution into specific steps or stages from start to finish.

Decision trees – This type of flowchart is helpful when diagramming actions that will happen as a result of other actions, whether they be in a software system or actions taken by people.

Cause and effect – Similar to a decision tree, a cause and effect flowchart is where you can analyze the potential results of various actions, past or present.

Check out our 20 flowchart templates that you can also easily edit !

When to use mind maps

Mind maps are great for brainstorming sessions, and non-linear problem solving. Here are some situations that are best visualized through a mind map.

Finding the problem – So, what is the problem exactly? Sometimes it’s hard to see. Making a mind map offers you the opportunity to see all the moving parts involved with a situation, and how they relate to one another, and can help you suss out the true problem.

Core and branching ideas – You start with a core idea, such as ‘online sales’, then add related ideas or issues branching off from that, like maybe ‘ad revenue’, or ‘social media campaigns’. Then those ideas can have their own branches. This is an easy way to analyze all aspects of a problem.

Source: Problem Solving with Mind Maps (Tutorial)

Looking to create your own flowchart? Gleek has the solution for you. With Gleek, you can create your own flowcharts using a text-based command center, without ever using your mouse. Not only can you create flowcharts, you can create many other UML-based diagrams that will wow your colleagues and bring new life to your presentations. Get started for free today .

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A step-by-step guide to creating a flowchart in Google Docs

7 stages of the product development process (flowchart example)

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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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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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Struggling to overcome challenges in your life? We all face problems, big and small, on a regular basis.

So how do you tackle them effectively? What are some key problem-solving strategies and skills that can guide you?

Effective problem-solving requires breaking issues down logically, generating solutions creatively, weighing choices critically, and adapting plans flexibly based on outcomes. Useful strategies range from leveraging past solutions that have worked to visualizing problems through diagrams. Core skills include analytical abilities, innovative thinking, and collaboration.

Want to improve your problem-solving skills? Keep reading to find out 17 effective problem-solving strategies, key skills, common obstacles to watch for, and tips on improving your overall problem-solving skills.

Key Takeaways:

• Effective problem-solving requires breaking down issues logically, generating multiple solutions creatively, weighing choices critically, and adapting plans based on outcomes.
• Useful problem-solving strategies range from leveraging past solutions to brainstorming with groups to visualizing problems through diagrams and models.
• Core skills include analytical abilities, innovative thinking, decision-making, and team collaboration to solve problems.
• Common obstacles include fear of failure, information gaps, fixed mindsets, confirmation bias, and groupthink.
• Boosting problem-solving skills involves learning from experts, actively practicing, soliciting feedback, and analyzing others’ success.
• Onethread’s project management capabilities align with effective problem-solving tenets – facilitating structured solutions, tracking progress, and capturing lessons learned.

What Is Problem-Solving?

Problem-solving is the process of understanding an issue, situation, or challenge that needs to be addressed and then systematically working through possible solutions to arrive at the best outcome.

It involves critical thinking, analysis, logic, creativity, research, planning, reflection, and patience in order to overcome obstacles and find effective answers to complex questions or problems.

The ultimate goal is to implement the chosen solution successfully.

What Are Problem-Solving Strategies?

Problem-solving strategies are like frameworks or methodologies that help us solve tricky puzzles or problems we face in the workplace, at home, or with friends.

Imagine you have a big jigsaw puzzle. One strategy might be to start with the corner pieces. Another could be looking for pieces with the same colors. 

Just like in puzzles, in real life, we use different plans or steps to find solutions to problems. These strategies help us think clearly, make good choices, and find the best answers without getting too stressed or giving up.

Why Is It Important To Know Different Problem-Solving Strategies?

Knowing different problem-solving strategies is important because different types of problems often require different approaches to solve them effectively. Having a variety of strategies to choose from allows you to select the best method for the specific problem you are trying to solve.

This improves your ability to analyze issues thoroughly, develop solutions creatively, and tackle problems from multiple angles. Knowing multiple strategies also aids in overcoming roadblocks if your initial approach is not working.

Here are some reasons why you need to know different problem-solving strategies:

• Different Problems Require Different Tools: Just like you can’t use a hammer to fix everything, some problems need specific strategies to solve them.
• Improves Creativity: Knowing various strategies helps you think outside the box and come up with creative solutions.
• Saves Time: With the right strategy, you can solve problems faster instead of trying things that don’t work.
• Reduces Stress: When you know how to tackle a problem, it feels less scary and you feel more confident.
• Better Outcomes: Using the right strategy can lead to better solutions, making things work out better in the end.
• Learning and Growth: Each time you solve a problem, you learn something new, which makes you smarter and better at solving future problems.

Knowing different ways to solve problems helps you tackle anything that comes your way, making life a bit easier and more fun!

17 Effective Problem-Solving Strategies

Effective problem-solving strategies include breaking the problem into smaller parts, brainstorming multiple solutions, evaluating the pros and cons of each, and choosing the most viable option. 

Critical thinking and creativity are essential in developing innovative solutions. Collaboration with others can also provide diverse perspectives and ideas. 

By applying these strategies, you can tackle complex issues more effectively.

Now, consider a challenge you’re dealing with. Which strategy could help you find a solution? Here we will discuss key problem strategies in detail.

1. Use a Past Solution That Worked

This strategy involves looking back at previous similar problems you have faced and the solutions that were effective in solving them.

It is useful when you are facing a problem that is very similar to something you have already solved. The main benefit is that you don’t have to come up with a brand new solution – you already know the method that worked before will likely work again.

However, the limitation is that the current problem may have some unique aspects or differences that mean your old solution is not fully applicable.

The ideal process is to thoroughly analyze the new challenge, identify the key similarities and differences versus the past case, adapt the old solution as needed to align with the current context, and then pilot it carefully before full implementation.

An example is using the same negotiation tactics from purchasing your previous home when putting in an offer on a new house. Key terms would be adjusted but overall it can save significant time versus developing a brand new strategy.

2. Brainstorm Solutions

This involves gathering a group of people together to generate as many potential solutions to a problem as possible.

It is effective when you need creative ideas to solve a complex or challenging issue. By getting input from multiple people with diverse perspectives, you increase the likelihood of finding an innovative solution.

The main limitation is that brainstorming sessions can sometimes turn into unproductive gripe sessions or discussions rather than focusing on productive ideation —so they need to be properly facilitated.

The key to an effective brainstorming session is setting some basic ground rules upfront and having an experienced facilitator guide the discussion. Rules often include encouraging wild ideas, avoiding criticism of ideas during the ideation phase, and building on others’ ideas.

For instance, a struggling startup might hold a session where ideas for turnaround plans are generated and then formalized with financials and metrics.

3. Work Backward from the Solution

This technique involves envisioning that the problem has already been solved and then working step-by-step backward toward the current state.

This strategy is particularly helpful for long-term, multi-step problems. By starting from the imagined solution and identifying all the steps required to reach it, you can systematically determine the actions needed. It lets you tackle a big hairy problem through smaller, reversible steps.

A limitation is that this approach may not be possible if you cannot accurately envision the solution state to start with.

The approach helps drive logical systematic thinking for complex problem-solving, but should still be combined with creative brainstorming of alternative scenarios and solutions.

An example is planning for an event – you would imagine the successful event occurring, then determine the tasks needed the week before, two weeks before, etc. all the way back to the present.

4. Use the Kipling Method

This method, named after author Rudyard Kipling, provides a framework for thoroughly analyzing a problem before jumping into solutions.

It consists of answering six fundamental questions: What, Where, When, How, Who, and Why about the challenge. Clearly defining these core elements of the problem sets the stage for generating targeted solutions.

The Kipling method enables a deep understanding of problem parameters and root causes before solution identification. By jumping to brainstorm solutions too early, critical information can be missed or the problem is loosely defined, reducing solution quality.

Answering the six fundamental questions illuminates all angles of the issue. This takes time but pays dividends in generating optimal solutions later tuned precisely to the true underlying problem.

The limitation is that meticulously working through numerous questions before addressing solutions can slow progress.

The best approach blends structured problem decomposition techniques like the Kipling method with spurring innovative solution ideation from a diverse team. 

An example is using this technique after a technical process failure – the team would systematically detail What failed, Where/When did it fail, How it failed (sequence of events), Who was involved, and Why it likely failed before exploring preventative solutions.

5. Try Different Solutions Until One Works (Trial and Error)

This technique involves attempting various potential solutions sequentially until finding one that successfully solves the problem.

Trial and error works best when facing a concrete, bounded challenge with clear solution criteria and a small number of discrete options to try. By methodically testing solutions, you can determine the faulty component.

A limitation is that it can be time-intensive if the working solution set is large.

The key is limiting the variable set first. For technical problems, this boundary is inherent and each element can be iteratively tested. But for business issues, artificial constraints may be required – setting decision rules upfront to reduce options before testing.

Furthermore, hypothesis-driven experimentation is far superior to blind trial and error – have logic for why Option A may outperform Option B.

Examples include fixing printer jams by testing different paper tray and cable configurations or resolving website errors by tweaking CSS/HTML line-by-line until the code functions properly.

6. Use Proven Formulas or Frameworks (Heuristics)

Heuristics refers to applying existing problem-solving formulas or frameworks rather than addressing issues completely from scratch.

This allows leveraging established best practices rather than reinventing the wheel each time.

It is effective when facing recurrent, common challenges where proven structured approaches exist.

However, heuristics may force-fit solutions to non-standard problems.

For example, a cost-benefit analysis can be used instead of custom weighting schemes to analyze potential process improvements.

Onethread allows teams to define, save, and replicate configurable project templates so proven workflows can be reliably applied across problems with some consistency rather than fully custom one-off approaches each time.

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7. Trust Your Instincts (Insight Problem-Solving)

Insight is a problem-solving technique that involves waiting patiently for an unexpected “aha moment” when the solution pops into your mind.

It works well for personal challenges that require intuitive realizations over calculated logic. The unconscious mind makes connections leading to flashes of insight when relaxing or doing mundane tasks unrelated to the actual problem.

Benefits include out-of-the-box creative solutions. However, the limitations are that insights can’t be forced and may never come at all if too complex. Critical analysis is still required after initial insights.

A real-life example would be a writer struggling with how to end a novel. Despite extensive brainstorming, they feel stuck. Eventually while gardening one day, a perfect unexpected plot twist sparks an ideal conclusion. However, once written they still carefully review if the ending flows logically from the rest of the story.

8. Reverse Engineer the Problem

This approach involves deconstructing a problem in reverse sequential order from the current undesirable outcome back to the initial root causes.

By mapping the chain of events backward, you can identify the origin of where things went wrong and establish the critical junctures for solving it moving ahead. Reverse engineering provides diagnostic clarity on multi-step problems.

However, the limitation is that it focuses heavily on autopsying the past versus innovating improved future solutions.

An example is tracing back from a server outage, through the cascade of infrastructure failures that led to it finally terminating at the initial script error that triggered the crisis. This root cause would then inform the preventative measure.

9. Break Down Obstacles Between Current and Goal State (Means-End Analysis)

This technique defines the current problem state and the desired end goal state, then systematically identifies obstacles in the way of getting from one to the other.

By mapping the barriers or gaps, you can then develop solutions to address each one. This methodically connects the problem to solutions.

A limitation is that some obstacles may be unknown upfront and only emerge later.

For example, you can list down all the steps required for a new product launch – current state through production, marketing, sales, distribution, etc. to full launch (goal state) – to highlight where resource constraints or other blocks exist so they can be addressed.

Onethread allows dividing big-picture projects into discrete, manageable phases, milestones, and tasks to simplify execution just as problems can be decomposed into more achievable components. Features like dependency mapping further reinforce interconnections.

Using Onethread’s issues and subtasks feature, messy problems can be decomposed into manageable chunks.

10. Ask “Why” Five Times to Identify the Root Cause (The 5 Whys)

This technique involves asking “Why did this problem occur?” and then responding with an answer that is again met with asking “Why?” This process repeats five times until the root cause is revealed.

Continually asking why digs deeper from surface symptoms to underlying systemic issues.

It is effective for getting to the source of problems originating from human error or process breakdowns.

However, some complex issues may have multiple tangled root causes not solvable through this approach alone.

An example is a retail store experiencing a sudden decline in customers. Successively asking why five times may trace an initial drop to parking challenges, stemming from a city construction project – the true starting point to address.

11. Evaluate Strengths, Weaknesses, Opportunities, and Threats (SWOT Analysis)

This involves analyzing a problem or proposed solution by categorizing internal and external factors into a 2×2 matrix: Strengths, Weaknesses as the internal rows; Opportunities and Threats as the external columns.

Systematically identifying these elements provides balanced insight to evaluate options and risks. It is impactful when evaluating alternative solutions or developing strategy amid complexity or uncertainty.

The key benefit of SWOT analysis is enabling multi-dimensional thinking when rationally evaluating options. Rather than getting anchored on just the upsides or the existing way of operating, it urges a systematic assessment through four different lenses:

• Internal Strengths: Our core competencies/advantages able to deliver success
• Internal Weaknesses: Gaps/vulnerabilities we need to manage
• External Opportunities: Ways we can differentiate/drive additional value
• External Threats: Risks we must navigate or mitigate

Multiperspective analysis provides the needed holistic view of the balanced risk vs. reward equation for strategic decision making amid uncertainty.

However, SWOT can feel restrictive if not tailored and evolved for different issue types.

Teams should view SWOT analysis as a starting point, augmenting it further for distinct scenarios.

An example is performing a SWOT analysis on whether a small business should expand into a new market – evaluating internal capabilities to execute vs. risks in the external competitive and demand environment to inform the growth decision with eyes wide open.

12. Compare Current vs Expected Performance (Gap Analysis)

This technique involves comparing the current state of performance, output, or results to the desired or expected levels to highlight shortfalls.

By quantifying the gaps, you can identify problem areas and prioritize address solutions.

Gap analysis is based on the simple principle – “you can’t improve what you don’t measure.” It enables facts-driven problem diagnosis by highlighting delta to goals, not just vague dissatisfaction that something seems wrong. And measurement immediately suggests improvement opportunities – address the biggest gaps first.

This data orientation also supports ROI analysis on fixing issues – the return from closing larger gaps outweighs narrowly targeting smaller performance deficiencies.

However, the approach is only effective if robust standards and metrics exist as the benchmark to evaluate against. Organizations should invest upfront in establishing performance frameworks.

Furthermore, while numbers are invaluable, the human context behind problems should not be ignored – quantitative versus qualitative gap assessment is optimally blended.

For example, if usage declines are noted during software gap analysis, this could be used as a signal to improve user experience through design.

13. Observe Processes from the Frontline (Gemba Walk)

A Gemba walk involves going to the actual place where work is done, directly observing the process, engaging with employees, and finding areas for improvement.

By experiencing firsthand rather than solely reviewing abstract reports, practical problems and ideas emerge.

The limitation is Gemba walks provide anecdotes not statistically significant data. It complements but does not replace comprehensive performance measurement.

An example is a factory manager inspecting the production line to spot jam areas based on direct reality rather than relying on throughput dashboards alone back in her office. Frontline insights prove invaluable.

14. Analyze Competitive Forces (Porter’s Five Forces)

This involves assessing the marketplace around a problem or business situation via five key factors: competitors, new entrants, substitute offerings, suppliers, and customer power.

