how is problem solving used in everyday life

10 Everyday uses for Problem Solving Skills

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Many employers are recognizing the value and placing significant investments in developing the problem solving skills of their employees.  While we often think about these skills in the work context, problem solving isn’t just helpful in the workplace.  Here are 10 everyday uses for problem solving skills that can you may not have thought about

1. Stuck in traffic and late for work, again

With busy schedules and competing demands for your time, getting where you need to be on time can be a real challenge.  When traffic backs up, problem solving skills can help you figure out alternatives to avoid congestion, resolve the immediate situation and develop a solution to avoid encountering the situation in the future.

2. What is that stain on the living room carpet?

Parents, pet owners and spouses face this situation all the time.  The living room carpet was clean yesterday but somehow a mysterious stain has appeared and nobody is claiming it.  In order to clean it effectively, first you need to figure out what it is.  Problem solving can help you track down the culprit, diagnose the cause of the stain and develop an action plan to get your home clean and fresh again.

3. What is that smell coming from my garden shed?

Drawing from past experiences, the seasoned problem solver in you suspects that the source of the peculiar odor likely lurks somewhere within the depths of the shed. Your challenge now lies in uncovering the origin of this scent, managing its effects, and formulating a practical plan to prevent such occurrences in the future.

4. I don’t think the car is supposed to make that thumping noise

As with many problems in the workplace, this may be a situation to bring in problem solving experts in the form of your trusted mechanic.  If that isn’t an option, problem solving skills can be helpful to diagnose and assess the impact of the situation to ensure you can get where you need to be.

5. Creating a budget

Tap into your problem-solving prowess as you embark on the journey of budgeting. Begin by determining what expenses to include in your budget, and strategize how to account for unexpected financial surprises. The challenge lies in crafting a comprehensive budget that not only covers your known expenses but also prepares you for the uncertainties that may arise.

6. My daughter has a science project – due tomorrow

Sometimes the challenge isn’t impact, its urgency.  Problem solving skills can help you quickly assess the situation and develop an action plan to get that science project done and turned in on time.

7. What should I get my spouse for his/her birthday?

As with many problems, this one may not have a “right answer” or apparent solution.  Its time to apply those problem solving skills to evaluate the effects of past decisions combined with current environmental signals and available resources to select the perfect gift to put a smile on your significant other’s face.

8. The office printer suddenly stopped working, and there are important documents that need to be printed urgently.

Uh oh, time to think quickly.  There is an urgent situation that must be addressed to get things back to normal, a cause to be identified (what’s causing the printer issue), and an action plan to resolve it.  Problem solving skills can help you avoid stress and ensure that your documents are printed on time.

9. I’m torn between two cars! Which one should I choose?

In a world brimming with countless choices, employ decision analysis as your trusty tool to navigate the sea of options. Whether you’re selecting a car (or any other product), the challenge is to methodically identify and evaluate the best choices that align with your unique needs and preferences.

10. What’s for dinner?

Whether you are planning to eat alone, with family or entertaining friends and colleagues, meal planning can be a cause of daily stress.  Applying problem solving skills can put the dinner dilemma into perspective and help get the food on the table and keep everyone happy.

Problem Solving skills aren’t just for the workplace – they can be applied in your everyday life.  Kepner-Tregoe can help you and your team develop your problem solving skills through a combination of training and consulting with our problem solving experts.

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Problem-Solving Strategies and Obstacles

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

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

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

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

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

From Dilemmas to Solutions: Problem-Solving Examples to Learn From

• by the PsychNewsDaily Staff
• May 21, 2023

Introduction to Problem-Solving

Life is full of challenges and dilemmas, both big and small.

But if there’s one skill that can help you navigate these, it’s problem-solving .

So, what exactly is problem-solving? And why is it such a crucial skill in daily life?

Understanding the Concept of Problem-Solving

Problem-solving is a mental process that involves identifying, analyzing, and resolving challenges or difficulties.

It’s like a journey that starts with a problem and ends with a solution.

It’s a skill that’s not just used in the field of psychology but in all aspects of life.

Whether you’re trying to decide on the best route to work, dealing with a disagreement with a friend, or figuring out how to fix a leaky faucet, you’re using your problem-solving skills.

When you’re faced with a problem, your brain goes through a series of steps to find a solution.

This process can be conscious or unconscious and can involve logical thinking, creativity, and prior knowledge.

Effective problem-solving can lead to better decisions and outcomes, making it a valuable tool in your personal and professional life.

Importance of Problem-Solving in Daily Life

Why is problem-solving so important in daily life? Well, it’s simple.

Problems are a part of life.

They arise in different shapes and sizes, and in different areas of life, including work, relationships, health, and personal growth.

Having strong problem-solving skills can help you navigate these challenges effectively and efficiently.

In your personal life, problem-solving can help you manage stress and conflict, make better decisions, and achieve your goals.

In the workplace, it can help you navigate complex projects, improve processes, and foster innovation.

Problem-solving is also a key skill in many professions and industries, from engineering and science to healthcare and customer service.

Moreover, problem-solving can contribute to your overall mental well-being.

It can give you a sense of control and agency, reduce feelings of stress and anxiety, and foster a positive attitude.

It’s also a key component of resilience, the ability to bounce back from adversity.

In conclusion, problem-solving is a fundamental skill in life.

It’s a tool you can use to tackle challenges, make informed decisions, and drive change.

By understanding the concept of problem-solving and recognizing its importance in daily life, you’re taking the first step toward becoming a more effective problem solver.

As we delve deeper into this topic, you’ll discover practical problem-solving examples, learn about different problem-solving techniques, and gain insights on how to improve your own problem-solving skills.

So, stay tuned and continue your exploration of introduction to psychology with us.

Stages of Problem-Solving

The process of problem-solving can be broken down into three key stages: identifying the problem , developing possible solutions , and implementing the best solution .

Each stage requires a different set of skills and strategies.

By understanding these stages, you can enhance your problem-solving abilities and tackle various challenges more effectively.

Identifying the Problem

The first step in problem-solving is recognizing that a problem exists.

This involves defining the issue clearly and understanding its root cause.

You might need to gather information, ask questions, and analyze the situation from multiple perspectives.

It can be helpful to write down the problem and think about how it impacts you or others involved.

For instance, if you’re struggling with time management, the problem might be that you have too many obligations and not enough time.

Or perhaps your methods of organizing your tasks aren’t effective.

It’s important to be as specific as possible when identifying the problem, as this will guide the rest of the problem-solving process.

Developing Possible Solutions

Once you’ve identified the problem, the next step is to brainstorm possible solutions.

This is where creativity comes into play.

Don’t limit yourself; even ideas that seem unrealistic or out of the box can lead to effective solutions.

Consider different strategies and approaches.