Evaluating these forces illuminates risks and opportunities for strategy development and issue resolution. It is effective for understanding dynamic external threats and opportunities when operating in a contested space.

However, over-indexing on only external factors can overlook the internal capabilities needed to execute solutions.

A startup CEO, for example, may analyze market entry barriers, whitespace opportunities, and disruption risks across these five forces to shape new product rollout strategies and marketing approaches.

15. Think from Different Perspectives (Six Thinking Hats)

The Six Thinking Hats is a technique developed by Edward de Bono that encourages people to think about a problem from six different perspectives, each represented by a colored “thinking hat.”

The key benefit of this strategy is that it pushes team members to move outside their usual thinking style and consider new angles. This brings more diverse ideas and solutions to the table.

It works best for complex problems that require innovative solutions and when a team is stuck in an unproductive debate. The structured framework keeps the conversation flowing in a positive direction.

Limitations are that it requires training on the method itself and may feel unnatural at first. Team dynamics can also influence success – some members may dominate certain “hats” while others remain quiet.

A real-life example is a software company debating whether to build a new feature. The white hat focuses on facts, red on gut feelings, black on potential risks, yellow on benefits, green on new ideas, and blue on process. This exposes more balanced perspectives before deciding.

Onethread centralizes diverse stakeholder communication onto one platform, ensuring all voices are incorporated when evaluating project tradeoffs, just as problem-solving should consider multifaceted solutions.

16. Visualize the Problem (Draw it Out)

Drawing out a problem involves creating visual representations like diagrams, flowcharts, and maps to work through challenging issues.

This strategy is helpful when dealing with complex situations with lots of interconnected components. The visuals simplify the complexity so you can thoroughly understand the problem and all its nuances.

Key benefits are that it allows more stakeholders to get on the same page regarding root causes and it sparks new creative solutions as connections are made visually.

However, simple problems with few variables don’t require extensive diagrams. Additionally, some challenges are so multidimensional that fully capturing every aspect is difficult.

A real-life example would be mapping out all the possible causes leading to decreased client satisfaction at a law firm. An intricate fishbone diagram with branches for issues like service delivery, technology, facilities, culture, and vendor partnerships allows the team to trace problems back to their origins and brainstorm targeted fixes.

17. Follow a Step-by-Step Procedure (Algorithms)

An algorithm is a predefined step-by-step process that is guaranteed to produce the correct solution if implemented properly.

Using algorithms is effective when facing problems that have clear, binary right and wrong answers. Algorithms work for mathematical calculations, computer code, manufacturing assembly lines, and scientific experiments.

Key benefits are consistency, accuracy, and efficiency. However, they require extensive upfront development and only apply to scenarios with strict parameters. Additionally, human error can lead to mistakes.

For example, crew members of fast food chains like McDonald’s follow specific algorithms for food prep – from grill times to ingredient amounts in sandwiches, to order fulfillment procedures. This ensures uniform quality and service across all locations. However, if a step is missed, errors occur.

The Problem-Solving Process

The problem-solving process typically includes defining the issue, analyzing details, creating solutions, weighing choices, acting, and reviewing results.

In the above, we have discussed several problem-solving strategies. For every problem-solving strategy, you have to follow these processes. Here’s a detailed step-by-step process of effective problem-solving:

Step 1: Identify the Problem

The problem-solving process starts with identifying the problem. This step involves understanding the issue’s nature, its scope, and its impact. Once the problem is clearly defined, it sets the foundation for finding effective solutions.

Identifying the problem is crucial. It means figuring out exactly what needs fixing. This involves looking at the situation closely, understanding what’s wrong, and knowing how it affects things. It’s about asking the right questions to get a clear picture of the issue. 

This step is important because it guides the rest of the problem-solving process. Without a clear understanding of the problem, finding a solution is much harder. It’s like diagnosing an illness before treating it. Once the problem is identified accurately, you can move on to exploring possible solutions and deciding on the best course of action.

Step 2: Break Down the Problem

Breaking down the problem is a key step in the problem-solving process. It involves dividing the main issue into smaller, more manageable parts. This makes it easier to understand and tackle each component one by one.

After identifying the problem, the next step is to break it down. This means splitting the big issue into smaller pieces. It’s like solving a puzzle by handling one piece at a time. 

By doing this, you can focus on each part without feeling overwhelmed. It also helps in identifying the root causes of the problem. Breaking down the problem allows for a clearer analysis and makes finding solutions more straightforward. 

Each smaller problem can be addressed individually, leading to an effective resolution of the overall issue. This approach not only simplifies complex problems but also aids in developing a systematic plan to solve them.

Step 3: Come up with potential solutions

Coming up with potential solutions is the third step in the problem-solving process. It involves brainstorming various options to address the problem, considering creativity and feasibility to find the best approach.

After breaking down the problem, it’s time to think of ways to solve it. This stage is about brainstorming different solutions. You look at the smaller issues you’ve identified and start thinking of ways to fix them. This is where creativity comes in. 

You want to come up with as many ideas as possible, no matter how out-of-the-box they seem. It’s important to consider all options and evaluate their pros and cons. This process allows you to gather a range of possible solutions. 

Later, you can narrow these down to the most practical and effective ones. This step is crucial because it sets the stage for deciding on the best solution to implement. It’s about being open-minded and innovative to tackle the problem effectively.

Step 4: Analyze the possible solutions

Analyzing the possible solutions is the fourth step in the problem-solving process. It involves evaluating each proposed solution’s advantages and disadvantages to determine the most effective and feasible option.

After coming up with potential solutions, the next step is to analyze them. This means looking closely at each idea to see how well it solves the problem. You weigh the pros and cons of every solution.

Consider factors like cost, time, resources, and potential outcomes. This analysis helps in understanding the implications of each option. It’s about being critical and objective, ensuring that the chosen solution is not only effective but also practical.

This step is vital because it guides you towards making an informed decision. It involves comparing the solutions against each other and selecting the one that best addresses the problem.

By thoroughly analyzing the options, you can move forward with confidence, knowing you’ve chosen the best path to solve the issue.

Step 5: Implement and Monitor the Solutions

Implementing and monitoring the solutions is the final step in the problem-solving process. It involves putting the chosen solution into action and observing its effectiveness, making adjustments as necessary.

Once you’ve selected the best solution, it’s time to put it into practice. This step is about action. You implement the chosen solution and then keep an eye on how it works. Monitoring is crucial because it tells you if the solution is solving the problem as expected. 

If things don’t go as planned, you may need to make some changes. This could mean tweaking the current solution or trying a different one. The goal is to ensure the problem is fully resolved. 

This step is critical because it involves real-world application. It’s not just about planning; it’s about doing and adjusting based on results. By effectively implementing and monitoring the solutions, you can achieve the desired outcome and solve the problem successfully.

Why This Process is Important

Following a defined process to solve problems is important because it provides a systematic, structured approach instead of a haphazard one. Having clear steps guides logical thinking, analysis, and decision-making to increase effectiveness. Key reasons it helps are:

• Clear Direction: This process gives you a clear path to follow, which can make solving problems less overwhelming.
• Better Solutions: Thoughtful analysis of root causes, iterative testing of solutions, and learning orientation lead to addressing the heart of issues rather than just symptoms.
• Saves Time and Energy: Instead of guessing or trying random things, this process helps you find a solution more efficiently.
• Improves Skills: The more you use this process, the better you get at solving problems. It’s like practicing a sport. The more you practice, the better you play.
• Maximizes collaboration: Involving various stakeholders in the process enables broader inputs. Their communication and coordination are streamlined through organized brainstorming and evaluation.
• Provides consistency: Standard methodology across problems enables building institutional problem-solving capabilities over time. Patterns emerge on effective techniques to apply to different situations.

The problem-solving process is a powerful tool that can help us tackle any challenge we face. By following these steps, we can find solutions that work and learn important skills along the way.

Key Skills for Efficient Problem Solving

Efficient problem-solving requires breaking down issues logically, evaluating options, and implementing practical solutions.

Key skills include critical thinking to understand root causes, creativity to brainstorm innovative ideas, communication abilities to collaborate with others, and decision-making to select the best way forward. Staying adaptable, reflecting on outcomes, and applying lessons learned are also essential.

With practice, these capacities will lead to increased personal and team effectiveness in systematically addressing any problem.

 Let’s explore the powers you need to become a problem-solving hero!

Critical Thinking and Analytical Skills

Critical thinking and analytical skills are vital for efficient problem-solving as they enable individuals to objectively evaluate information, identify key issues, and generate effective solutions. 

These skills facilitate a deeper understanding of problems, leading to logical, well-reasoned decisions. By systematically breaking down complex issues and considering various perspectives, individuals can develop more innovative and practical solutions, enhancing their problem-solving effectiveness.

Communication Skills

Effective communication skills are essential for efficient problem-solving as they facilitate clear sharing of information, ensuring all team members understand the problem and proposed solutions. 

These skills enable individuals to articulate issues, listen actively, and collaborate effectively, fostering a productive environment where diverse ideas can be exchanged and refined. By enhancing mutual understanding, communication skills contribute significantly to identifying and implementing the most viable solutions.

Decision-Making

Strong decision-making skills are crucial for efficient problem-solving, as they enable individuals to choose the best course of action from multiple alternatives. 

These skills involve evaluating the potential outcomes of different solutions, considering the risks and benefits, and making informed choices. Effective decision-making leads to the implementation of solutions that are likely to resolve problems effectively, ensuring resources are used efficiently and goals are achieved.

Planning and Prioritization

Planning and prioritization are key for efficient problem-solving, ensuring resources are allocated effectively to address the most critical issues first. This approach helps in organizing tasks according to their urgency and impact, streamlining efforts towards achieving the desired outcome efficiently.

Emotional Intelligence

Emotional intelligence enhances problem-solving by allowing individuals to manage emotions, understand others, and navigate social complexities. It fosters a positive, collaborative environment, essential for generating creative solutions and making informed, empathetic decisions.

Leadership skills drive efficient problem-solving by inspiring and guiding teams toward common goals. Effective leaders motivate their teams, foster innovation, and navigate challenges, ensuring collective efforts are focused and productive in addressing problems.

Time Management

Time management is crucial in problem-solving, enabling individuals to allocate appropriate time to each task. By efficiently managing time, one can ensure that critical problems are addressed promptly without neglecting other responsibilities.

Data Analysis

Data analysis skills are essential for problem-solving, as they enable individuals to sift through data, identify trends, and extract actionable insights. This analytical approach supports evidence-based decision-making, leading to more accurate and effective solutions.

Research Skills

Research skills are vital for efficient problem-solving, allowing individuals to gather relevant information, explore various solutions, and understand the problem’s context. This thorough exploration aids in developing well-informed, innovative solutions.

Becoming a great problem solver takes practice, but with these skills, you’re on your way to becoming a problem-solving hero. 

How to Improve Your Problem-Solving Skills?

Improving your problem-solving skills can make you a master at overcoming challenges. Learn from experts, practice regularly, welcome feedback, try new methods, experiment, and study others’ success to become better.

Learning from Experts

Improving problem-solving skills by learning from experts involves seeking mentorship, attending workshops, and studying case studies. Experts provide insights and techniques that refine your approach, enhancing your ability to tackle complex problems effectively.

To enhance your problem-solving skills, learning from experts can be incredibly beneficial. Engaging with mentors, participating in specialized workshops, and analyzing case studies from seasoned professionals can offer valuable perspectives and strategies. 

Experts share their experiences, mistakes, and successes, providing practical knowledge that can be applied to your own problem-solving process. This exposure not only broadens your understanding but also introduces you to diverse methods and approaches, enabling you to tackle challenges more efficiently and creatively.

Improving problem-solving skills through practice involves tackling a variety of challenges regularly. This hands-on approach helps in refining techniques and strategies, making you more adept at identifying and solving problems efficiently.

One of the most effective ways to enhance your problem-solving skills is through consistent practice. By engaging with different types of problems on a regular basis, you develop a deeper understanding of various strategies and how they can be applied. 

This hands-on experience allows you to experiment with different approaches, learn from mistakes, and build confidence in your ability to tackle challenges.

Regular practice not only sharpens your analytical and critical thinking skills but also encourages adaptability and innovation, key components of effective problem-solving.

Openness to Feedback

Being open to feedback is like unlocking a secret level in a game. It helps you boost your problem-solving skills. Improving problem-solving skills through openness to feedback involves actively seeking and constructively responding to critiques. 

This receptivity enables you to refine your strategies and approaches based on insights from others, leading to more effective solutions. 

Learning New Approaches and Methodologies

Learning new approaches and methodologies is like adding new tools to your toolbox. It makes you a smarter problem-solver. Enhancing problem-solving skills by learning new approaches and methodologies involves staying updated with the latest trends and techniques in your field. 

This continuous learning expands your toolkit, enabling innovative solutions and a fresh perspective on challenges.

Experimentation

Experimentation is like being a scientist of your own problems. It’s a powerful way to improve your problem-solving skills. Boosting problem-solving skills through experimentation means trying out different solutions to see what works best. This trial-and-error approach fosters creativity and can lead to unique solutions that wouldn’t have been considered otherwise.

Analyzing Competitors’ Success

Analyzing competitors’ success is like being a detective. It’s a smart way to boost your problem-solving skills. Improving problem-solving skills by analyzing competitors’ success involves studying their strategies and outcomes. Understanding what worked for them can provide valuable insights and inspire effective solutions for your own challenges. 

Challenges in Problem-Solving

Facing obstacles when solving problems is common. Recognizing these barriers, like fear of failure or lack of information, helps us find ways around them for better solutions.

Fear of Failure

Fear of failure is like a big, scary monster that stops us from solving problems. It’s a challenge many face. Because being afraid of making mistakes can make us too scared to try new solutions. 

How can we overcome this? First, understand that it’s okay to fail. Failure is not the opposite of success; it’s part of learning. Every time we fail, we discover one more way not to solve a problem, getting us closer to the right solution. Treat each attempt like an experiment. It’s not about failing; it’s about testing and learning.

Lack of Information

Lack of information is like trying to solve a puzzle with missing pieces. It’s a big challenge in problem-solving. Because without all the necessary details, finding a solution is much harder. 

How can we fix this? Start by gathering as much information as you can. Ask questions, do research, or talk to experts. Think of yourself as a detective looking for clues. The more information you collect, the clearer the picture becomes. Then, use what you’ve learned to think of solutions. 

Fixed Mindset

A fixed mindset is like being stuck in quicksand; it makes solving problems harder. It means thinking you can’t improve or learn new ways to solve issues. 

How can we change this? First, believe that you can grow and learn from challenges. Think of your brain as a muscle that gets stronger every time you use it. When you face a problem, instead of saying “I can’t do this,” try thinking, “I can’t do this yet.” Look for lessons in every challenge and celebrate small wins. 

Everyone starts somewhere, and mistakes are just steps on the path to getting better. By shifting to a growth mindset, you’ll see problems as opportunities to grow. Keep trying, keep learning, and your problem-solving skills will soar!

Jumping to Conclusions

Jumping to conclusions is like trying to finish a race before it starts. It’s a challenge in problem-solving. That means making a decision too quickly without looking at all the facts. 

How can we avoid this? First, take a deep breath and slow down. Think about the problem like a puzzle. You need to see all the pieces before you know where they go. Ask questions, gather information, and consider different possibilities. Don’t choose the first solution that comes to mind. Instead, compare a few options. 

Feeling Overwhelmed

Feeling overwhelmed is like being buried under a mountain of puzzles. It’s a big challenge in problem-solving. When we’re overwhelmed, everything seems too hard to handle. 

How can we deal with this? Start by taking a step back. Breathe deeply and focus on one thing at a time. Break the big problem into smaller pieces, like sorting puzzle pieces by color. Tackle each small piece one by one. It’s also okay to ask for help. Sometimes, talking to someone else can give you a new perspective. 

Confirmation Bias

Confirmation bias is like wearing glasses that only let you see what you want to see. It’s a challenge in problem-solving. Because it makes us focus only on information that agrees with what we already believe, ignoring anything that doesn’t. 

How can we overcome this? First, be aware that you might be doing it. It’s like checking if your glasses are on right. Then, purposely look for information that challenges your views. It’s like trying on a different pair of glasses to see a new perspective. Ask questions and listen to answers, even if they don’t fit what you thought before.

Groupthink is like everyone in a group deciding to wear the same outfit without asking why. It’s a challenge in problem-solving. It means making decisions just because everyone else agrees, without really thinking it through. 

How can we avoid this? First, encourage everyone in the group to share their ideas, even if they’re different. It’s like inviting everyone to show their unique style of clothes. 

Listen to all opinions and discuss them. It’s okay to disagree; it helps us think of better solutions. Also, sometimes, ask someone outside the group for their thoughts. They might see something everyone in the group missed.

Overcoming obstacles in problem-solving requires patience, openness, and a willingness to learn from mistakes. By recognizing these barriers, we can develop strategies to navigate around them, leading to more effective and creative solutions.

What are the most common problem-solving techniques?

The most common techniques include brainstorming, the 5 Whys, mind mapping, SWOT analysis, and using algorithms or heuristics. Each approach has its strengths, suitable for different types of problems.

What’s the best problem-solving strategy for every situation?

There’s no one-size-fits-all strategy. The best approach depends on the problem’s complexity, available resources, and time constraints. Combining multiple techniques often yields the best results.

How can I improve my problem-solving skills?

Improve your problem-solving skills by practicing regularly, learning from experts, staying open to feedback, and continuously updating your knowledge on new approaches and methodologies.

Are there any tools or resources to help with problem-solving?

Yes, tools like mind mapping software, online courses on critical thinking, and books on problem-solving techniques can be very helpful. Joining forums or groups focused on problem-solving can also provide support and insights.

What are some common mistakes people make when solving problems?

Common mistakes include jumping to conclusions without fully understanding the problem, ignoring valuable feedback, sticking to familiar solutions without considering alternatives, and not breaking down complex problems into manageable parts.

Final Words

Mastering problem-solving strategies equips us with the tools to tackle challenges across all areas of life. By understanding and applying these techniques, embracing a growth mindset, and learning from both successes and obstacles, we can transform problems into opportunities for growth. Continuously improving these skills ensures we’re prepared to face and solve future challenges more effectively.

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Learn Creative Problem Solving Techniques to Stimulate Innovation in Your Organization

By Kate Eby | October 20, 2017 (updated August 27, 2021)

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In today’s competitive business landscape, organizations need processes in place to make strong, well-informed, and innovative decisions. Problem solving - in particular creative problem solving (CPS) - is a key skill in learning how to accurately identify problems and their causes, generate potential solutions, and evaluate all the possibilities to arrive at a strong corrective course of action. Every team in any organization, regardless of department or industry, needs to be effective, creative, and quick when solving problems. 

In this article, we’ll discuss traditional and creative problem solving, and define the steps, best practices, and common barriers associated. After that, we’ll provide helpful methods and tools to identify the cause(s) of problematic situations, so you can get to the root of the issue and start to generate solutions. Then, we offer nearly 20 creative problem solving techniques to implement at your organization, or even in your personal life. Along the way, experts weigh in on the importance of problem solving, and offer tips and tricks. 

What Is Problem Solving and Decision Making?

Problem solving is the process of working through every aspect of an issue or challenge to reach a solution. Decision making is choosing one of multiple proposed solutions  — therefore, this process also includes defining and evaluating all potential options. Decision making is often one step of the problem solving process, but the two concepts are distinct. 

Collective problem solving is problem solving that includes many different parties and bridges the knowledge of different groups. Collective problem solving is common in business problem solving because workplace decisions typically affect more than one person. 

Problem solving, especially in business, is a complicated science. Not only are business conflicts multifaceted, but they often involve different personalities, levels of authority, and group dynamics. In recent years, however, there has been a rise in psychology-driven problem solving techniques, especially for the workplace. In fact, the psychology of how people solve problems is now studied formally in academic disciplines such as psychology and cognitive science.

Joe Carella is the Assistant Dean for Executive Education at the University of Arizona . Joe has over 20 years of experience in helping executives and corporations in managing change and developing successful business strategies. His doctoral research and executive education engagements have seen him focus on corporate strategy, decision making and business performance with a variety of corporate clients including Hershey’s, Chevron, Fender Musical Instruments Corporation, Intel, DP World, Essilor, BBVA Compass Bank.

He explains some of the basic psychology behind problem solving: “When our brain is engaged in the process of solving problems, it is engaged in a series of steps where it processes and organizes the information it receives while developing new knowledge it uses in future steps. Creativity is embedded in this process by incorporating diverse inputs and/or new ways of organizing the information received.”

Laura MacLeod is a Professor of Social Group Work at City University of New York, and the creator of From The Inside Out Project® , a program that coaches managers in team leadership for a variety of workplaces. She has a background in social work and over two decades of experience as a union worker, and currently leads talks on conflict resolution, problem solving, and listening skills at conferences across the country. 

MacLeod thinks of problem solving as an integral practice of successful organizations. “Problem solving is a collaborative process — all voices are heard and connected, and resolution is reached by the group,” she says. “Problems and conflicts occur in all groups and teams in the workplace, but if leaders involve everyone in working through, they will foster cohesion, engagement, and buy in. Everybody wins.”

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What Is the First Step in Solving a Problem?

Although problem solving techniques vary procedurally, experts agree that the first step in solving a problem is defining the problem. Without a clear articulation of the problem at stake, it is impossible to analyze all the key factors and actors, generate possible solutions, and then evaluate them to pick the best option. 

Dr. Elliott Jaffa is a behavioral and management psychologist with over 25 years of problem solving training and management experience. “Start with defining the problem you want to solve,” he says, “And then define where you want to be, what you want to come away with.” He emphasizes these are the first steps in creating an actionable, clear solution. 

Bryan Mattimore is Co-Founder of Growth Engine, an 18-year old innovation agency based in Norwalk, CT. Bryan has facilitated over 1,000 ideation sessions and managed over 200 successful innovation projects leading to over $3 billion in new sales. His newest book is 21 Days to a Big Idea . When asked about the first critical component to successful problem solving, Mattimore says, “Defining the challenge correctly, or ‘solving the right problem’ … The three creative techniques we use to help our clients ‘identify the right problem to be solved’ are questioning assumptions, 20 questions, and problem redefinition. A good example of this was a new product challenge from a client to help them ‘invent a new iron. We got them to redefine the challenge as first: a) inventing new anti-wrinkle devices, and then b) inventing new garment care devices.”

What Are Problem Solving Skills?

To understand the necessary skills in problem solving, you should first understand the types of thinking often associated with strong decision making. Most problem solving techniques look for a balance between the following binaries:

• Convergent vs. Divergent Thinking: Convergent thinking is bringing together disparate information or ideas to determine a single best answer or solution. This thinking style values logic, speed, and accuracy, and leaves no chance for ambiguity. Divergent thinking is focused on generating new ideas to identify and evaluate multiple possible solutions, often uniting ideas in unexpected combinations. Divergent thinking is characterized by creativity, complexity, curiosity, flexibility, originality, and risk-taking.
• Pragmatics vs. Semantics: Pragmatics refer to the logic of the problem at hand, and semantics is how you interpret the problem to solve it. Both are important to yield the best possible solution.
• Mathematical vs. Personal Problem Solving: Mathematical problem solving involves logic (usually leading to a single correct answer), and is useful for problems that involve numbers or require an objective, clear-cut solution. However, many workplace problems also require personal problem solving, which includes interpersonal, collaborative, and emotional intuition and skills. 

The following basic methods are fundamental problem solving concepts. Implement them to help balance the above thinking models.

• Reproductive Thinking: Reproductive thinking uses past experience to solve a problem. However, be careful not to rely too heavily on past solutions, and to evaluate current problems individually, with their own factors and parameters. 
• Idea Generation: The process of generating many possible courses of action to identify a solution. This is most commonly a team exercise because putting everyone’s ideas on the table will yield the greatest number of potential solutions. 

However, many of the most critical problem solving skills are “soft” skills: personal and interpersonal understanding, intuitiveness, and strong listening. 

Mattimore expands on this idea: “The seven key skills to be an effective creative problem solver that I detail in my book Idea Stormers: How to Lead and Inspire Creative Breakthroughs are: 1) curiosity 2) openness 3) a willingness to embrace ambiguity 4) the ability to identify and transfer principles across categories and disciplines 5) the desire to search for integrity in ideas, 6) the ability to trust and exercise “knowingness” and 7) the ability to envision new worlds (think Dr. Seuss, Star Wars, Hunger Games, Harry Potter, etc.).”

“As an individual contributor to problem solving it is important to exercise our curiosity, questioning, and visioning abilities,” advises Carella. “As a facilitator it is essential to allow for diverse ideas to emerge, be able to synthesize and ‘translate’ other people’s thinking, and build an extensive network of available resources.”

MacLeod says the following interpersonal skills are necessary to effectively facilitate group problem solving: “The abilities to invite participation (hear all voices, encourage silent members), not take sides, manage dynamics between the monopolizer, the scapegoat, and the bully, and deal with conflict (not avoiding it or shutting down).” 

Furthermore, Jaffa explains that the skills of a strong problem solver aren’t measurable. The best way to become a creative problem solver, he says, is to do regular creative exercises that keep you sharp and force you to think outside the box. Carella echoes this sentiment: “Neuroscience tells us that creativity comes from creating novel neural paths. Allow a few minutes each day to exercise your brain with novel techniques and brain ‘tricks’ – read something new, drive to work via a different route, count backwards, smell a new fragrance, etc.”

What Is Creative Problem Solving? History, Evolution, and Core Principles

Creative problem solving (CPS) is a method of problem solving in which you approach a problem or challenge in an imaginative, innovative way. The goal of CPS is to come up with innovative solutions, make a decision, and take action quickly. Sidney Parnes and Alex Osborn are credited with developing the creative problem solving process in the 1950s. The concept was further studied and developed at SUNY Buffalo State and the Creative Education Foundation. 

The core principles of CPS include the following:

• Balance divergent and convergent thinking
• Ask problems as questions
• Defer or suspend judgement
• Focus on “Yes, and…” rather than “No, but…”

According to Carella, “Creative problem solving is the mental process used for generating innovative and imaginative ideas as a solution to a problem or a challenge. Creative problem solving techniques can be pursued by individuals or groups.”

When asked to define CPS, Jaffa explains that it is, by nature, difficult to create boundaries for. “Creative problem solving is not cut and dry,” he says, “If you ask 100 different people the definition of creative problem solving, you’ll get 100 different responses - it’s a non-entity.”

Business presents a unique need for creative problem solving. Especially in today’s competitive landscape, organizations need to iterate quickly, innovate with intention, and constantly be at the cutting-edge of creativity and new ideas to succeed. Developing CPS skills among your workforce not only enables you to make faster, stronger in-the-moment decisions, but also inspires a culture of collaborative work and knowledge sharing. When people work together to generate multiple novel ideas and evaluate solutions, they are also more likely to arrive at an effective decision, which will improve business processes and reduce waste over time. In fact, CPS is so important that some companies now list creative problem solving skills as a job criteria.

MacLeod reiterates the vitality of creative problem solving in the workplace. “Problem solving is crucial for all groups and teams,” she says. “Leaders need to know how to guide the process, hear all voices and involve all members - it’s not easy.”

“This mental process [of CPS] is especially helpful in work environments where individuals and teams continuously struggle with new problems and challenges posed by their continuously changing environment,” adds Carella. 

Problem Solving Best Practices

By nature, creative problem solving does not have a clear-cut set of do’s and don’ts. Rather, creating a culture of strong creative problem solvers requires flexibility, adaptation, and interpersonal skills. However, there are a several best practices that you should incorporate:

• Use a Systematic Approach: Regardless of the technique you use, choose a systematic method that satisfies your workplace conditions and constraints (time, resources, budget, etc.). Although you want to preserve creativity and openness to new ideas, maintaining a structured approach to the process will help you stay organized and focused. 
• View Problems as Opportunities: Rather than focusing on the negatives or giving up when you encounter barriers, treat problems as opportunities to enact positive change on the situation. In fact, some experts even recommend defining problems as opportunities, to remain proactive and positive.
• Change Perspective: Remember that there are multiple ways to solve any problem. If you feel stuck, changing perspective can help generate fresh ideas. A perspective change might entail seeking advice of a mentor or expert, understanding the context of a situation, or taking a break and returning to the problem later. “A sterile or familiar environment can stifle new thinking and new perspectives,” says Carella. “Make sure you get out to draw inspiration from spaces and people out of your usual reach.”
• Break Down Silos: To invite the greatest possible number of perspectives to any problem, encourage teams to work cross-departmentally. This not only combines diverse expertise, but also creates a more trusting and collaborative environment, which is essential to effective CPS. According to Carella, “Big challenges are always best tackled by a group of people rather than left to a single individual. Make sure you create a space where the team can concentrate and convene.”
• Employ Strong Leadership or a Facilitator: Some companies choose to hire an external facilitator that teaches problem solving techniques, best practices, and practicums to stimulate creative problem solving. But, internal managers and staff can also oversee these activities. Regardless of whether the facilitator is internal or external, choose a strong leader who will value others’ ideas and make space for creative solutions.  Mattimore has specific advice regarding the role of a facilitator: “When facilitating, get the group to name a promising idea (it will crystalize the idea and make it more memorable), and facilitate deeper rather than broader. Push for not only ideas, but how an idea might specifically work, some of its possible benefits, who and when would be interested in an idea, etc. This fleshing-out process with a group will generate fewer ideas, but at the end of the day will yield more useful concepts that might be profitably pursued.” Additionally, Carella says that “Executives and managers don’t necessarily have to be creative problem solvers, but need to make sure that their teams are equipped with the right tools and resources to make this happen. Also they need to be able to foster an environment where failing fast is accepted and celebrated.”
• Evaluate Your Current Processes: This practice can help you unlock bottlenecks, and also identify gaps in your data and information management, both of which are common roots of business problems.

MacLeod offers the following additional advice, “Always get the facts. Don’t jump too quickly to a solution – working through [problems] takes time and patience.”

Mattimore also stresses that how you introduce creative problem solving is important. “Do not start by introducing a new company-wide innovation process,” he says. “Instead, encourage smaller teams to pursue specific creative projects, and then build a process from the ground up by emulating these smaller teams’ successful approaches. We say: ‘You don’t innovate by changing the culture, you change the culture by innovating.’”