You could try using techniques like mind mapping, listing pros and cons, or consulting with others for fresh perspectives.

Remember, the goal is to generate a variety of options, not to choose a solution at this stage.

Implementing the Best Solution

The final stage of problem-solving is to select the best solution and put it into action.

Review the options you’ve developed, evaluate their potential effectiveness, and make a decision.

Keep in mind that the “best” solution isn’t necessarily the perfect one (as there might not be a perfect solution), but rather the one that seems most likely to achieve your desired outcome given the circumstances.

Once you’ve chosen a solution, plan out the steps needed to implement it and then take action.

Monitor the results and adjust your approach as necessary.

If the problem persists, don’t be discouraged; return to the previous stages, reassess the problem and your potential solutions, and try again.

Remember, problem-solving is a dynamic process that often involves trial and error.

It’s an essential skill in many areas of life, from everyday challenges to workplace dilemmas.

To learn more about the psychology behind problem-solving and decision-making, check out our introduction to psychology article.

Problem-Solving Examples

Understanding the concept of problem-solving is one thing, but seeing it in action is another.

To help you grasp the practical application of problem-solving strategies, let’s explore three different problem-solving examples from daily life, the workplace, and relationships.

Daily Life Problem-Solving Example

Imagine you’re trying to lose weight but struggle with late-night snacking.

The issue isn’t uncommon, but it’s hindering your progress towards your weight loss goal.

• Identifying the Problem : Late-night snacking is causing you to consume extra calories, preventing weight loss.
• Developing Possible Solutions : You could consider eating an earlier dinner, having a healthier snack option, or practicing mindful eating.
• Implementing the Best Solution : After trying out different solutions, you find that preparing a healthy snack in advance minimizes your calorie intake and satisfies your late-night cravings, helping you stay on track with your weight loss goal.

Workplace Problem-Solving Example

Let’s consider a scenario where a team at work is failing to meet project deadlines consistently.

• Identifying the Problem : The team is not completing projects on time, causing delays in the overall project timeline.
• Developing Possible Solutions : The team could consider improving their time management skills, using project management tools, or redistributing tasks among team members.
• Implementing the Best Solution : After trying out different strategies, the team finds that using a project management tool helps them stay organized, delegate tasks effectively, and complete projects within the given timeframe.

For more insights on effective management styles that can help in problem-solving at the workplace, check out our articles on autocratic leadership , democratic leadership style , and laissez faire leadership .

Relationship Problem-Solving Example

In a romantic relationship, conflicts can occasionally arise.

Let’s imagine a common issue where one partner feels the other isn’t spending enough quality time with them.

• Identifying the Problem : One partner feels neglected due to a lack of quality time spent together.
• Developing Possible Solutions : The couple could consider scheduling regular date nights, engaging in shared hobbies, or setting aside a specific time each day for undisturbed conversation.
• Implementing the Best Solution : The couple decides to implement a daily “unplugged” hour where they focus solely on each other without distractions. This results in improved relationship satisfaction.

For more on navigating relationship challenges, check out our articles on anxious avoidant attachment and emotional awareness .

These problem-solving examples illustrate how the process of identifying a problem, developing possible solutions, and implementing the best solution can be applied to various situations.

By understanding and applying these strategies, you can improve your problem-solving skills and navigate challenges more effectively.

Techniques for Effective Problem-Solving

As you navigate the world of problem-solving, you’ll find that there are multiple techniques you can use to arrive at a solution.

Each technique offers a unique approach to identifying issues, generating potential solutions, and choosing the best course of action.

In this section, we’ll explore three common techniques: Brainstorming , Root Cause Analysis , and SWOT Analysis .

Brainstorming

Brainstorming is a free-thinking method used to generate a large number of ideas related to a specific problem.

You do this by suspending criticism and allowing your creativity to flow.

The aim is to produce as many ideas as possible, even if they seem far-fetched.

You then evaluate these ideas to identify the most beneficial solutions.

By using brainstorming, you can encourage out-of-the-box thinking and possibly discover innovative solutions to challenging problems.

Root Cause Analysis

Root Cause Analysis (RCA) is a method used to identify the underlying causes of a problem.

The goal is to address these root causes rather than the symptoms of the problem.

This technique helps to prevent the same issue from recurring in the future.

There are several RCA methods, such as the “5 Whys” technique, where you ask “why” multiple times until you uncover the root cause of the problem.

By identifying and addressing the root cause, you tackle the problem at its source, which can lead to more effective and long-lasting solutions.

SWOT Analysis

SWOT Analysis is a strategic planning technique that helps you identify your Strengths, Weaknesses, Opportunities, and Threats related to a problem.

This approach encourages you to examine the problem from different angles, helping you understand the resources you have at your disposal (Strengths), the areas where you could improve (Weaknesses), the external factors that could benefit you (Opportunities), and the external factors that could cause problems (Threats).

With this comprehensive understanding, you can develop a well-informed strategy to solve the problem.

Each of these problem-solving techniques provides a distinct approach to identifying and resolving issues.

By understanding and utilizing these methods, you can enhance your problem-solving skills and increase your effectiveness in dealing with challenges.

For more insights into effective problem-solving and other psychological topics, explore our introduction to psychology .

Improving Your Problem-Solving Skills

Learning to solve problems effectively is a skill that can be honed with time and practice.

The following are some ways to enhance your problem-solving capabilities.

Practice Makes Perfect

The saying “practice makes perfect” holds true when it comes to problem-solving.

The more problems you tackle, the better you’ll become at devising and implementing effective solutions.

Seek out opportunities to practice your problem-solving skills both in everyday life and in more complex situations.

This could involve resolving a dispute at work, figuring out a puzzle, or even strategizing in a board game.

Each problem you encounter is a new opportunity to apply and refine your skills.

Learning from Others’ Experiences

There’s much to be gained from observing how others approach problem-solving.

Whether it’s reading about problem solving examples from renowned psychologists or discussing strategies with colleagues, you can learn valuable techniques and perspectives from the experiences of others.

Consider participating in group activities that require problem-solving, such as escape rooms or team projects.

Observe how team members identify problems, brainstorm solutions, and decide on the best course of action.

Embracing a Growth Mindset

A key component of effective problem-solving is adopting a growth mindset.

This mindset, coined by psychologist Carol Dweck, is the belief that abilities and intelligence can be developed through dedication and hard work.

When you embrace a growth mindset, you view challenges as opportunities to learn and grow rather than as insurmountable obstacles.

Believing in your ability to develop and enhance your problem-solving skills over time can make the process less daunting and more rewarding.

So, when you encounter a problem, instead of thinking, “I can’t do this,” try thinking, “I can’t do this yet, but with effort and practice, I can learn.”

For more on the growth mindset, you might want to check out our article on what is intrinsic motivation which includes how a growth mindset can fuel your motivation to improve.