Barriers to Effective Problem Solving

Learning how to effectively solve problems is difficult and takes time and continual adaptation. There are several common barriers to successful CPS, including:

• Confirmation Bias: The tendency to only search for or interpret information that confirms a person’s existing ideas. People misinterpret or disregard data that doesn’t align with their beliefs.
• Mental Set: People’s inclination to solve problems using the same tactics they have used to solve problems in the past. While this can sometimes be a useful strategy (see Analogical Thinking in a later section), it often limits inventiveness and creativity.
• Functional Fixedness: This is another form of narrow thinking, where people become “stuck” thinking in a certain way and are unable to be flexible or change perspective.
• Unnecessary Constraints: When people are overwhelmed with a problem, they can invent and impose additional limits on solution avenues. To avoid doing this, maintain a structured, level-headed approach to evaluating causes, effects, and potential solutions.
• Groupthink: Be wary of the tendency for group members to agree with each other — this might be out of conflict avoidance, path of least resistance, or fear of speaking up. While this agreeableness might make meetings run smoothly, it can actually stunt creativity and idea generation, therefore limiting the success of your chosen solution.
• Irrelevant Information: The tendency to pile on multiple problems and factors that may not even be related to the challenge at hand. This can cloud the team’s ability to find direct, targeted solutions.
• Paradigm Blindness: This is found in people who are unwilling to adapt or change their worldview, outlook on a particular problem, or typical way of processing information. This can erode the effectiveness of problem solving techniques because they are not aware of the narrowness of their thinking, and therefore cannot think or act outside of their comfort zone.

According to Jaffa, the primary barrier of effective problem solving is rigidity. “The most common things people say are, ‘We’ve never done it before,’ or ‘We’ve always done it this way.’” While these feelings are natural, Jaffa explains that this rigid thinking actually precludes teams from identifying creative, inventive solutions that result in the greatest benefit.

“The biggest barrier to creative problem solving is a lack of awareness – and commitment to – training employees in state-of-the-art creative problem-solving techniques,” Mattimore explains. “We teach our clients how to use ideation techniques (as many as two-dozen different creative thinking techniques) to help them generate more and better ideas. Ideation techniques use specific and customized stimuli, or ‘thought triggers’ to inspire new thinking and new ideas.” 

MacLeod adds that ineffective or rushed leadership is another common culprit. “We're always in a rush to fix quickly,” she says. “Sometimes leaders just solve problems themselves, making unilateral decisions to save time. But the investment is well worth it — leaders will have less on their plates if they can teach and eventually trust the team to resolve. Teams feel empowered and engagement and investment increases.”

Strategies for Problem Cause Identification

As discussed, most experts agree that the first and most crucial step in problem solving is defining the problem. Once you’ve done this, however, it may not be appropriate to move straight to the solution phase. Rather, it is often helpful to identify the cause(s) of the problem: This will better inform your solution planning and execution, and help ensure that you don’t fall victim to the same challenges in the future. 

Below are some of the most common strategies for identifying the cause of a problem:

• Root Cause Analysis: This method helps identify the most critical cause of a problem. A factor is considered a root cause if removing it prevents the problem from recurring. Performing a root cause analysis is a 12 step process that includes: define the problem, gather data on the factors contributing to the problem, group the factors based on shared characteristics, and create a cause-and-effect timeline to determine the root cause. After that, you identify and evaluate corrective actions to eliminate the root cause.

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Problem Solving Techniques and Strategies

In this section, we’ll explain several traditional and creative problem solving methods that you can use to identify challenges, create actionable goals, and resolve problems as they arise. Although there is often procedural and objective crossover among techniques, they are grouped by theme so you can identify which method works best for your organization.

Divergent Creative Problem Solving Techniques

Brainstorming: One of the most common methods of divergent thinking, brainstorming works best in an open group setting where everyone is encouraged to share their creative ideas. The goal is to generate as many ideas as possible – you analyze, critique, and evaluate the ideas only after the brainstorming session is complete. To learn more specific brainstorming techniques, read this article . 

Mind Mapping: This is a visual thinking tool where you graphically depict concepts and their relation to one another. You can use mind mapping to structure the information you have, analyze and synthesize it, and generate solutions and new ideas from there. The goal of a mind map is to simplify complicated problems so you can more clearly identify solutions.

Appreciative Inquiry (AI): The basic assumption of AI is that “an organization is a mystery to be embraced.” Using this principle, AI takes a positive, inquisitive approach to identifying the problem, analyzing the causes, and presenting possible solutions. The five principles of AI emphasize dialogue, deliberate language and outlook, and social bonding. 

Lateral Thinking: This is an indirect problem solving approach centered on the momentum of idea generation. As opposed to critical thinking, where people value ideas based on their truth and the absence of errors, lateral thinking values the “movement value” of new ideas: This means that you reward team members for producing a large volume of new ideas rapidly. With this approach, you’ll generate many new ideas before approving or rejecting any.

Problem Solving Techniques to Change Perspective

Constructive Controversy: This is a structured approach to group decision making to preserve critical thinking and disagreement while maintaining order. After defining the problem and presenting multiple courses of action, the group divides into small advocacy teams who research, analyze, and refute a particular option. Once each advocacy team has presented its best-case scenario, the group has a discussion (advocacy teams still defend their presented idea). Arguing and playing devil’s advocate is encouraged to reach an understanding of the pros and cons of each option. Next, advocacy teams abandon their cause and evaluate the options openly until they reach a consensus. All team members formally commit to the decision, regardless of whether they advocated for it at the beginning. You can learn more about the goals and steps in constructive controversy here . 

Carella is a fan of this approach. “Create constructive controversy by having two teams argue the pros and cons of a certain idea,” he says. “It forces unconscious biases to surface and gives space for new ideas to formulate.”

Abstraction: In this method, you apply the problem to a fictional model of the current situation. Mapping an issue to an abstract situation can shed extraneous or irrelevant factors, and reveal places where you are overlooking obvious solutions or becoming bogged down by circumstances. 

Analogical Thinking: Also called analogical reasoning , this method relies on an analogy: using information from one problem to solve another problem (these separate problems are called domains). It can be difficult for teams to create analogies among unrelated problems, but it is a strong technique to help you identify repeated issues, zoom out and change perspective, and prevent the problems from occurring in the future. .

CATWOE: This framework ensures that you evaluate the perspectives of those whom your decision will impact. The factors and questions to consider include (which combine to make the acronym CATWOE):

• Customers: Who is on the receiving end of your decisions? What problem do they currently have, and how will they react to your proposed solution?
• Actors: Who is acting to bring your solution to fruition? How will they respond and be affected by your decision?
• Transformation Process: What processes will you employ to transform your current situation and meet your goals? What are the inputs and outputs?
• World View: What is the larger context of your proposed solution? What is the larger, big-picture problem you are addressing?
• Owner: Who actually owns the process? How might they influence your proposed solution (positively or negatively), and how can you influence them to help you?
• Environmental Constraints: What are the limits (environmental, resource- and budget-wise, ethical, legal, etc.) on your ideas? How will you revise or work around these constraints?

Complex Problem Solving

Soft Systems Methodology (SSM): For extremely complex problems, SSM can help you identify how factors interact, and determine the best course of action. SSM was borne out of organizational process modeling and general systems theory, which hold that everything is part of a greater, interconnected system: This idea works well for “hard” problems (where logic and a single correct answer are prioritized), and less so for “soft” problems (i.e., human problems where factors such as personality, emotions, and hierarchy come into play). Therefore, SSM defines a seven step process for problem solving: 

• Begin with the problem or problematic situation 
• Express the problem or situation and build a rich picture of the themes of the problem 
• Identify the root causes of the problem (most commonly with CATWOE)
• Build conceptual models of human activity surrounding the problem or situation
• Compare models with real-world happenings
• Identify changes to the situation that are both feasible and desirable
• Take action to implement changes and improve the problematic situation

SSM can be used for any complex soft problem, and is also a useful tool in change management . 

Failure Mode and Effects Analysis (FMEA): This method helps teams anticipate potential problems and take steps to mitigate them. Use FMEA when you are designing (redesigning) a complex function, process, product, or service. First, identify the failure modes, which are the possible ways that a project could fail. Then, perform an effects analysis to understand the consequences of each of the potential downfalls. This exercise is useful for internalizing the severity of each potential failure and its effects so you can make adjustments or safeties in your plan. 

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Problem Solving Based on Data or Logic (Heuristic Methods)

TRIZ: A Russian-developed problem solving technique that values logic, analysis, and forecasting over intuition or soft reasoning. TRIZ (translated to “theory of inventive problem solving” or TIPS in English) is a systematic approach to defining and identifying an inventive solution to difficult problems. The method offers several strategies for arriving at an inventive solution, including a contradictions matrix to assess trade-offs among solutions, a Su-Field analysis which uses formulas to describe a system by its structure, and ARIZ (algorithm of inventive problem solving) which uses algorithms to find inventive solutions. 

Inductive Reasoning: A logical method that uses evidence to conclude that a certain answer is probable (this is opposed to deductive reasoning, where the answer is assumed to be true). Inductive reasoning uses a limited number of observations to make useful, logical conclusions (for example, the Scientific Method is an extreme example of inductive reasoning). However, this method doesn’t always map well to human problems in the workplace — in these instances, managers should employ intuitive inductive reasoning , which allows for more automatic, implicit conclusions so that work can progress. This, of course, retains the principle that these intuitive conclusions are not necessarily the one and only correct answer. 

Process-Oriented Problem Solving Methods

Plan Do Check Act (PDCA): This is an iterative management technique used to ensure continual improvement of products or processes. First, teams plan (establish objectives to meet desired end results), then do (implement the plan, new processes, or produce the output), then check (compare expected with actual results), and finally act (define how the organization will act in the future, based on the performance and knowledge gained in the previous three steps). 

Means-End Analysis (MEA): The MEA strategy is to reduce the difference between the current (problematic) state and the goal state. To do so, teams compile information on the multiple factors that contribute to the disparity between the current and goal states. Then they try to change or eliminate the factors one by one, beginning with the factor responsible for the greatest difference in current and goal state. By systematically tackling the multiple factors that cause disparity between the problem and desired outcome, teams can better focus energy and control each step of the process. 

Hurson’s Productive Thinking Model: This technique was developed by Tim Hurson, and is detailed in his 2007 book Think Better: An Innovator’s Guide to Productive Thinking . The model outlines six steps that are meant to give structure while maintaining creativity and critical thinking: 1) Ask “What is going on?” 2) Ask “What is success?” 3) Ask “What is the question?” 4) Generate answers 5) Forge the solution 6) Align resources. 

Control Influence Accept (CIA): The basic premise of CIA is that how you respond to problems determines how successful you will be in overcoming them. Therefore, this model is both a problem solving technique and stress-management tool that ensures you aren’t responding to problems in a reactive and unproductive way. The steps in CIA include:

• Control: Identify the aspects of the problem that are within your control.
• Influence: Identify the aspects of the problem that you cannot control, but that you can influence.
• Accept: Identify the aspects of the problem that you can neither control nor influence, and react based on this composite information. 

GROW Model: This is a straightforward problem solving method for goal setting that clearly defines your goals and current situation, and then asks you to define the potential solutions and be realistic about your chosen course of action. The steps break down as follows:

• Goal: What do you want?
• Reality: Where are you now?
• Options: What could you do?
• Will: What will you do?

OODA Loop: This acronym stands for observe, orient, decide, and act. This approach is a decision-making cycle that values agility and flexibility over raw human force. It is framed as a loop because of the understanding that any team will continually encounter problems or opponents to success and have to overcome them.

There are also many un-named creative problem solving techniques that follow a sequenced series of steps. While the exact steps vary slightly, they all follow a similar trajectory and aim to accomplish similar goals of problem, cause, and goal identification, idea generation, and active solution implementation.

MacLeod offers her own problem solving procedure, which echoes the above steps:

“1. Recognize the Problem: State what you see. Sometimes the problem is covert. 2. Identify: Get the facts — What exactly happened? What is the issue? 3. and 4. Explore and Connect: Dig deeper and encourage group members to relate their similar experiences. Now you're getting more into the feelings and background [of the situation], not just the facts.  5. Possible Solutions: Consider and brainstorm ideas for resolution. 6. Implement: Choose a solution and try it out — this could be role play and/or a discussion of how the solution would be put in place.  7. Evaluate: Revisit to see if the solution was successful or not.”

Many of these problem solving techniques can be used in concert with one another, or multiple can be appropriate for any given problem. It’s less about facilitating a perfect CPS session, and more about encouraging team members to continually think outside the box and push beyond personal boundaries that inhibit their innovative thinking. So, try out several methods, find those that resonate best with your team, and continue adopting new techniques and adapting your processes along the way. 

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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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Flow Charts Video

Video transcript.

Learn how to use flow charts to explain how processes work clearly to your team.

Have you ever had to teach someone how to do a new task, or use a new process? If so, you'll know how easy it is for them to misunderstand instructions, or even forget them, along the way.

This is why flow charts are so useful.

Flow charts show a step-by-step picture of a process or task. Certain actions are represented by standard symbols so that people can quickly understand what they need to do at each stage.

Most flow charts use three main shapes. The first is an elongated circle. This signifies the start or the end of the process. The next is a rectangle, which represents instructions or actions. The other is a diamond. This indicates where a decision needs to be made.

All of these symbols are connected to one another by arrows, which show the flow of activity from one step to the next.

There are many other symbols that you can use, but keep in mind that these charts are used for communication . If you include a lot of obscure shapes, people might get confused. It's best to keep things as simple as possible.

Before you create your flow chart, brainstorm   every step that must be taken, and every decision that must be made, to complete the process successfully. Ask yourself, "What really needs to happen in this process? Does a decision need to be made before the next step?"

When you're ready to draw your flow chart, start with the elongated circle. Then, move on to the next stage of the process.

For instance, imagine you're creating a flow chart to show your team how to handle customer calls. The first step is to answer the phone and to say, "How can I help you?" This is an action, so it would go into a rectangle. Then, your team must respond to the customer's query. This involves a decision, so this step would go into a diamond shape.

Your flow chart is going to divide into different directions here, since there are several options to consider. First, the customer might want to place an order. So you'd draw an arrowed line off to one side to create a new set of steps for product ordering. If the customer needs help with a product-related problem, then you would do the same but going straight down.

Once you've completed your flow chart, so that every step, action and decision is represented in it, your team should be able to answer customer calls correctly just by looking at it.

You can find out more about using flow charts in the article   that accompanies this video.

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Comments (4)

• Over a month ago Midgie wrote What I like about flow charts is that it can capture a process in an easy to follow diagram. Although written procedures are good to explain how each step works, a flow chart diagram gives you a picture 'at a glance'! I'm going to be getting my toastmasters committee to produce flow charts of what they do so that anyone else on the committee can pick up their responsibility and do it, if need be! The intention is to streamline the flow of work and make our workings as a club more efficient! Who else has experiences with flow charts and what has it been like? Midgie
• Over a month ago RuthH wrote Hi Everyone We’ve given this popular article a review, and the updated version is now at : http://www.mindtools.com/community/pages/article/newTMC_97.php Discuss the article by replying to this post! Thanks Ruth
• Over a month ago James wrote Hi everyone Just letting your know that we’ve just published a new video for this topic. Click here to watch the video: http://www.mindtools.com/community/pages/main/videos.php#flow-charts James

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What is a Flowchart?   Flowchart is a graphical representation of an algorithm. Programmers often use it as a program-planning tool to solve a problem. It makes use of symbols which are connected among them to indicate the flow of information and processing.  The process of drawing a flowchart for an algorithm is known as “flowcharting”. 