By practicing regularly, learning from others, and embracing a growth mindset, you can continually improve your problem-solving skills and become more adept at overcoming challenges you encounter.

Related posts:

• Embrace the Change: Embodying the Democratic Leadership Style
• Taking Charge by Doing Nothing: Understanding Laissez Faire Leadership
• Mastering Leadership: Unraveling the Contingency Theory

Introduction to Problem Solving Skills

What is problem solving and why is it important.

The ability to solve problems is a basic life skill and is essential to our day-to-day lives, at home, at school, and at work. We solve problems every day without really thinking about how we solve them. For example: it’s raining and you need to go to the store. What do you do? There are lots of possible solutions. Take your umbrella and walk. If you don't want to get wet, you can drive, or take the bus. You might decide to call a friend for a ride, or you might decide to go to the store another day. There is no right way to solve this problem and different people will solve it differently.

Problem solving is the process of identifying a problem, developing possible solution paths, and taking the appropriate course of action.

Why is problem solving important? Good problem solving skills empower you not only in your personal life but are critical in your professional life. In the current fast-changing global economy, employers often identify everyday problem solving as crucial to the success of their organizations. For employees, problem solving can be used to develop practical and creative solutions, and to show independence and initiative to employers.

Throughout this case study you will be asked to jot down your thoughts in idea logs. These idea logs are used for reflection on concepts and for answering short questions. When you click on the "Next" button, your responses will be saved for that page. If you happen to close the webpage, you will lose your work on the page you were on, but previous pages will be saved. At the end of the case study, click on the "Finish and Export to PDF" button to acknowledge completion of the case study and receive a PDF document of your idea logs.

What Does Problem Solving Look Like?

The ability to solve problems is a skill, and just like any other skill, the more you practice, the better you get. So how exactly do you practice problem solving? Learning about different problem solving strategies and when to use them will give you a good start. Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic.

Algorithmic strategies are traditional step-by-step guides to solving problems. They are great for solving math problems (in algebra: multiply and divide, then add or subtract) or for helping us remember the correct order of things (a mnemonic such as “Spring Forward, Fall Back” to remember which way the clock changes for daylight saving time, or “Righty Tighty, Lefty Loosey” to remember what direction to turn bolts and screws). Algorithms are best when there is a single path to the correct solution.

But what do you do when there is no single solution for your problem? Heuristic methods are general guides used to identify possible solutions. A popular one that is easy to remember is IDEAL [ Bransford & Stein, 1993 ] :

• I dentify the problem
• D efine the context of the problem
• E xplore possible strategies
• A ct on best solution

IDEAL is just one problem solving strategy. Building a toolbox of problem solving strategies will improve your problem solving skills. With practice, you will be able to recognize and use multiple strategies to solve complex problems.

Watch the video

What is the best way to get a peanut out of a tube that cannot be moved? Watch a chimpanzee solve this problem in the video below [ Geert Stienissen, 2010 ].

[PDF transcript]

Describe the series of steps you think the chimpanzee used to solve this problem.

• [Page 2: What does Problem Solving Look Like?] Describe the series of steps you think the chimpanzee used to solve this problem.

Think of an everyday problem you've encountered recently and describe your steps for solving it.

• [Page 2: What does Problem Solving Look Like?] Think of an everyday problem you've encountered recently and describe your steps for solving it.

Developing Problem Solving Processes

Problem solving is a process that uses steps to solve problems. But what does that really mean? Let's break it down and start building our toolbox of problem solving strategies.

What is the first step of solving any problem? The first step is to recognize that there is a problem and identify the right cause of the problem. This may sound obvious, but similar problems can arise from different events, and the real issue may not always be apparent. To really solve the problem, it's important to find out what started it all. This is called identifying the root cause .

Example: You and your classmates have been working long hours on a project in the school's workshop. The next afternoon, you try to use your student ID card to access the workshop, but discover that your magnetic strip has been demagnetized. Since the card was a couple of years old, you chalk it up to wear and tear and get a new ID card. Later that same week you learn that several of your classmates had the same problem! After a little investigation, you discover that a strong magnet was stored underneath a workbench in the workshop. The magnet was the root cause of the demagnetized student ID cards.

The best way to identify the root cause of the problem is to ask questions and gather information. If you have a vague problem, investigating facts is more productive than guessing a solution. Ask yourself questions about the problem. What do you know about the problem? What do you not know? When was the last time it worked correctly? What has changed since then? Can you diagram the process into separate steps? Where in the process is the problem occurring? Be curious, ask questions, gather facts, and make logical deductions rather than assumptions.

Watch Adam Savage from Mythbusters, describe his problem solving process [ ForaTv, 2010 ]. As you watch this section of the video, try to identify the questions he asks and the different strategies he uses.

Adam Savage shared many of his problem solving processes. List the ones you think are the five most important. Your list may be different from other people in your class—that's ok!

• [Page 3: Developing Problem Solving Processes] Adam Savage shared many of his problem solving processes. List the ones you think are the five most important.

“The ability to ask the right question is more than half the battle of finding the answer.” — Thomas J. Watson , founder of IBM

Voices From the Field: Solving Problems

In manufacturing facilities and machine shops, everyone on the floor is expected to know how to identify problems and find solutions. Today's employers look for the following skills in new employees: to analyze a problem logically, formulate a solution, and effectively communicate with others.

In this video, industry professionals share their own problem solving processes, the problem solving expectations of their employees, and an example of how a problem was solved.

Meet the Partners:

• Taconic High School in Pittsfield, Massachusetts, is a comprehensive, fully accredited high school with special programs in Health Technology, Manufacturing Technology, and Work-Based Learning.
• Berkshire Community College in Pittsfield, Massachusetts, prepares its students with applied manufacturing technical skills, providing hands-on experience at industrial laboratories and manufacturing facilities, and instructing them in current technologies.
• H.C. Starck in Newton, Massachusetts, specializes in processing and manufacturing technology metals, such as tungsten, niobium, and tantalum. In almost 100 years of experience, they hold over 900 patents, and continue to innovate and develop new products.
• Nypro Healthcare in Devens, Massachusetts, specializes in precision injection-molded healthcare products. They are committed to good manufacturing processes including lean manufacturing and process validation.

Making Decisions

Now that you have a couple problem solving strategies in your toolbox, let's practice. In this exercise, you are given a scenario and you will be asked to decide what steps you would take to identify and solve the problem.

Scenario: You are a new employee and have just finished your training. As your first project, you have been assigned the milling of several additional components for a regular customer. Together, you and your trainer, Bill, set up for the first run. Checking your paperwork, you gather the tools and materials on the list. As you are mounting the materials on the table, you notice that you didn't grab everything and hurriedly grab a few more items from one of the bins. Once the material is secured on the CNC table, you load tools into the tool carousel in the order listed on the tool list and set the fixture offsets.

Bill tells you that since this is a rerun of a job several weeks ago, the CAD/CAM model has already been converted to CNC G-code. Bill helps you download the code to the CNC machine. He gives you the go-ahead and leaves to check on another employee. You decide to start your first run.

What problems did you observe in the video?

• [Page 5: Making Decisions] What problems did you observe in the video?
• What do you do next?
• Try to fix it yourself.
• Ask your trainer for help.

As you are cleaning up, you think about what happened and wonder why it happened. You try to create a mental picture of what happened. You are not exactly sure what the end mill hit, but it looked like it might have hit the dowel pin. You wonder if you grabbed the correct dowel pins from the bins earlier.

You can think of two possible next steps. You can recheck the dowel pin length to make sure it is the correct length, or do a dry run using the CNC single step or single block function with the spindle empty to determine what actually happened.

• Check the dowel pins.
• Use the single step/single block function to determine what happened.

You notice that your trainer, Bill, is still on the floor and decide to ask him for help. You describe the problem to him. Bill asks if you know what the end mill ran into. You explain that you are not sure but you think it was the dowel pin. Bill reminds you that it is important to understand what happened so you can fix the correct problem. He suggests that you start all over again and begin with a dry run using the single step/single block function, with the spindle empty, to determine what it hit. Or, since it happened at the end, he mentions that you can also check the G-code to make sure the Z-axis is raised before returning to the home position.

• Run the single step/single block function.
• Edit the G-code to raise the Z-axis.

You finish cleaning up and check the CNC for any damage. Luckily, everything looks good. You check your paperwork and gather the components and materials again. You look at the dowel pins you used earlier, and discover that they are not the right length. As you go to grab the correct dowel pins, you have to search though several bins. For the first time, you are aware of the mess - it looks like the dowel pins and other items have not been put into the correctly labeled bins. You spend 30 minutes straightening up the bins and looking for the correct dowel pins.

Finally finding them, you finish setting up. You load tools into the tool carousel in the order listed on the tool list and set the fixture offsets. Just to make sure, you use the CNC single step/single block function, to do a dry run of the part. Everything looks good! You are ready to create your first part. The first component is done, and, as you admire your success, you notice that the part feels hotter than it should.

You wonder why? You go over the steps of the process to mentally figure out what could be causing the residual heat. You wonder if there is a problem with the CNC's coolant system or if the problem is in the G-code.

• Look at the G-code.

After thinking about the problem, you decide that maybe there's something wrong with the setup. First, you clean up the damaged materials and remove the broken tool. You check the CNC machine carefully for any damage. Luckily, everything looks good. It is time to start over again from the beginning.

You again check your paperwork and gather the tools and materials on the setup sheet. After securing the new materials, you use the CNC single step/single block function with the spindle empty, to do a dry run of the part. You watch carefully to see if you can figure out what happened. It looks to you like the spindle barely misses hitting the dowel pin. You determine that the end mill was broken when it hit the dowel pin while returning to the start position.

After conducting a dry run using the single step/single block function, you determine that the end mill was damaged when it hit the dowel pin on its return to the home position. You discuss your options with Bill. Together, you decide the best thing to do would be to edit the G-code and raise the Z-axis before returning to home. You open the CNC control program and edit the G-code. Just to make sure, you use the CNC single step/single block function, to do another dry run of the part. You are ready to create your first part. It works. You first part is completed. Only four more to go.

As you are cleaning up, you notice that the components are hotter than you expect and the end mill looks more worn than it should be. It dawns on you that while you were milling the component, the coolant didn't turn on. You wonder if it is a software problem in the G-code or hardware problem with the CNC machine.

It's the end of the day and you decide to finish the rest of the components in the morning.

• You decide to look at the G-code in the morning.
• You leave a note on the machine, just in case.

You decide that the best thing to do would be to edit the G-code and raise the Z-axis of the spindle before it returns to home. You open the CNC control program and edit the G-code.

While editing the G-code to raise the Z-axis, you notice that the coolant is turned off at the beginning of the code and at the end of the code. The coolant command error caught your attention because your coworker, Mark, mentioned having a similar issue during lunch. You change the coolant command to turn the mist on.

• You decide to talk with your supervisor.
• You discuss what happened with a coworker over lunch.

As you reflect on the residual heat problem, you think about the machining process and the factors that could have caused the issue. You try to think of anything and everything that could be causing the issue. Are you using the correct tool for the specified material? Are you using the specified material? Is it running at the correct speed? Is there enough coolant? Are there chips getting in the way?

Wait, was the coolant turned on? As you replay what happened in your mind, you wonder why the coolant wasn't turned on. You decide to look at the G-code to find out what is going on.

From the milling machine computer, you open the CNC G-code. You notice that there are no coolant commands. You add them in and on the next run, the coolant mist turns on and the residual heat issues is gone. Now, its on to creating the rest of the parts.

Have you ever used brainstorming to solve a problem? Chances are, you've probably have, even if you didn't realize it.

You notice that your trainer, Bill, is on the floor and decide to ask him for help. You describe the problem with the end mill breaking, and how you discovered that items are not being returned to the correctly labeled bins. You think this caused you to grab the incorrect length dowel pins on your first run. You have sorted the bins and hope that the mess problem is fixed. You then go on to tell Bill about the residual heat issue with the completed part.

Together, you go to the milling machine. Bill shows you how to check the oil and coolant levels. Everything looks good at the machine level. Next, on the CNC computer, you open the CNC G-code. While looking at the code, Bill points out that there are no coolant commands. Bill adds them in and when you rerun the program, it works.

Bill is glad you mentioned the problem to him. You are the third worker to mention G-code issues over the last week. You noticed the coolant problems in your G-code, John noticed a Z-axis issue in his G-code, and Sam had issues with both the Z-axis and the coolant. Chances are, there is a bigger problem and Bill will need to investigate the root cause .

Talking with Bill, you discuss the best way to fix the problem. Bill suggests editing the G-code to raise the Z-axis of the spindle before it returns to its home position. You open the CNC control program and edit the G-code. Following the setup sheet, you re-setup the job and use the CNC single step/single block function, to do another dry run of the part. Everything looks good, so you run the job again and create the first part. It works. Since you need four of each component, you move on to creating the rest of them before cleaning up and leaving for the day.

It's a new day and you have new components to create. As you are setting up, you go in search of some short dowel pins. You discover that the bins are a mess and components have not been put away in the correctly labeled bins. You wonder if this was the cause of yesterday's problem. As you reorganize the bins and straighten up the mess, you decide to mention the mess issue to Bill in your afternoon meeting.

You describe the bin mess and using the incorrect length dowels to Bill. He is glad you mentioned the problem to him. You are not the first person to mention similar issues with tools and parts not being put away correctly. Chances are there is a bigger safety issue here that needs to be addressed in the next staff meeting.