Basic Symbols used in Flowchart Designs

• Terminal: The oval symbol indicates Start, Stop and Halt in a program’s logic flow. A pause/halt is generally used in a program logic under some error conditions. Terminal is the first and last symbols in the flowchart.   

• Input/Output: A parallelogram denotes any function of input/output type. Program instructions that take input from input devices and display output on output devices are indicated with parallelogram in a flowchart.   

• Processing: A box represents arithmetic instructions. All arithmetic processes such as adding, subtracting, multiplication and division are indicated by action or process symbol.   

• Decision Diamond symbol represents a decision point. Decision based operations such as yes/no question or true/false are indicated by diamond in flowchart.   

• Connectors: Whenever flowchart becomes complex or it spreads over more than one page, it is useful to use connectors to avoid any confusions. It is represented by a circle.   

• Flow lines: Flow lines indicate the exact sequence in which instructions are executed. Arrows represent the direction of flow of control and relationship among different symbols of flowchart. 

Rules For Creating Flowchart :

A flowchart is a graphical representation of an algorithm.it should follow some rules while creating a flowchart Rule 1: Flowchart opening statement must be ‘start’ keyword. Rule 2:  Flowchart ending statement must be ‘end’ keyword. Rule 3: All symbols in the flowchart must be connected with an arrow line. Rule 4: The decision symbol in the flowchart is associated with the arrow line.  

Advantages of Flowchart:

• Flowcharts are a better way of communicating the logic of the system.
• Flowcharts act as a guide for blueprint during program designed.
• Flowcharts help in debugging process.
• With the help of flowcharts programs can be easily analyzed.
• It provides better documentation.
• Flowcharts serve as a good proper documentation.
• Easy to trace errors in the software.
• Easy to understand.
• The flowchart can be reused for inconvenience in the future.
• It helps to provide correct logic.  

Disadvantages of Flowchart:

• It is difficult to draw flowcharts for large and complex programs.
• There is no standard to determine the amount of detail.
• Difficult to reproduce the flowcharts.
• It is very difficult to modify the Flowchart.
• Making a flowchart is costly.
• Some developer thinks that it is waste of time.
• It makes software processes low.
• If changes are done in software, then the flowchart must be redrawn  

Example : Draw a flowchart to input two numbers from the user and display the largest of two numbers    

References:   Computer Fundamentals by Pradeep K. Sinha and Priti Sinha  

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How can procedural flowcharts support the development of mathematics problem-solving skills?

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Supporting students’ problem-solving skills, solution planning and sequencing of different stages that are involved in successfully developing a meaningful solution to a problem has been a challenge for teachers. This case study was informed by reflective investigation methodology which explored how procedural flowcharts can support student mathematics problem solving in a senior Mathematical Methods subject in Queensland. The paper used thematic analysis to analyse and report on teachers’ perceptions of the utility of procedural flowcharts during problem solving as well as content analysis on how student-developed flowcharts can support their problem-solving skills. Results show that development of procedural flowcharts can support problem solving as it helps with integration of problem-solving stages.

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Introduction

Problem solving is central to teaching and learning of mathematics (see Cai, 2010 ; Lester, 2013 ; Schoenfeld et al., 2014 ). For decades, research in mathematics problem solving, including special issues from leading mathematics education journals (see, Educational Studies in Mathematics, (Vol. 83, no. 2013); The Mathematics Enthusiast, (Vol. 10, nos. 1–2); ZDM , (Vol. 39, nos. 5–6)), have offered significant insights but struggled to produce well-articulated guidelines for educational practice (English & Gainsburg, 2016 ). This could possibly be the reason why mathematics teachers’ efforts to improve students’ problem-solving skills have not produced the desired results (Anderson, 2014 ; English & Gainsburg, 2016 ). Despite Polya’s ( 1945 ) heuristics being so valuable in problem solving, there appears to be limited success when translated into the classroom environment (English & Gainsburg, 2016 ). English and Gainsburg went further to posit that one of the issues to be addressed is how to support problem-solving competency in students during the process of problem solving. Thus, teachers’ perceptions in this study are a valuable part in evaluating how procedural flowcharts can support problem solving.

The problem-solving process is a dialogue between the prior knowledge the problem solver possesses, the tentative plan of solving the problem and other relevant thoughts and facts (Schoenfeld, 1983 ). However, research is still needed on tools that teachers can use to support students during problem solving (Lester & Cai, 2016 ). Although research in mathematics problem solving has been progressing, it has remained largely theoretical (Lester, 2013 ). Schoenfeld ( 2013 ) suggests that research focus should now advance from the framework for examining problem solving to explore how ideas grow and are presented and shared during the problem-solving process. Recently, Kaitera and Harmoinen ( 2022 ) emphasised the need to support teachers through resources that can help students develop problem solving skills. They went on to posit that resources that can assist students in presenting different approaches to a solution and displaying their understanding are critical to build their problem-solving skills.

The study by Kaitera and Harmoinen ( 2022 ) introduced mathematics students to ‘problem-solving keys’ which are heuristics for problem solving that students are to follow as they engage with tasks. Their conclusion was also noted by Vale and Barbosa ( 2018 ) who observed that a key area that would benefit from further research is the identification of strategies or plan that support students’ ability to construct and present their mathematical knowledge effectively during problem solving, particularly if complex processes such as integration and modification of several procedures are involved. Similarly, students face challenges in connecting or bringing all the ideas together and showing how they relate as they work towards the solution (Reinholz, 2020 ). Problem solving in mathematics is challenging for students (Ahmad et al., 2010 ), and therefore, supporting students’ problem-solving skills needs urgent attention (Schoenfeld, 2016 ). Furthermore, Mason ( 2016 ) posits that the crucial yet not significantly understood issue for adopting a problem-solving approach to teaching is the issue of “when to introduce explanatory tasks, when to intervene and in what way” (p. 263). Therefore, teachers also need resources to support the teaching of problem-solving skills, often because they were not taught these approaches when they were school students (Kaitera & Harmoinen, 2022 ; Sakshaug & Wohlhuter, 2010 ).

Flowcharts have been widely used in problem solving across different fields. In a technology-rich learning environment such as Lego Robotics, creating flowcharts to explain processes was observed to facilitate understanding, thinking, making sense of how procedures relate, investigating and communicating the solution (Norton et al., 2007 ). They are effective in guiding students during problem solving (Gencer, 2023 ), enhancing achievement and improving problem-solving skills in game-based intelligent tutoring (Hooshyar et al., 2016 ). Flowcharts have been identified as an effective problem-solving tool in health administration (McGowan & Boscia, 2016 ). In mathematics education, heuristic trees and flowcharts were observed to supplement each other in influencing students’ problem solving behaviour (Bos & van den Bogaart, 2022 ). Importantly, McGowan and Boscia emphasised that “one of the greatest advantages of a flowchart is its ability to provide for the visualisation of complex processes, aiding in the understanding of the flow of work, identifying nonvalue-adding activities and areas of concern, and leading to improved problem-solving and decision-making” (p. 213). Identifying the most appropriate strategy and making the correct decision at the right stage are keys to problem solving. Teaching students to use visual representations like flowcharts as part of problem solving supports the ability to easily identify new relationships among different procedures and assess the solution being communicated faster as visual representations are more understandable (Vale et al., 2018 ).

The purpose of this case study was to explore, through an in-depth teacher’s interview, and student-developed artefacts, the utility of procedural flowcharts in supporting the development of students’ problem-solving skills in mathematics. The study will focus on problem solving in Mathematical Methods which is one of the calculus-based mathematics subjects at senior school in Queensland. The aim was to investigate if the development of procedural flowcharts supported students in planning, logically connecting and integrating mathematical procedures (knowledge) and to communicate the solution effectively during problem solving. The use of flowcharts in this study was underpinned by the understanding that visual aids that support cognitive processes and interlinking of ideas and procedures influence decision-making, which is vital in problem-based learning (McGowan & Boscia, 2016 ). Moreover, flowcharts are effective tools for communicating the processes that need to be followed in problem solving (Krohn, 1983 ).

Problem-solving learning in mathematics education

The drive to embrace a problem-solving approach to develop and deepen students’ mathematics knowledge has been a priority in mathematics education (Koellner et al., 2011 ; Sztajn et al., 2017 ). In the problem-solving approach, the teacher provides the problem to be investigated by students who then design ways to solve it (Colburn, 2000 ). To engage in problem solving, students are expected to use concepts and procedures that they have learnt (prior knowledge) and apply them in unfamiliar situations (Matty, 2016 ). Teachers are encouraged to promote problem-solving activities as they involve students engaging with a mathematics task where the procedure or method to the solution is not known in advance (National Council of Teachers of Mathematics [NCTM], 2000 ), thus providing opportunities for deep understanding as well as providing students with the opportunity to develop a unique solution (Queensland Curriculum and Assessment Authority [QCAA], 2018 ). Using this approach, students are given a more active role through applying and adapting procedures to solve a non-routine problem and then communicating the method (Karp & Wasserman, 2015 ). The central role problem solving plays in developing students’ mathematical understanding has resulted in the development of different problem-solving models over the years.

The process of problem solving in mathematics requires knowledge to be organised as the solution is developed and then communicated. Polya is among the first to systematise problem solving in mathematics (Voskoglou, 2021 ). Students need to understand the problem, plan the solution, execute the plan and reflect on the solution and process (Polya, 1971 ). Voskoglou’s ( 2021 ) problem-solving model emphasised that the process of modelling involves analysis of problem, mathematisation, solution development, validation and implementation. Similarly, problem solving is guided by four phases: discover, devise, develop and defend (Makar, 2012 ). During problem solving, students engage with an unfamiliar real-world problem, develop plans in response, justify mathematically through representation, then evaluate and communicate the solution (Artigue & Blomhøj, 2013 ). Furthermore, Schoenfeld ( 1980 ) posited that problem solving involves problem analysis, exploration, design, implementation and verification of the solution. When using a problem-solving approach, students can pose questions, develop way(s) to answer problems (which might include drawing diagrams, carrying out calculations, defining relationships and making conclusions), interpreting, evaluating and communicating the solution (Artigue et al., 2020 ; Dorier & Maass, 2020 ). Problem solving involves understanding the problem, devising and executing the plan and evaluating (Nieuwoudt, 2015 ). Likewise, Blum and Leiß ( 2007 ) developed a modelling approach that was informed by these stages, understanding, simplifying, mathematising, working mathematically, interpreting and validating.

Similarly, mathematical modelling involves problem identification from a contextualised real-world problem, linking the solution to mathematics concepts, carrying out mathematic manipulations, justifying and evaluating the solution in relation to the problem and communicating findings (Geiger et al., 2021 ). Likewise, in modelling, Galbraith and Stillman ( 2006 ) suggested that further research is needed in fostering students’ ability to transition effectively from one phase to the next. “Mathematical modelling is a special kind of problem solving which formulates and solves mathematically real-world problems connected to science and everyday life situations” (Voskoglou, 2021 p. 85). As part of problem solving, mathematical modelling requires students to interpret information from a variety of narrative, expository and graphic texts that reflect authentic real-life situations (Doyle, 2005 ).

There are different approaches to problem solving and modelling, but all of them focus on the solving of real-world problems using mathematical procedures and strategies (Hankeln, 2020 ). A literature synthesis is critical where several models exist as it can be used to develop an overarching conceptual model (Snyder, 2019 ). Torraco ( 2005 ) noted that literature synthesis can be used to integrate different models that address the same phenomenon. For example, in this study, it was used to integrate problem solving models cited in the literature. Moreover, the review was necessitated by the need to reconceptualise the problem-solving model by Polya ( 1971 ) to include the understanding that the definition of problem solving has now broadened to include modelling. Torraco went further to suggest that as literature grows, and knowledge expands on a topic which might accommodate new insights, there is a need for literature synthesis with the aim to reflect the changes. Thus, the model in Fig.  1 took into consideration the key stages broadly identified by the researchers and the understanding that modelling is part of problem solving. Problem solving and modelling is generally a linear process that can include loops depending on how the problem identification, mathematisation and implementation effectively address the problem (Blum & Leiß, 2007 ; Polya, 1957 ).

Stages of mathematics problem solving

Figure  1 identifies the main stages that inform mathematics problem solving from the literature.

Problem identification and the design to solve the problem might be revisited if the procedures that were identified and their mathematical justification do not address the problem. Likewise, justification and evaluation after implementation might prompt the problem solver to realise that the problem was incorrectly identified. The loop is identified by the backward arrow, and the main problem-solving stages are identified by the linear arrows. The Australian Curriculum, Assessment and Reporting Authority notes that during problem solving:

Students solve problems when they use mathematics to represent unfamiliar situations, when they design investigations and plan their approaches, when they apply their existing knowledge to seek solutions, and when they verify that their answers are reasonable. Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. (Australia Curriculum and Reporting Authority, 2014 , p. 5)

Therefore, during problem solving, students have to plan the solution to the problem and be able to communicate all the key processes involved. However, although problem solving is highly recommended in mathematics education, it presents several challenges for teachers in terms of how they can best support students to connect the processes and mathematics concepts into something coherent that can lead to a meaningful solution (Hacker, 1998 ). Therefore, relevant tools that support problem solving and decision-making can make a difference for both mathematics teachers and students (McGowan & Boscia, 2016 ).

Students can solve problems better if they can think critically (Kules, 2016 ). Problem solving requires their active engagement in analysing, conceptualising, applying concepts, evaluating, comparing, sequencing, synthesising, reasoning, reflecting and communicating, which are skills that are said to promote critical thinking (Kim et al., 2012 ; King, 1995 ; Moon, 2008 ; QCAA, 2018 ). Similarly, the ability to undertake problem solving is supported when students are provided with the opportunity to sequence ideas logically and evaluate the optimal strategy to solve the problem (Parvaneh & Duncan, 2021 ). However, finding tools that can support problem solving has been a focus for researchers for a long time but with very limited breakthroughs (McCormick et al., 2015 ). This study explored how procedural flowcharts as visual representations can support students in organising ideas, execute procedures, justify solutions and communicate their solution.

Importance of visual representations in mathematics problem-solving

Research on how visual representations support mathematics discovery and structural thinking in problem solving has come a long way (see Hadamard, 1945 ; Krutetskii, 1976 ; Polya, 1957 ). Visual representations are classified as graphs, tables, maps, diagrams, networks and icons and are widely used to convey information in a recognisable form that can be easily interpreted without resorting to tedious computations (Lohse et al., 1994 ). Visual representations can be used as a tool to capture mathematics relations and processes (van Garderen et al., 2021 ) and used in many cognitive tasks such as problem solving, reasoning and decision making (Zhang, 1997 ). Indeed, representations can be modes of communicating during concepts exploration and problem solving (Roth & McGinn, 1998 ). Likewise, visual representations can be a powerful way of presenting the solution to a problem, including self-monitoring on how the problem is being solved (Kingsdorf & Krawec, 2014 ; Krawec, 2014 ). Using visualisations created by teachers or students in mathematics can support students’ problem-solving abilities (Csíkos et al., 2012 ).