In any workplace, following proper safety and cleanup procedures is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly and sometimes dangerous equipment. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money.

You now know that the end mill was damaged when it hit the dowel pin. It seems to you that the easiest thing to do would be to edit the G-code and raise the Z-axis position of the spindle before it returns to the home position. You open the CNC control program and edit the G-code, raising the Z-axis. Starting over, you follow the setup sheet and re-setup the job. This time, you use the CNC single step/single block function, to do another dry run of the part. Everything looks good, so you run the job again and create the first part.

At the end of the day, you are reviewing your progress with your trainer, Bill. After you describe the day's events, he reminds you to always think about safety and the importance of following work procedures. He decides to bring the issue up in the next morning meeting as a reminder to everyone.

In any workplace, following proper procedures (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. One tool to improve communication is the morning meeting or huddle.

The next morning, you check the G-code to determine what is wrong with the coolant. You notice that the coolant is turned off at the beginning of the code and also at the end of the code. This is strange. You change the G-code to turn the coolant on at the beginning of the run and off at the end. This works and you create the rest of the parts.

Throughout the day, you keep wondering what caused the G-code error. At lunch, you mention the G-code error to your coworker, John. John is not surprised. He said that he encountered a similar problem earlier this week. You decide to talk with your supervisor the next time you see him.

You are in luck. You see your supervisor by the door getting ready to leave. You hurry over to talk with him. You start off by telling him about how you asked Bill for help. Then you tell him there was a problem and the end mill was damaged. You describe the coolant problem in the G-code. Oh, and by the way, John has seen a similar problem before.

Your supervisor doesn't seem overly concerned, errors happen. He tells you "Good job, I am glad you were able to fix the issue." You are not sure whether your supervisor understood your explanation of what happened or that it had happened before.

The challenge of communicating in the workplace is learning how to share your ideas and concerns. If you need to tell your supervisor that something is not going well, it is important to remember that timing, preparation, and attitude are extremely important.

It is the end of your shift, but you want to let the next shift know that the coolant didn't turn on. You do not see your trainer or supervisor around. You decide to leave a note for the next shift so they are aware of the possible coolant problem. You write a sticky note and leave it on the monitor of the CNC control system.

How effective do you think this solution was? Did it address the problem?

In this scenario, you discovered several problems with the G-code that need to be addressed. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring and avoid injury to personnel. The challenge of communicating in the workplace is learning how and when to share your ideas and concerns. If you need to tell your co-workers or supervisor that there is a problem, it is important to remember that timing and the method of communication are extremely important.

You are able to fix the coolant problem in the G-code. While you are glad that the problem is fixed, you are worried about why it happened in the first place. It is important to remember that if a problem keeps reappearing, you may not be fixing the right problem. You may only be addressing the symptoms.

You decide to talk to your trainer. Bill is glad you mentioned the problem to him. You are the third worker to mention G-code issues over the last week. You noticed the coolant problems in your G-code, John noticed a Z-axis issue in his G-code, and Sam had issues with both the Z-axis and the coolant. Chances are, there is a bigger problem and Bill will need to investigate the root cause .

Over lunch, you ask your coworkers about the G-code problem and what may be causing the error. Several people mention having similar problems but do not know the cause.

You have now talked to three coworkers who have all experienced similar coolant G-code problems. You make a list of who had the problem, when they had the problem, and what each person told you.

When you see your supervisor later that afternoon, you are ready to talk with him. You describe the problem you had with your component and the damaged bit. You then go on to tell him about talking with Bill and discovering the G-code issue. You show him your notes on your coworkers' coolant issues, and explain that you think there might be a bigger problem.

You supervisor thanks you for your initiative in identifying this problem. It sounds like there is a bigger problem and he will need to investigate the root cause. He decides to call a team huddle to discuss the issue, gather more information, and talk with the team about the importance of communication.

Root Cause Analysis

Root cause analysis ( RCA ) is a method of problem solving that identifies the underlying causes of an issue. Root cause analysis helps people answer the question of why the problem occurred in the first place. RCA uses clear cut steps in its associated tools, like the "5 Whys Analysis" and the "Cause and Effect Diagram," to identify the origin of the problem, so that you can:

• Determine what happened.
• Determine why it happened.
• Fix the problem so it won’t happen again.

RCA works under the idea that systems and events are connected. An action in one area triggers an action in another, and another, and so on. By tracing back these actions, you can discover where the problem started and how it developed into the problem you're now facing. Root cause analysis can prevent problems from recurring, reduce injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money. There are many different RCA techniques available to determine the root cause of a problem. These are just a few:

• Root Cause Analysis Tools
• 5 Whys Analysis
• Fishbone or Cause and Effect Diagram
• Pareto Analysis

How Huddles Work

Communication is a vital part of any setting where people work together. Effective communication helps employees and managers form efficient teams. It builds trusts between employees and management, and reduces unnecessary competition because each employee knows how their part fits in the larger goal.

One tool that management can use to promote communication in the workplace is the huddle . Just like football players on the field, a huddle is a short meeting where everyone is standing in a circle. A daily team huddle ensures that team members are aware of changes to the schedule, reiterated problems and safety issues, and how their work impacts one another. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

The most important thing to remember about huddles is that they are short, lasting no more than 10 minutes, and their purpose is to communicate and identify. In essence, a huddle’s purpose is to identify priorities, communicate essential information, and discover roadblocks to productivity.

Who uses huddles? Many industries and companies use daily huddles. At first thought, most people probably think of hospitals and their daily patient update meetings, but lots of managers use daily meetings to engage their employees. Here are a few examples:

• Brian Scudamore, CEO of 1-800-Got-Junk? , uses the daily huddle as an operational tool to take the pulse of his employees and as a motivational tool. Watch a morning huddle meeting .
• Fusion OEM, an outsourced manufacturing and production company. What do employees take away from the daily huddle meeting .
• Biz-Group, a performance consulting group. Tips for a successful huddle .

Brainstorming

One tool that can be useful in problem solving is brainstorming . Brainstorming is a creativity technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in 1953 by Alex Faickney Osborn in the book Applied Imagination . The goal is to come up with as many ideas as you can in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually. Like most problem solving techniques, brainstorming is a process.

• Define a clear objective.
• Have an agreed a time limit.
• During the brainstorming session, write down everything that comes to mind, even if the idea sounds crazy.
• If one idea leads to another, write down that idea too.
• Combine and refine ideas into categories of solutions.
• Assess and analyze each idea as a potential solution.

When used during problem solving, brainstorming can offer companies new ways of encouraging staff to think creatively and improve production. Brainstorming relies on team members' diverse experiences, adding to the richness of ideas explored. This means that you often find better solutions to the problems. Team members often welcome the opportunity to contribute ideas and can provide buy-in for the solution chosen—after all, they are more likely to be committed to an approach if they were involved in its development. What's more, because brainstorming is fun, it helps team members bond.

• Watch Peggy Morgan Collins, a marketing executive at Power Curve Communications discuss How to Stimulate Effective Brainstorming .
• Watch Kim Obbink, CEO of Filter Digital, a digital content company, and her team share their top five rules for How to Effectively Generate Ideas .

Importance of Good Communication and Problem Description

Communication is one of the most frequent activities we engage in on a day-to-day basis. At some point, we have all felt that we did not effectively communicate an idea as we would have liked. The key to effective communication is preparation. Rather than attempting to haphazardly improvise something, take a few minutes and think about what you want say and how you will say it. If necessary, write yourself a note with the key points or ideas in the order you want to discuss them. The notes can act as a reminder or guide when you talk to your supervisor.

Tips for clear communication of an issue:

• Provide a clear summary of your problem. Start at the beginning, give relevant facts, timelines, and examples.
• Avoid including your opinion or personal attacks in your explanation.
• Avoid using words like "always" or "never," which can give the impression that you are exaggerating the problem.
• If this is an ongoing problem and you have collected documentation, give it to your supervisor once you have finished describing the problem.
• Remember to listen to what's said in return; communication is a two-way process.

Not all communication is spoken. Body language is nonverbal communication that includes your posture, your hands and whether you make eye contact. These gestures can be subtle or overt, but most importantly they communicate meaning beyond what is said. When having a conversation, pay attention to how you stand. A stiff position with arms crossed over your chest may imply that you are being defensive even if your words state otherwise. Shoving your hands in your pockets when speaking could imply that you have something to hide. Be wary of using too many hand gestures because this could distract listeners from your message.

The challenge of communicating in the workplace is learning how and when to share your ideas or concerns. If you need to tell your supervisor or co-worker about something that is not going well, keep in mind that good timing and good attitude will go a long way toward helping your case.

Like all skills, effective communication needs to be practiced. Toastmasters International is perhaps the best known public speaking organization in the world. Toastmasters is open to anyone who wish to improve their speaking skills and is willing to put in the time and effort to do so. To learn more, visit Toastmasters International .

Methods of Communication

Communication of problems and issues in any workplace is important, particularly when safety is involved. It is therefore crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. As issues and problems arise, they need to be addressed in an efficient and timely manner. Effective communication is an important skill because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money.

There are many different ways to communicate: in person, by phone, via email, or written. There is no single method that fits all communication needs, each one has its time and place.

In person: In the workplace, face-to-face meetings should be utilized whenever possible. Being able to see the person you need to speak to face-to-face gives you instant feedback and helps you gauge their response through their body language. Be careful of getting sidetracked in conversation when you need to communicate a problem.

Email: Email has become the communication standard for most businesses. It can be accessed from almost anywhere and is great for things that don’t require an immediate response. Email is a great way to communicate non-urgent items to large amounts of people or just your team members. One thing to remember is that most people's inboxes are flooded with emails every day and unless they are hyper vigilant about checking everything, important items could be missed. For issues that are urgent, especially those around safety, email is not always be the best solution.

Phone: Phone calls are more personal and direct than email. They allow us to communicate in real time with another person, no matter where they are. Not only can talking prevent miscommunication, it promotes a two-way dialogue. You don’t have to worry about your words being altered or the message arriving on time. However, mobile phone use and the workplace don't always mix. In particular, using mobile phones in a manufacturing setting can lead to a variety of problems, cause distractions, and lead to serious injury.

Written: Written communication is appropriate when detailed instructions are required, when something needs to be documented, or when the person is too far away to easily speak with over the phone or in person.

There is no "right" way to communicate, but you should be aware of how and when to use the appropriate form of communication for your situation. When deciding the best way to communicate with a co-worker or manager, put yourself in their shoes, and think about how you would want to learn about the issue. Also, consider what information you would need to know to better understand the issue. Use your good judgment of the situation and be considerate of your listener's viewpoint.

Did you notice any other potential problems in the previous exercise?

• [Page 6:] Did you notice any other potential problems in the previous exercise?

Summary of Strategies

In this exercise, you were given a scenario in which there was a problem with a component you were creating on a CNC machine. You were then asked how you wanted to proceed. Depending on your path through this exercise, you might have found an easy solution and fixed it yourself, asked for help and worked with your trainer, or discovered an ongoing G-code problem that was bigger than you initially thought.

When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. Although, each path in this exercise ended with a description of a problem solving tool for your toolbox, the first step is always to identify the problem and define the context in which it happened.

There are several strategies that can be used to identify the root cause of a problem. Root cause analysis (RCA) is a method of problem solving that helps people answer the question of why the problem occurred. RCA uses a specific set of steps, with associated tools like the “5 Why Analysis" or the “Cause and Effect Diagram,” to identify the origin of the problem, so that you can:

Once the underlying cause is identified and the scope of the issue defined, the next step is to explore possible strategies to fix the problem.

If you are not sure how to fix the problem, it is okay to ask for help. Problem solving is a process and a skill that is learned with practice. It is important to remember that everyone makes mistakes and that no one knows everything. Life is about learning. It is okay to ask for help when you don’t have the answer. When you collaborate to solve problems you improve workplace communication and accelerates finding solutions as similar problems arise.

One tool that can be useful for generating possible solutions is brainstorming . Brainstorming is a technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in 1953 by Alex Faickney Osborn in the book Applied Imagination. The goal is to come up with as many ideas as you can, in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually.

Depending on your path through the exercise, you may have discovered that a couple of your coworkers had experienced similar problems. This should have been an indicator that there was a larger problem that needed to be addressed.

In any workplace, communication of problems and issues (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they be addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money.

One strategy for improving communication is the huddle . Just like football players on the field, a huddle is a short meeting with everyone standing in a circle. A daily team huddle is a great way to ensure that team members are aware of changes to the schedule, any problems or safety issues are identified and that team members are aware of how their work impacts one another. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

To learn more about different problem solving strategies, choose an option below. These strategies accompany the outcomes of different decision paths in the problem solving exercise.

• View Problem Solving Strategies Select a strategy below... Root Cause Analysis How Huddles Work Brainstorming Importance of Good Problem Description Methods of Communication

Communication is one of the most frequent activities we engage in on a day-to-day basis. At some point, we have all felt that we did not effectively communicate an idea as we would have liked. The key to effective communication is preparation. Rather than attempting to haphazardly improvise something, take a few minutes and think about what you want say and how you will say it. If necessary, write yourself a note with the key points or ideas in the order you want to discuss them. The notes can act as a reminder or guide during your meeting.

• Provide a clear summary of the problem. Start at the beginning, give relevant facts, timelines, and examples.