Visual representations show thoughts in non-linguistic format, which is effective for communication and reflection. “Visual representations serve as tools for thinking about and solving problems. They also help students communicate their thinking to others” (NCTM, 2000 , p. 206). In mathematics, visual representation plays a significant role in showing the cognitive constructs of the solution (Owens & Clements, 1998 ), a view echoed by Arcavi ( 2003 ), who said that visual representations can be appreciated as a central part of reasoning and as a resource to use in problem solving. More importantly, they can be used to represent the logical progression of ideas and reasoning during problem solving (Roam, 2009 ). However, there is need to explore how visual representations can be used to support and illustrate the problem-solving process and to create connections among concepts (Stylianou, 2010 ). Importantly, developing diagrams is often a recommended strategy for solving mathematics problems (Pape & Tchoshanov, 2001 ; Jitendra et al., 2013 ; Zahner & Corter, 2010 ). Therefore, this study will explore the utility of procedural flowcharts as a visual representation and resource in supporting problem analysis, problem understanding, solution development and evaluation, while communicating the whole problem-solving process effectively. It will go further to explore how development of procedural flowcharts can support educational practice in Mathematical Methods subject.

Procedural flowcharts are a visual representation of procedures, corresponding steps and stages of evaluation of a solution to a problem (Chinofunga et al., 2022 ). These authors noted that procedural flowcharts developed by the teacher can guide students during the inquiry process and highlight key procedures and stages for decision-making during the process of problem solving. This is because “a procedural flowchart graphically displays the information–decision–action sequences in the proposed order” (Krohn, 1983 , p. 573). Similarly, Chinofunga and colleagues ( 2022 ) emphasised that procedural flowcharts can be used to visually represent procedural flexibility as more than one procedure can be accommodated, making it easier to compare the effectiveness of different procedures as they are being applied. They further posited that student-developed procedural flowcharts provide students with the opportunity to comprehensively engage with the problem and brainstorm different ways of solving it, thus deepening their mathematics knowledge. Moreover, a procedural flowchart can be a visual presentation of an individual or group solution during problem solving.

Research has identified extended benefits of problem solving in small groups (Laughlin et al., 2006 ). Giving groups an opportunity to present a solution visually can be a quicker way to evaluate a group solution because visual representations can represent large amounts of information (even from different sources) in a simple way (Raiyn, 2016 ). Equally, Vale and colleagues encouraged visual representation of solutions with multisolutions as a tool to teach students problem solving ( 2018 ). Therefore, students can be asked to develop procedural flowcharts individually then come together to synthesise different procedural flowcharts.

Similarly, flowcharts are a visual aid used to represent how procedures interrelate and function together. “They are tools to visually break down complex information into individual building blocks and how the blocks are connected” (Grosskinsky et al., 2019 , p. 24). They outlay steps in a procedure and show how they can be applied, thus helping to visualise the process (Ledin & Machin, 2020 ; Reingewertz, 2013 ). Flowcharts can also be used when a logical and sequenced approach is needed to address a problem (Cantatore & Stevens, 2016 ). Importantly, in schools, Norton and colleagues ( 2007 ) noted that “planning facilitated through the use of flow charts should be actively encouraged and scaffolded so that students can appreciate the potential of flow charts to facilitate problem-solving capabilities” (p. 15). This was because the use of flowcharts in problem solving provided a mental representation of a proposed approach to solve a task (Jonassen, 2012 ). The success of flowcharts in problem solving in different fields can be attributed to their ability to facilitate deep engagement in planning the solution to the problem.

Flowcharts use has distinct advantages that can benefit problem solving. Norton and colleagues ( 2007 ) posited that using a well-planned and well-constructed flowchart in problem solving results in a good-quality solution. Furthermore, flowcharts can also be a two-way communication resource between a teacher and students or among students (Grosskinsky et al., 2019 ). These authors further noted that flowcharts can help in checking students’ progress, tracking their progress and guide them. They can also be used to highlight important procedures that students can follow during the process of problem solving.

Similarly, flowcharts can be used to provide a bigger picture of the solution to a problem (Davidowitz & Rollnick, 2001 ). Flowcharts help students gain an overall and coherent understanding of the procedures involved in solving the problem as they promote conceptual chunking (Norton et al., 2007 ). Importantly, “they may function to amplify the zone of proximal development for students by simplifying tasks in the zone” (Davidowitz & Rollnick, 2001 , p. 22). Use of flowcharts by students reduces the cognitive load which then may help them focus on more complex tasks (Berger, 1998 ; Sweller et al., 2019 ). Indeed, development of problem-solving skills can be supported when teachers introduce learning tools such as flowcharts, because they can help structure how the solution is organised (Santoso & Syarifuddin, 2020 ). Therefore, the use of procedural flowcharts in mathematics problem solving has the potential to transform the process.

The research question in this study was informed by the understanding that limited resources are available to teachers to support students’ problem-solving abilities. In addition, the literature indicates that visual representation such as procedural flowcharts can support students’ potential in problem solving. Therefore, the research described in this study addressed the following research question: What are teachers’ perceptions of how procedural flowcharts can support the development of students’ problem-solving skills in the Mathematical Methods subject?

Methodology

The case study draws from the reflective investigation methodology (Trouche et al., 2018 ,  2020 ). The methodology explores how teaching and learning was supported by facilitating a teacher’s reflection on the unexpected use of a resource, in this case procedural flowcharts. The reflective methodology emphasises a teacher’s active participation through soliciting views on the current practice and recollection on previous work (Trouche et al., 2020 ). Using the methodology, a teacher is asked to reflect on and describe the resource used, the structure (related to the activity), the implementation and the outcomes (Huang et al., 2023 ).

This case study focuses on phases three and four of a broad PhD study that involved four phases. The broad study was informed by constructivism. Firstly, phase one investigated Queensland senior students’ mathematics enrolment in different mathematics curricula options from 2010 to 2020. Secondly, phase two developed and introduced pedagogical resources that could support planning, teaching and learning of calculus-based mathematics with a special focus on functions in mathematical methods. The pedagogical resources included a framework on mathematics content sequencing which was developed through literature synthesis to guide teachers on how to sequence mathematics content during planning. Furthermore, the phase also introduced concept maps as a resource for linking prior knowledge to new knowledge in a constructivist setting. Procedural flowcharts were also introduced to teachers in this phase as a resource to support development of procedural fluency in mathematics. Importantly, a conference workshop organised by the Queensland Association of Mathematics Teachers (Cairns Region) provided an opportunity for teachers to contribute their observations on ways that concept maps and procedural flowcharts can be used to support teaching. Thirdly, phase three was a mixed-method study that focused on evaluating the pedagogical resources that were developed or introduced in phase two with 16 purposively sampled senior mathematics teachers in Queensland who had been given a full school term to use the resources in their practice. Some qualitative data collected through semistructured interviews from phase three were included in the results of the study reported here. During the analysis of the qualitative data, a new theme emerged which pointed to the unexpected use of procedural flowcharts during teaching and learning beyond developing procedural fluency. As a result, the researchers decided to explore how development of procedural flowcharts supported teaching and learning of mathematics as an additional phase. Phase four involved an in-depth interview with Ms. Simon (pseudonym) a teacher who had unexpectedly applied procedural flowcharts in a problem-solving task, which warranted further investigation. Ms. Simon’s use of procedural flowcharts was unexpected as she had used them outside the context and original focus of the broader study. Importantly, in phase four, artefacts created by the teacher and her four students in the problem-solving task were also collected.

Ms. Simon (pseudonym) had explored the use of procedural flowcharts in a problem-solving and modelling task (PSMT) in her year 11 Mathematical Methods class. This included an introduction to procedural flowcharts, followed by setting the students a task whereby they were asked to develop a procedural flowchart as an overview on how they would approach a problem-solving task. The students were expected to first develop the procedural flowcharts independently then to work collaboratively to develop and structure an alternative solution to the same task. The student-developed procedural flowcharts (artefacts) and the in-depth interview with Ms. Simon were included in the analysis. As this was an additional study, an ethics amendment was applied for and granted by the James Cook University Ethics committee, approval Number H8201, as the collection of students’ artefacts was not covered by the main study ethics approval for teachers.

Research context of phase four of the study

In the state of Queensland, senior mathematics students engage with three formal assessments (set by schools but endorsed by QCAA) in year 12 before the end of year external examination. The formal internal assessments consist of two written examinations and a problem-solving and modelling task (PSMT). The PSMT is expected to cover content from Unit 3 (Further Calculus). The summative external examination contributes 50% and the PSMT 20% of the overall final mark, demonstrating that the PSMT carries the highest weight among the three formal internal assessments.

The PSMT is the first assessment in the first term of year 12 and is set to be completed in 4 weeks. Students are given 3 h of class time to work on the task within the 4 weeks and write a report of up to 10 pages or 2000 words. The 4 weeks are divided into four check points, one per week with the fourth being the submission date. On the other three checkpoints, students are expected to email their progress to the teacher. At checkpoint one, the student will formulate a general plan on how to solve the problem which is detailed enough for the teacher to provide meaningful feedback. Checkpoint one is where this study expects teachers to provide students with the opportunity to develop a procedural flowchart of the plan to reach the solution. Importantly at checkpoint one, teachers are interested in understanding which mathematics concepts students will select and apply to try and solve the problem and how the concepts integrate or complement each other to develop a mathematically coherent, valid and appropriate solution. Moreover, teachers are expected to have provided students with opportunities to develop skills in undertaking problem-solving and modelling task before they engage with this formal internal assessment. The QCAA has provided a flowchart to guide teachers and students on how to approach a PSMT ( Appendix 1 )

Participants in phase four of the study

Ms. Simon and a group of four students were the participants in this study. Ms. Simon had studied mathematics as part of her undergraduate education degree, which set her as a highly qualified mathematics teacher. At the time of this study, she was the Head of Science and Mathematics and a senior mathematics teacher at one of the state high schools in Queensland. She had 35 years’ experience in teaching mathematics across Australia in both private and state schools, 15 of which were as a curriculum leader. She was also part of the science, technology, engineering and mathematics (STEM) state-wide professional working group. Since the inception of the external examination in Queensland in 2020, she had been an external examination marker and an assessment endorser for Mathematical Methods with QCAA. The students who were part of this study were aged between 17 and 18 years and were from Ms. Simon’s Mathematical Methods senior class. Two artefacts were from individual students, and the third was a collaborative work from the two students.

Phase four data collection

First, data were collected through an in-depth interview between the researcher and Ms. Simon. The researcher used pre-prepared questions and incidental questions arising from the interview. The questions focused on exploring how she had used procedural flowcharts in a PSMT with her students. The interview also focused on her experiences, observations, opinions, perceptions and results, comparing the new experience with how she had previously engaged her students in such tasks. The interview lasted 40 min, was transcribed and coded so as to provide evidence of the processes involved in the problem solving. Some of the pre-prepared questions were as follows:

What made you consider procedural flowcharts as a resource that can be used in a PSMT?

How have you used procedural flowcharts in PSMT?

How has the use of procedural flowcharts transformed students’ problem-solving skills?

How have you integrated procedural flowcharts to complement the QCAA flowchart on PSMT in mathematics?

What was your experience of using procedural flowcharts in a collaborative setting?

How can procedural flowcharts aid scaffolding of problem-solving tasks?

Second, Ms. Simon shared her formative practice PSMT task (described in detail below), and three of her students’ artefacts. The artefacts that she shared (with the students’ permission) were a critical source of data as they were a demonstration of how procedural flowcharts produced by students can support the development of problem solving and provided an insight into the use of procedural flowcharts in a PSMT.

Problem-solving and assessment task

The formative practice PSMT that Ms. Simon shared is summarised below under the subheadings: Scenario, Task, Checkpoints and Scaffolding.

You are part of a team that is working on opening a new upmarket Coffee Café. Your team has decided to cater for mainly three different types of customers. Those who:

Consume their coffee fast.

Have a fairly good amount of time to finish their coffee.

Want to drink their coffee very slowly as they may be reading a book or chatting.

The team has tasked you to come up with a mode or models that can be used to understand the cooling of coffee in relation to the material the cup is made from and the temperature of the surroundings.

Write a mathematical report of at most 2000 words or up to 10 pages that explains how you developed the cooling model/s and took into consideration the open cup, the material the cup was made from, the cooling time, the initial temperature of the coffee and the temperature of the surroundings.

Design an experiment that investigates the differences in the time of cooling of a liquid in open cups made from different materials. Record your data in a table.

Develop a procedural flowchart that shows the steps that you used to arrive at a solution for the problem.

Justify your procedures and decisions by explaining mathematical reasoning.

Provide a mathematical analysis of formulating and evaluating models using both mathematical manipulation and technology.

Provide a mathematical analysis that involves differentiation (rate of change) and/or anti-differentiation (area under a curve) to satisfy the needs of each category of customers.

Evaluate the reasonableness of solutions.

You must consider Newton’s Law of Cooling which states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the temperature of its surroundings. For a body that has a higher temperature than its surroundings, Newton’s Law of Cooling can model the rate at which the object is cooling in its surroundings through an exponential equation. This equation can be used to model any object cooling in its surroundings: 

y is the difference between the temperature of the body and its surroundings after t minutes,

A 0 is the difference between the initial temperature of the body and its surroundings,

k is the cooling constant.

Checkpoints

Week 1: Students provide individual data from the experiment and create a procedural flowchart showing the proposed solution to the problem. Teacher provides individual feedback. Week 2: Students provide a consolidated group procedural flowchart. Teacher provides group feedback Week 3: Students email a copy of their individually developed draft report for feedback. Week 4: Students submit individual final response in digital (PDF format) by emailing a copy to their teacher, providing a printed copy to their teacher and saving a copy in their Maths folder.

Additional requirements/instructions

The response must be presented using an appropriate mathematical genre (i.e., a mathematical report).

The approach to problem-solving and mathematical modelling must be used.

All sources must be referenced.

Data analysis

The analysis of data includes some observations and perceptions of mathematics teachers which were collected through surveys and interviews from phase three of the broader PhD study. The survey and interviews data in the broader study including phase four in-depth interview with Ms. Simon were transcribed and coded using thematic analysis (TA). TA is widely used in qualitative research to identify and describe patterns of meaning within data (Braun & Clarke, 2006 ; Ozuem et al., 2022 ). The thematic validity was ensured using theory triangulation. It involves sharing qualitative responses among colleagues at different status positions in the field and then comparing findings and conclusions (Guion et al., 2011 ). The study adopted the inductive approach which produces codes that are solely reflective of the contents of the data (Byrne, 2022 ).

Coding was done with no pre-set codes, and line-by-line coding was used as this was mainly an inductive analysis. The research team comprising of the researcher and two advisors/supervisors met to set the initial coding mechanism and code part of the data for consistency before independent coding of all the data. This is supported by King ( 2004 ) who suggested that when searching for themes, it is best to start with a few codes to help guide analysis. The data covered a wide variety of concepts, so initially the different concepts that grouped the research questions as ‘conceptual themes’ were utilised to organise the data. The research team examined the codes, checking their meaning and relationships between them to determine which ones were underpinned by a central concept. In Excel, codes that shared a core idea from the initial phase that used data from the open-ended responses and interview transcripts were colour coded. After the independent thematic analysis, the filter function in Excel was used to sort the codes using cell colour. Moreover, Excel provided the opportunity to identify duplicates as codes were collated from the three researchers. Same coloured codes were synthesised to develop a general pattern of meaning, which we referred to as candidate themes. The sorting and collation approach would bring together all codes under each theme which then would facilitate further analysis and review (Bree et al., 2014 ).