In person: In the workplace, face-to-face meetings should be utilized whenever possible. Being able to see the person you need to speak to face-to-face gives you instant feedback and helps you gauge their response in their body language. Be careful of getting sidetracked in conversation when you need to communicate a problem.

There is no "right" way to communicate, but you should be aware of how and when to use the appropriate form of communication for the situation. When deciding the best way to communicate with a co-worker or manager, put yourself in their shoes, and think about how you would want to learn about the issue. Also, consider what information you would need to know to better understand the issue. Use your good judgment of the situation and be considerate of your listener's viewpoint.

"Never try to solve all the problems at once — make them line up for you one-by-one.” — Richard Sloma

Problem Solving: An Important Job Skill

Problem solving improves efficiency and communication on the shop floor. It increases a company's efficiency and profitability, so it's one of the top skills employers look for when hiring new employees. Recent industry surveys show that employers consider soft skills, such as problem solving, as critical to their business’s success.

The 2011 survey, "Boiling Point? The skills gap in U.S. manufacturing ," polled over a thousand manufacturing executives who reported that the number one skill deficiency among their current employees is problem solving, which makes it difficult for their companies to adapt to the changing needs of the industry.

In this video, industry professionals discuss their expectations and present tips for new employees joining the manufacturing workforce.

Quick Summary

• [Quick Summary: Question1] What are two things you learned in this case study?
• What question(s) do you still have about the case study?
• [Quick Summary: Question2] What question(s) do you still have about the case study?
• Is there anything you would like to learn more about with respect to this case study?
• [Quick Summary: Question3] Is there anything you would like to learn more about with respect to this case study?

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What is an example of problem-solving?

What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.

Problems come in all shapes and sizes — from workplace conflict to budget cuts.

Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge. 

Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem . 

Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.

Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.

To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high. 

Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one. 

Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions. 

This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.

They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.

The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.

Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving. 

Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.

1. Identify the problem

The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem. 

The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions. 

Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .

2. Break the problem down 

Identifying the problem allows you to see which steps need to be taken to solve it. 

First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage.

3. Generate potential solutions

At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible. 

Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.

Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.

4. Evaluate the possible solutions

Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist. 

There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:

• Will my team be on board with the proposition?
• Does the solution align with organizational goals ?
• Is the solution likely to achieve the desired outcomes?
• Is the solution realistic and possible with current resources and constraints?
• Will the solution solve the problem without causing additional unintended problems?

5. Implement and monitor the solutions

Once you’ve identified your solution and got buy-in from your team, it’s time to implement it. 

But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem. 

Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.

If the solution doesn’t achieve your desired results, start this step-by-step process again.

There are many different ways to approach problem-solving. Each is suitable for different types of problems. 

The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.

Here are 10 effective problem-solving strategies for you to try:

• Use a solution that worked before
• Brainstorming
• Work backward
• Use the Kipling method
• Draw the problem
• Use trial and error
• Sleep on it
• Get advice from your peers
• Use the Pareto principle
• Add successful solutions to your toolkit

Let’s break each of these down.

1. Use a solution that worked before

It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.

2. Brainstorming

The more people you enlist to help solve the problem, the more potential solutions you can come up with.

Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.

3. Work backward

Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.

Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.

4. Use the Kipling method

This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .” 

• What is the problem?
• Why is the problem important?
• When did the problem arise, and when does it need to be solved?
• How did the problem happen?
• Where is the problem occurring?
• Who does the problem affect?

Answering these questions can help you identify possible solutions.

5. Draw the problem

Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.

This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.

6. Use trial-and-error

A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.

7. Sleep on it

Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.

A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level. 

If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.

8. Get advice from your peers

Getting input from a group of people can help you find solutions you may not have thought of on your own. 

For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group. 

For leaders , it might be consulting other members of the leadership team or working with a business coach .

It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone. 

9. Use the Pareto principle

The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.

Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales. 

You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.

10. Add successful solutions to your toolkit

Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit. 

These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.

Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:

• Critical thinking and analytical skills
• Communication skills , including active listening
• Decision-making
• Planning and prioritization
• Emotional intelligence , including empathy and emotional regulation
• Time management
• Data analysis
• Research skills
• Project management

And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.

Ready to work on your problem-solving abilities? Get started with these seven tips.

1. Build your problem-solving skills

One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .

2. Practice

Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life. 

Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.

3. Don’t try to find a solution right away

Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.

Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking. 

4. Ask for feedback

Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve. 

5. Learn new approaches and methodologies

There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject. 

We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman. 

6. Experiment

Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches. 

Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.

7. Analyze the success of your competitors

Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem. 

For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster. 

But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007. 

If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.

Use problem-solving strategies to uplevel your business

When facing a problem, it’s worth taking the time to find the right solution. 

Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.

Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.

If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.

Elizabeth Perry, ACC

Elizabeth Perry is a Coach Community Manager at BetterUp. She uses strategic engagement strategies to cultivate a learning community across a global network of Coaches through in-person and virtual experiences, technology-enabled platforms, and strategic coaching industry partnerships. With over 3 years of coaching experience and a certification in transformative leadership and life coaching from Sofia University, Elizabeth leverages transpersonal psychology expertise to help coaches and clients gain awareness of their behavioral and thought patterns, discover their purpose and passions, and elevate their potential. She is a lifelong student of psychology, personal growth, and human potential as well as an ICF-certified ACC transpersonal life and leadership Coach.

8 creative solutions to your most challenging problems

5 problem-solving questions to prepare you for your next interview, what are metacognitive skills examples in everyday life, what is lateral thinking 7 techniques to encourage creative ideas, 31 examples of problem solving performance review phrases, leadership activities that encourage employee engagement, learn what process mapping is and how to create one (+ examples), can dreams help you solve problems 6 ways to try, how much do distractions cost 8 effects of lack of focus, similar articles, the pareto principle: how the 80/20 rule can help you do more with less, thinking outside the box: 8 ways to become a creative problem solver, experimentation brings innovation: create an experimental workplace, effective problem statements have these 5 components, contingency planning: 4 steps to prepare for the unexpected, stay connected with betterup, get our newsletter, event invites, plus product insights and research..

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Problem solving is for everyday life, too!

Felicia is a business analyst in our Hong Kong office. After graduating from Dartmouth College in 2016 with a double major in government and psychology, Felicia worked in sales and trading at JPMorgan for two years before joining McKinsey. She’s interested in exploring a variety of functions and industries, especially e-commerce, fintech, and digital transformation. Outside of work, Felicia enjoys horse riding, seeking out breathtaking views, and trying out new products from startups.