The research team went on to review the relationship of the data and the codes that informed the themes. This is supported by Braun and Clarke ( 2012 , 2021 ) who posited that researchers should conduct a recursive review of the candidate themes in relation to the coded data items and the entire dataset. During the review, whenever themes were integrated or codes were moved to another theme, a new spreadsheet was created so that if further review was necessary, the old data and layout would still be available. Importantly, if the codes form a coherent and meaningful pattern, the theme makes a logical argument and may be representative of the data (Nowell et al., 2017 ). Furthermore, the team also reviewed the themes in relation to the data. This is because Nowell and others posited that themes should provide the most accurate interpretation of the data. The research team also discussed and wrote detailed analysis for each candidate theme identifying the main story behind each theme and how each one fit into the overall story about the data through the lens of the research questions. Finally, the researchers also linked quotes to final themes reached during the analysis. Illustrating findings with direct quotations from the participants strengthen the face validity and credibility of the research (Bryne, 2022 ; Patton, 2002 ; Nowell et al., 2017 ).

Student artefacts

The students’ artefacts (procedural flowcharts) in Figs.  5 , 6 and 7 were analysed using content analysis. Content analysis can be used to analyse written, verbal or visual representations (Cole, 1988 ; Elo & Kyngäs, 2008 ). Content analysis is ideal when there is a greater need to identify critical processes (Lederman, 1991 ). Unlike interviews, documents that are ideal for qualitative analysis should be developed independently without the researcher’s involvement (Merriam & Tisdell, 2015 ). In fact, the documents should not have been prepared for the purpose of research (Hughes & Goodwin, 2014 ), hence they are a stable and discrete data source (De Massis & Kotlar, 2014 ; Merriam & Tisdell, 2015 ). The students’ artefacts used in this study were not prepared for the purpose of the study but as a mathematics task. Deductive content analysis is used when the structure of analysis is implemented on the basis of previous knowledge and the purpose of the study is model testing or confirmation (Burns & Grove, 2009 ). Similarly, it is an analytical method that aims to test existing concepts, models or hypotheses in a new context (Kyngäs et al., 2020 ). They went further to note that researchers can use deductive analysis to determine how a model fit a new context.

Deductive content analysis follows three main stages: preparation, organising and reporting (Elo et al., 2014 ; Elo & Kyngäs, 2008 ). Firstly, preparation involves identifying the unit of analysis (Guthrie et al., 2004 ). In this study, the unit of analysis are the artefacts developed by the students. Furthermore, the phase requires the researcher to be immersed in the data reading and digesting to make sense of the whole set of data through reflexivity, open-mindedness and following the rationale of what guided participants’ narratives or in developing the artefact (Azungah, 2018 ). Secondly, a categorisation matrix based on existing knowledge should be developed or identified to facilitate the coding of the data according to categories (Hsieh & Shannon, 2005 ) (Table  1 ). Importantly, when using deductive content analysis, researchers require a theoretical structure or model from which they can build an analysis matrix (Kyngäs et al., 2020 ). Finally, the analysis results should be reported in ways that promote interpretation of the data and the results, for example, in tabular form (Elo & Kyngäs, 2008 ) (Fig.  2 ).

Stages followed during analysis of procedural flowcharts

The students’ procedural flowcharts were coded and interpreted on how they respond to different stages of problem solving. The researcher’s codes, interpretations and findings should be clearly derived and justified using the available data and then inform conclusions and interpretations for confirmability (Tobin & Begley, 2004 ). The artefacts were shared between the researcher and his supervisors; the analysis was done independently then reviewed by the researcher and his supervisors. Schreier ( 2012 ) recommended that analysis should be done by more than one person to promote thoroughness and broaden the interpretation of the data. Schreier went further to note that if the categorisation matrix is clear and of high quality, the coding should produce very little discrepancies. Very little discrepancies were observed except that some stages on the students’ procedural flowcharts overlapped between skills.

This section presents results from the analysis of the interviews data and student artefacts.

Semi-structured interviews

The thematic analysis of interviews resulted in two themes:

The utility of procedural flowcharts in supporting mathematics problem solving.

The utility of procedural flowcharts in supporting the integration of the four stages of mathematics problem solving.

In phase three, which prompted the targeted phase four study described in this study, teachers were asked the question, “How have you used procedural flowcharts to enhance teaching and learning of mathematics?” The question was not specific to problem solving but the teachers’ observations and perceptions strongly related to problem-solving and student-centred learning.

Theme 1 The utility of procedural flowcharts generally supports mathematics problem solving

The visual nature of procedural flowcharts was seen as an advantage to both teachers and students. For students, drawing a flowchart was easier than writing paragraphs to explain how they had arrived at the intended solution. For teachers, the flowchart was easier to process for timely feedback to students. Developing a procedural flowchart at the first checkpoint in the PSMT allows teachers to provide valuable feedback as the procedural flowchart can be used to represent several processes compared to written because of its visual nature. Engagement can be promoted because students can use the targeted feedback to improve their solutions as they will have provided a detailed overview of how they propose to solve the problem.

They present steps in diagrammatic form which is easy to process and easy to understand and process… students prefer them more as its in diagrammatic form and I have witnessed more students engaging. (Participant 8, phase three study) I find it (visual) a really efficient way for me to look at the proposed individual students processes and provide relevant feedback to the student or for the student to consider. And, you know, once the students are comfortable with using these procedural flowcharts you know, I find it much easier for me to give them relevant feedback, and I actually find that feedback more worthwhile than feedback we used to give them, you know, that was just based on what they wrote in paragraphs,…students get to practice in creating their own visual display, which communicates their intended strategies to solve the problem, then they have opportunities to use it, and fine tune it as they work out the problem … student developed procedural flow charts, they represent a student’s maths knowledge in a visual way. (Ms. Simon).

Identifying students’ competencies early was seen as central to successful problem solving as it provided opportunities for early intervention. Results showed that teachers viewed procedural flowcharts as a resource that could be used to identify gaps in skills, level of understanding and misconceptions that could affect successful and meaningful execution of a problem-solving task. Going through a student-developed flowchart during problem solving provided the teachers with insight into the student’s level of understanding of the problem and how the effectiveness of the procedures proposed to address the problem. This is critical for tasks that require students to develop a report detailing the solution at the end of developing the solution. Teachers can get the opportunity to gain an insight of the proposed solution before the student commit to write the report. The procedural flowchart provides the bigger picture of the solution plan which might expose gaps in knowledge.

I found it quite useful because I can identify what kids or which kids are competent in what, which sort of problem-solving skills. And I can identify misconceptions that students have or gaps in students understanding. (Participant 1, phase three study) It also to me highlights gaps in students’ knowledge in unique ways that students intend to reach a solution because the use of the procedural flow chart encourages students to explain the steps or procedures behind any mathematical manipulation that you know they're intending to use. And it's something that was much more difficult to determine prior to using procedural flow charts… I've also used you know, student developed procedural flow charts to ascertain how narrow or wide the students’ knowledge is and that's also something that wasn't obvious to make a judgement about prior to using procedural flow charts. (Ms. Simon)

Problem solving was seen as student-centred. If procedural flowcharts could be used to support problem solving, then they could facilitate an environment where students were the ones to do most of the work. The students could develop procedural flowcharts showing how they will solve a PSMT task using concepts and procedures they have learnt. The open-ended nature of the problem in a PSMT provides opportunities for diverse solutions that are validated through mathematical justifications. The visual nature of procedural flowcharts makes them more efficient to navigate compared to text.

Mathematics goes from being very dry and dusty to being something which is actually creative and interesting and evolving, starting to get kids actually engaging and having to back themselves. (Participant 7, phase three study) As a teacher, I find that procedural flowcharts are a really efficient way to ascertain the ways that students have considered and how they are going to solve a problem … It engages the students from start to finish, you know in different ways this method demands students to compare, interpret, analyse, reason, evaluate, and to an extent justify as they develop this solution. (Ms. Simon)

Similarly, results showed that procedural flowcharts could be used as a resource to promote collaborative learning and scaffolding. Students could be asked to collaboratively develop a procedural flowchart or could be provided with one to follow as they worked towards solving the problem. Collaborative development of procedural flowcharts can support problem solving as students can bring their different mathematical understanding to develop a solution from different perspectives.

Sometimes, you know, I get students to work on it in groups as they share ideas and get that mathematisation happening. So, it's really helpful there … I looked at the PSMT and its Marking Guide, and develop a more detailed procedural flowchart for students to use as a scaffold to guide them through the process. So, procedural flowcharts provide a structure in a more visual way for students to know what to do next. (Ms. Simon)

Ms. Simon shared her detailed procedural flowchart in Fig.  3 that she used to guide students in PSMTs.

Ms. Simon’s procedural flowchart on problem solving

The participants also observed that procedural flowcharts could be used to promote opportunities for solution evaluation which played an important role in problem solving. Loops can be introduced in procedural flowcharts to provide opportunities for reflection and reasoning as alternative paths provide flexibility while the solution is being developed. Following Fig.  4 are participants’ comments referring to the figure which was among procedural flowcharts shared with participants as examples of how they can be used to teach syllabus identified Mathematical Methods concepts. The Mathematical Methods syllabus expects students to “recognise the distinction between functions and relations and use the vertical line test to determine whether a relation is a function” (QCAA, 2018 p. 20).

The cycle approach, the feeding back in the feeding back out that type of stuff, you know, that is when we starting to teach students how to think . (Participant 7, phase three study) Complex procedural flowcharts like the one you provided guide students in making key decisions as they work through solutions which is key to critical thinking and judgement and these two are very important in maths. (Participant 8, phase three study) I also sincerely believe that procedural flowcharts are a way to get students to develop and demonstrate the critical thinking skills, which PSMTs are designed to assess. Students inadvertently have to use their critical thinking skills to analyse and reason as they search for different ways to obtain a solution to the problem presented in the PSMT … the use of procedural flowcharts naturally permits students to develop their critical thinking skills as it gets their brain into a problem-solving mode as they go through higher order thinking skills such as analysis, reasoning and synthesis and the like … this visual way of presenting solution provides students with opportunities to think differently, which they're not used to do, and it leads them to reflect and compare. (Ms. Simon)

Procedural flowchart on distinguishing functions and relations

Problem solving of non-routine problems uses a structure that should be followed. Resources that are intended to support problem solving in students can be used to support the integration of the stages involved in problem solving.

Theme 2 The utility of procedural flowcharts in supporting the integration of the four stages of mathematics problem solving.

Procedural flowcharts can support the flow of ideas and processes in the four stages during problem-solving and modelling task in Mathematical Methods subject. Literature synthesis in this study identified the four stages as:

Identification of problem and mathematics strategies than can solve the problem.

Implementation.

Evaluation and justification.

Communicating the solution.

Similarly, QCAA flowchart on PSMT identifies the four stages as formulate, solve, evaluate and verify, and communicate.

The logical sequencing of the stages of mathematics problem solving is crucial to solving and communicating the solution to the problem. Development of procedural flowcharts can play an important role in problem solving through fostering the logical sequencing of processes to reach a solution. Participants noted that the development of procedural flowcharts provides opportunities for showing the flow of ideas and processes which lay out an overview of how different stages connect into a bigger framework of the solution. Furthermore, it can help show how different pieces of a puzzle interconnect, in this case how all the components of the solution interconnect and develop to address the problem. In fact, procedural flowcharts can be used to show how the different mathematics concepts students have learnt can be brought together in a logical way to respond to a problem.

Procedural flowcharts help students sum up and connect the pieces together… connect the bits of knowledge together. (Participant 4, phase three study) Really good how it organises the steps and explains where you need to go if you're at a certain part in a procedure. (Participant 2, phase three study) Potentially, it's also an excellent visual presentation, which shows a student's draft of their logical sequence of processes that they're intending to develop to solve the problem … So, the steps students need to follow actually flows logically. So really given a real-life scenario they need to solve in a PSMT students need to mathematise it and turn it into a math plan, where they execute their process, evaluate and verify it and then conclude … so we use procedural flowcharts to reinforce the structure of how to approach problem-solving … kids, you know, they really struggling, you know, presenting things in a logical way, because they presume that we know what they're thinking . (Ms. Simon)

Developing procedural flowcharts provided students with opportunities to plan the solution informed by the stages of problem solving. Teachers could reinforce the structure of problem solving by telling students what they could expect to be included on the procedural flowchart. Procedural flowcharts can be used as a visual tool to highlight all the critical stages that are included during the planning of the solution.

I tell the students, “I need to see how you have interpreted the problem that you need to solve. I need to see how you formulated your model that involves the process of mathematisation, where you move from the real world into the maths world, and I need to see all the different skills you're intending to use to arrive at your solution.” (Ms. Simon)

Similarly, procedural flowcharts could visually represent more than one strategy in the “identify and execute mathematics procedures that can solve the problem” stage, thereby providing a critical resource to demonstrate flexibility. When there are multiple ways of addressing a problem, developing a procedural flowchart can provide an opportunity of showing all possible paths or relationships between different paths to the solution, thus promoting flexibility. Procedural flowcharts provide an opportunity to show how different procedures can be used or integrated to solve a problem.

Students are expected to show evidence that they have the knowledge of solving the problem using several ways to get to the same solution. So, it goes beyond the students’ preferred way of answering a question and actually highlights the importance of flexibility when it comes to processes and strategies of solving a problem … By using procedural flowcharts, I'm saying to the students, “Apart from your preferred way of solving the problem, give me a map of other routes, you can also use to get to your destination.” (Ms. Simon)

The results also indicated that procedural flowcharts could be used to identify strengths and limitations of procedures in the “evaluate solution” stage and thus demonstrate the reasonableness of the answer. Having more than one way of solving a problem on a procedural flowchart helps in comparing and evaluating the most ideal way to address the problem.

And I'm finding that, you know, as students go through, and they compare the different processes, you know, the strengths and limitations, literally stare them in the face. So, they don't have to. They're not ... they don't struggle as much as they used to in coming up with those sorts of answers … it's also a really easy way that once the students reach the next phase, which is the evaluating verified stage, they can go back to their procedural flow chart and identify and explain strengths and limitations of their model … It's a convenient way for students to show their reasonableness of their solution by comparing strengths and weaknesses of all the strategies presented on the procedural flowchart, something that they've struggled with in the past. (Ms. Simon)

The results from the interview show that the procedural flowcharts supported efficient communication of the steps to be followed in developing the solution to the problem. Student-developed procedural flowcharts allowed the teacher to have an insight and overview of the solution to the problem earlier in the assessment task. In addition, they provided an alternative way of presenting their solution to the teacher.

I expect students to use the procedural flowchart as a way to communicate to me how they're planning to solve the scenario in the PSMT…It's also one of the parts that students are expected to hand in to me on one of the check points, and I find it a really efficient way for me to look at, you know, a proposed individual students processes, and provide relevant feedback to the student to consider in a really efficient way…I just found that it helps students communicate their solution to a problem in lots of different ways that challenges students to logically present a solution. (Ms. Simon)

She went on to say,

Students also found it challenging to communicate their ideas in one or two paragraphs, when more than one process or step was required to solve the problem. So, I found that, you know, procedural flowcharts, have filled this gap really nicely, as that provides students with a simple tool that they can use to present a visual overview of the processes they've chosen to use to solve the problem. And so, for me, as a teacher, procedural flowcharts are an efficient way for me to scan the intended processes that an individual student is proposing to use to solve the problem in their authentic way and provide them with valuable feedback.

In summary, the teacher’s experiences, views and perceptions showed that procedural flowcharts can be a valuable resource in supporting students in all four stages of problem solving.

Students’ artefacts

The student-generated flowcharts in this part of the research gave an insight into students’ understanding as they planned how to solve the problem presented to them. Students were expected to use the problem-solving stages to successfully develop solutions to problems. Their de-identified procedural flowcharts are shown in Figs.  5 , 6 and 7 .

Procedural flowchart developed by student 1

Procedural flowchart developed by student 2

Collaboratively developed procedural flowchart

Students 1 and 2 also collaboratively developed a procedural flowchart, shown as Fig.  7 .

This discussion is presented as two sections: (1) how developing procedural flowcharts can support mathematics problem solving and (2) how developing procedural flowcharts support the integration of the different stages of mathematics problem solving. This study although limited by sample size highlighted how developing procedural flowcharts can support mathematics problem solving, can reinforce the structure of the solution to a problem and can help develop metacognitive skills among students. The different stages involved in problem solving inform the process of developing the solution to the problem. The focus on problem-based learning has signified the need to introduce resources that can support students and teachers in developing and structuring solutions to problems. Results from this study have also provided discussion points on how procedural flowcharts can have a positive impact in mathematics problem solving.

Procedural flowcharts can support mathematics problem solving

Procedural flowcharts help in visualising the process of problem solving. The results described in this study show that student-generated flowcharts can provide an overview of the proposed solution to the problem. The study noted that students preferred developing procedural flowcharts rather than writing how they planned to find a solution to the problem. The teachers also preferred visual aids because they were easier and quicker to process and facilitated understanding of the steps taken to reach the solution. These results are consistent with the findings of other researchers (McGowan & Boscia, 2016 ; Raiyn, 2016 ). The results are also consistent with Grosskinsky and colleagues’ ( 2019 ) findings that flowcharts break complex information into different tasks and show how they are connected, thereby enhancing understanding of the process. Consequently, they allow teachers to provide timely feedback at a checkpoint compared to the time a teacher would take to go through a written draft. Procedural flowcharts connect procedures and processes in a solution to the problem (Chinofunga et al., 2022 ). Thus, the feedback provided by the teacher can be more targeted to a particular stage identified on the procedural flowchart, making the feedback more effective and worthwhile. The development of a procedural flowchart during problem solving can be viewed as a visual representation of students’ plan and understanding of how they plan to solve the problem as demonstrated in Figs.  5 , 6 and 7 .

In this study, Ms. Simon noted that procedural flowcharts can represented students’ knowledge or thinking in a visual form, which is consistent with Owens and Clements’ ( 1998 ) findings that visual representations are cognitive constructs. Consequently, they can facilitate evaluation of such knowledge. This study noted that developing procedural flowcharts can provide opportunities to identify gaps in students’ understanding and problem-solving skills. It also noted that providing students with opportunities to develop procedural flowcharts may expose students’ misconceptions, the depth and breadth of their understanding of the problem and how they plan to solve the problem. This is supported by significant research (Grosskinsky et al., 2019 ; Norton et al., 2007 ; Vale & Barbosa, 2018 ), which identified flowcharts as a resource in helping visualise and recognise students’ understanding of a problem and communication of the solution. Thus, providing teachers with opportunities to have an insight into students’ thinking can facilitate intervention early in the process. The results in this study showed that when students develop their own plan on how to respond to a problem, they are at the centre of their learning. However, scaffolding and collaborative learning can also support problem solving.

Vygotsky ( 1978 ) posited that in the Zone of Proximal Development, collaborative learning and scaffolding can facilitate understanding. In this study, the results indicated that a teacher-developed procedural flowchart can be used to guide students in developing a solution to a problem. These results are consistent with Davidowitz and Rollnick’s study that concluded that flowcharts provide a bigger picture of how to solve the problem. In Queensland, the QCAA has developed a flowchart (see Appendix 1 ) to guide schools on problem-solving and modelling tasks. It highlights the significant stages to be considered during the process and how they relate to each other. Teachers are encouraged to contextualise official documents to suit their school and classes. In such cases, a procedural flowchart acts as a scaffolding resource in directing students on how to develop the solution to the problem. The findings are consistent with previous literature that flowcharts can give an overall direction of the process, help explain what is involved, may help reduce cognitive load and allow students to focus on complex tasks (Davidowitz & Rollnick, 2001 ; Norton et al., 2007 ; Sweller et al., 2019 ).

In addition to being a scaffolding resource, results showed that procedural flowcharts can be developed collaboratively providing students with an opportunity to share their solution to the problem. Being a scaffolding resource or a resource to use in a community of learning highlights the importance of procedural flowcharts in promoting learning within a zone of proximal development, as posited by Davidowitz and Rollnick ( 2001 ). Scaffolding students to problem solve and develop procedural flowcharts collaboratively provides students with the opportunity to be at the centre of problem solving.

Research has identified problem solving as student-centred learning (Ahmad et al., 2010 ; Karp & Wasserman, 2015 ; Reinholz, 2020 ; Vale & Barbosa, 2018 ). The process of developing the procedural flowcharts as students plan for the solution provides students with opportunities to engage more with the problem. Results showed that when students developed procedural flowcharts themselves, mathematics learning transformed from students just being told what to do or follow procedures into something creative and interesting. As students develop procedural flowcharts, they use concepts they have learnt to develop a solution to an unfamiliar problem (Matty, 2016 ), thus engaging with learning from the beginning of the process until they finalise the solution. The results indicated that developing procedural flowcharts promoted students’ ability to not only integrate different procedures to solve the problem but also determine how and when the conditions were ideal to address the problem, providing opportunities to justify and evaluate the procedures that were used.

Deeper understanding of mathematics and relationships between concepts plays an important role in problem solving, and the results from this study showed that different procedures can be integrated to develop a solution to a problem. The participants observed that developing procedural flowcharts could support the brainstorming ideas as they developed the flowchart, as ideas may interlink in a non-linear way. Moreover, students are expected at different stages to make key decisions about the direction they will need to take to reach the solution to the problem, as more than one strategy may be available. For example, student 1 planned on using only technology to develop the models while student 2 considered both technology and algebra. This showed that student 2 applied flexibility in using alternative methods, thus demonstrating a deeper understanding of the problem. Equally important, Ms. Simon observed that as students developed their procedural flowcharts while planning the steps to reach a solution, they were required to analyse, conceptualise, reason, analyse, synthesise and evaluate, which are important attributes of deeper understanding. Fostering deeper understanding of mathematics is the key goal of using problem solving (Kim et al., 2012 ; King, 1995 ; Moon, 2008 ; QCAA, 2018 ). The results are additionally consistent with findings from Owens and Clements ( 1998 ) and Roam ( 2009 ), who posited that visual aids foster reasoning and show cognitive constructs. Similarly, logical sequencing of procedures and ways to execute a strategy expected when developing procedural flowchart can support deeper understanding, as posited by Parvaneh and Duncan ( 2021 ). When developing procedural flowchart, students are required to link ideas that are related or feed into another, creating a web of knowledge. Students are also required to identify the ways in which a concept is applied as they develop a solution, and this requires deeper understanding of mathematics. Working collaboratively can also support deeper and broader understanding of mathematics.

The procedural flowchart that was developed collaboratively by the two students demonstrated some of the skills that they did not demonstrate in their individual procedural flowcharts. Like student 2, the collaboratively developed flowchart included use of technology and algebra to determine the models for the three different cups. The students considered both rate of change and area under a curve in the task analysis. Apart from planning to use rate at a point, average rate and definite integration, they added the trapezoidal rule. Both average rate and definite integration were to be applied within the same intervals, building the scope for comparison. The trapezoidal rule would also compare with integration. The complexity of the collaboratively developed procedural flowchart concurred with Rogoff and others ( 1984 ) and Stone ( 1998 ), who suggested that a community of learning can expand current skills to higher levels than individuals could achieve on their own. It seems the students used the feedback provided by the teacher on their individually developed procedural flowcharts as scaffolding to develop a much more complex procedural flowchart with competing procedures to address the problem. Their individually developed flowcharts might have acted as reference points, as their initial plans were still included in the collaboratively developed plan but with better clarity. This observation is consistent with Guk and Kellogg ( 2007 ), Kirova and Jamison ( 2018 ) and Ouyang and colleagues ( 2022 ), who noted that scaffolding involving peers, teacher and other resources enhances complex problem-solving tasks and transfer of skills.

Supporting the integration of the different stages of mathematics problem solving

When students develop procedural flowcharts, it supports the logical sequencing of ideas from different stages into a process that ends with a solution. Problem solving follows a proposed order and procedural flowcharts visually display decision and/or action sequences in a logical order (Krohn, 1983 ). They are used when a sequenced order of ideas is emphasised, such as in problem solving (Cantatore & Stevens, 2016 ). This study concurs with Krohn, Cantatore and Stevens, as the results showed that procedural flowcharts could be used to organise steps and ideas logically as students worked towards developing a solution. Students’ procedural flowcharts are expected to be developed through the following stages: problem identification, problem mathematisation, planning and execution and finally evaluation. Such a structure can be reinforced by teachers by sharing a generic problem-solving flowchart outlining the stages so that students can then develop a problem-specific version. Importantly, students’ artefacts in Figs.  5 , 6 and 7 provided evidence of how procedural flowcharts support the different stages of problem-solving stages to create a logical and sequential flow of the solution (see Appendix 1 ). Similarly, Ms. Simon noted that while her students had previously had problems in presenting the steps to their solution in a logical way, she witnessed a significant improvement after she asked them to develop procedural flowcharts first. Further, the results are consistent with Chinofunga et al.’s ( 2022 ) work that procedural flowcharts can support procedural flexibility, as they can accommodate more than one procedure in the “identify and execute mathematics procedures that can solve the problem” stage. Thus, stages that require one procedure or more than one procedure can all be accommodated in a single procedural flowchart. Evaluating the different procedures is also a key stage in problem solving.

As students develop the solution to the problem and identify ways to address the problem, they also have to evaluate the procedures, reflecting on the limitations and strengths of the solutions they offer. Ms. Simon observed that her students had previously struggled with identifying strengths and weaknesses of different procedures. However, she noted that procedural flowcharts gave students the opportunity to reflect and compare as they planned the solution. For example, students could have the opportunity to reflect and compare rate at a point, average rate and integration so they can evaluate which strategy can best address he problem. The artefacts identified the different procedures the students used in planning the solution, enabling them to evaluate the effectiveness of each strategy. Thus, enhancing students’ capacity to make decisions and identify the optimal strategy to solve a problem aligns with the work of McGowan and Boscia ( 2016 ). Similarly, Chinofunga and colleagues’ findings noted that developing procedural flowcharts can be effective in evaluating different procedures as they can accommodate several procedures. The different stages that need to be followed during problem solving and the way the solution to the problem is logically presented are central to how the final product is communicated.

In this study, procedural flowcharts were used to communicate the plan to reach the solution to a problem. The length of time given to students to work on their problem-solving tasks in Queensland is fairly long (4 weeks) and students may struggle to remember some key processes along the way. Developing procedural flowcharts to gain an overview of the solution to the problem and share it with the teacher at an early checkpoint is of significant importance. In this study, Ms. Simon expected her students to share their procedural flowcharts early in the process for her to give feedback, thus making the flowcharts a communication tool. The procedural flowcharts developed by the students in Figs.  5 , 6 and 7 show how students proposed solving the problem. This result lends further support to the NCTM ( 2000 ) findings that visual representations can help students communicate their thinking before applying those thoughts to solving a problem. Ms. Simon also noted that before introducing students to procedural flowcharts, they did not have an overall coherent structure to follow, which presented challenges when they wanted to communicate a plan that involved more than one strategy. However, the students’ artefacts were meaningful, clearly articulating how the solution to the problem was being developed, thus demonstrating that procedural flowcharts can provide the structure that supports the coherent and logical communication of the solution to the problem by both teachers and students (Norton et al., 2007 ). The visual nature of the students’ responses in the form of procedural flowcharts is key to communicating the proposed solution to the problem.

Visual representations are a favourable alternative to narrative communication. Procedural flowcharts can help teachers to check students’ work faster and provide critical feedback in a timely manner. Ms. Simon noted that the use of procedural flowcharts provided her with the opportunity to provide feedback faster and more effectively earlier in the task because the charts provided her with an overview of the whole proposed solution. Considering that students are expected to write a report of 2000 words or 10 pages on the task, the procedural flowchart provides the opportunity to present large amounts of information in just one visual representation. Raiyn ( 2016 ) noted that visual representations can be a quicker way to evaluate a solution and represent large amounts of information.

The procedural flowcharts that were created by students in this study demonstrate that they can be effective in supporting the development of problem-solving skills. This study suggests that including procedural flowcharts in problem solving may support teachers and students in communicating efficiently about how to solve the problem. For students, it is a resource that provides the solution overview, while teachers can consider it as a mental representation of students’ thinking as they plan the steps to reach a solution. Student-developed procedural flowcharts may represent how a student visualises a solution to a problem after brainstorming different pathways and different decision-making stages.

Moreover, as highlighted in this study, the visual nature of procedural flowcharts may offer a diverse range of support for problem solving. Procedural flowcharts make it easy to process and provide timely feedback that in turn might help students engage with the problem meaningfully. Furthermore, they may also provide a structure of the problem-solving process and guide students through the problem-solving process. Navigating through stages of problem solving might be supported by having students design procedural flowcharts first and then execute the plan. Indeed, this study showed that the ability of procedural flowcharts to represent multiple procedures, evaluation stages or loops and alternative paths helps students reflect and think about how to present a logically cohesive solution. Importantly, procedural flowcharts have also been identified as a resource that can help students communicate the solution to the problem. Procedural flowcharts have been noted to support deeper understanding as it may facilitate analysis, logical sequencing, reflection, reasoning, evaluation and communication. Although the in-depth study involved one teacher and three artefacts from her students, which is a very small sample to be conclusive, it identified the numerous advantages that procedural flowcharts bring to mathematics learning and teaching, particularly in terms of supporting the development of problem-solving skills. The study calls for further investigation on how procedural flowcharts can support students’ problem solving.

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Musarurwa David Chinofunga, Philemon Chigeza & Subhashni Taylor

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A research report which is part of a PhD study by the first author who is an experienced high school mathematics teacher in Queensland, Australia. The second and third authors are primary and secondary advisors respectively. Correspondence concerning this article should be addressed to David Chinofunga, College of Arts, Society and Education, Nguma-bada Campus, Smithfield, Building A4, Cairns, PO Box 6811 Cairns QLD 4870, Australia.

Appendix 1 An approach to problem solving and mathematical modelling

Appendix 2 Phases three and four thematic analysis themes

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Chinofunga, M.D., Chigeza, P. & Taylor, S. How can procedural flowcharts support the development of mathematics problem-solving skills?. Math Ed Res J (2024). https://doi.org/10.1007/s13394-024-00483-3

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DOI : https://doi.org/10.1007/s13394-024-00483-3

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