November 8, 2019 There are so many reasons to work at McKinsey. You can learn from smart people, explore a variety of different industries and functions, and receive excellent professional training. I understood and expected these experiences when joining McKinsey, but what surprised me is that the skills gained at work have substantially driven my personal growth as well.  Specifically, three behaviors I’ve picked up along the way—a can-do attitude, structured thinking, and mindful communication—have really helped me make sound decisions and build better relationships. First, I’ve realized that having a can-do attitude is a great start to any challenge. For example, my mother recently asked me whether we should sell the family apartment in Hong Kong. Without any experience in real estate, my initial reaction was one of bewilderment. However, I quickly realized that like any other problem, common sense goes a long way, and that I did have the critical thinking skills to put together a coherent analysis.

Second, adding structure to my thoughts almost always bring additional clarity, and the tools we use to problem solve at McKinsey are versatile and applicable to all types of issues. One decision I’ve been struggling with is whether to apply to business school. I found myself easily swayed by others’ opinions, and so I decided to draw an issue tree (please see picture). An issue tree is a tool we use to structure problem solving, and it breaks the problem down into mutually exclusive and collectively exhaustive components. Putting together an issue tree helped me realize which specific matters are at stake and identify areas where I need to do a bit more research. Third, practicing mindful communication has helped me become a better friend. At McKinsey, we’re taught the iceberg metaphor, which is used to illustrate that people’s words or actions may be influenced by dynamics that are not immediately visible. It’s encouraged me to dig deeper when having a difficult conversation. The person in front of me may be saying something or behaving in a certain way that confuses me, but instead of getting frustrated, I try to push myself to understand his or her underlying thoughts, feelings, and beliefs at that point in time. Remembering the iceberg metaphor has helped me become a more understanding person, and probably saved me from a few interpersonal conflicts. Looking back at my McKinsey experience, I feel grateful and empowered to have learned these life lessons. Problem solving can be for everyday life, too! Felicia

HOW STEM IS ACTIVELY SOLVING REAL-WORLD PROBLEMS

• STEM EDUCATION ARTICLES & OPINIONS
• How STEM is Actively Solving Real-World Problems

STEM education has been a topic of hot debate for a few years now and its existence is under unending scrutiny. At a first glance this “third-degree” may feel like an annoying, rude, and uneducated attack on what is arguably one of the most progressive ideas to be set into action in schools in over 100 years. However, this scrutiny is actually proof that STEM is making its intended impact on the future generation of innovative, thoughtful, and resourceful leaders. Science, technology, engineering, and mathematics all require that individuals employ critical thinking skills in a variety of settings to accomplish tasks both big and small. You may thank those in the STEM fields for everything from shoes that protect your feet from whatever is on the ground to the mobile device that you have likely used at least once today for your own personal purposes. Beyond these useful, but not vital, components in your everyday life, STEM is actively being used to help solve some of the world’s greatest and most demanding problems.

Taming World Hunger

World hunger is an issue that is facing thousands of communities all over the world. Entire villages, towns, and cities are facing food shortages for various reasons including: dry seasons, climate change, changes in the environment, animal disturbances in farms and gardens, and simply lack of money. STEM is stepping up and solving these problems on a regular basis by teaching individuals how to grow gardens and providing communities in adverse situations with greenhouses and farming technology to help combat this very real problem.

Facilitating Worldwide Communications

If you are using a computer, tablet, smartphone, or other mobile device to view this page, then you are witnessing first-hand how the internet is connecting you with people, places, businesses, and products all over the world. The device that you are using to view this material is a prime example of how technology has been used to facilitate worldwide communication efforts around the world. This helps to inform individuals of disasters, politics, travel, and social situations across the world without physically having to travel. It is a much cheaper, faster, and more efficient way to spread important information than what was used just a few decades ago.

Safer World Travel

Have you ever booked a flight only to have it canceled or delayed by a winter storm? Not only are you annoyed, upset, or concerned about having to wait to get wherever you are going, you are actually facing the reality that you could be entering into a dangerous situation once you finally do board that plane. Why? Planes that fly in wintery, frozen precipitation accumulate ice on the wings. To combat this problem, flights are delayed, and the plane is sprayed down with an antifreeze-type substance to keep ice from forming on the wings. Unfortunately, this substance wears down and some planes are forced into emergency landings. Science is currently researching the possibility of planes releasing this anti-freezing liquid in mid-air and making travel a safer experience for all involved.

Life Saving Medicine

All areas of STEM education are currently working together to research the medical procedures and medications that are given to individuals in order to save their lives. Vaccines for conditions like Polio have nearly eradicated these deadly diseases. Heart, lung, and kidney transplants have literally saved lives thanks to the efforts made by individuals in STEM-related fields. Researchers have an entire list of diseases and conditions that they are working on tackling in the future as new and bright minds enter these STEM careers.

Decreasing Homelessness

3D printing is one of the newest, most innovative, and relatively inexpensive methods of providing strong homes for people in areas of the world that are highly populated. These homes can be built in as little as one day and can be customized to meet all of the requirements that an individual could ever need or want. These homes are sturdy, readily available, and incredibly affordable. Communities in places like Japan are already utilizing these 3D printed homes and efforts around the world have taken place to raise the money necessary to build such homes for the truly homeless to use.

Saving Wildlife

In places like New York City where skyscrapers are plentiful and glass walls are everywhere, birds and other flying animals are dying in the thousands. These animals do not see the glass and will literally fly into it, fall to the ground, and die either from the impact of flying into the glass or from the impact of hitting the ground from such a high altitude. Researchers are currently testing different types of glass with different patterns in an effort to design an aesthetically pleasing glass that birds can see and avoid. As of now, there STEM researchers have discovered that birds do see certain patterns in glass and the journey to providing these types of glass at an affordable price to the public is moving forward.

Providing Fresh Water

Dry, hot, and barren areas of the world are constantly faced with a lack of quality, clean, drinking water. It is often easier to access saltwater than freshwater in these areas, and the little freshwater that is available is usually too dirty to consume. To solve this issue, researchers are actively working on technology that can desalinate saltwater for the purpose of turning it into safe drinking water.

Creating “Green” Alternative, Renewable Energy Sources

You have probably heard that you have what is called a “carbon footprint”. This means that a portion of your daily life is made possible by the burning of limited carbon resources like coal. Individuals in the STEM field have committed their time to finding resources that can replace carbon-based fossil fuels without harsh negative ecological effects. Once a viable source has been discovered [such as water or wind sources], it takes an entire crew of people to develop the technology necessary to harness that energy and distribute it to communities all around the world. Not only are these resources viable "green" alternatives, but they are renewable and therefore feasibly sustainable methods of powering everyday life.

STEM is providing young generations with the incentive to tackle world problems like those listed above. While it is impossible to get everyone on the same page with agreeing opinions of its structure, it is worth noting that STEM-oriented individuals are making a difference in the world.

For those that question whether a STEM education is worth pursuing because of its exclusion of other important topics like arts, physical education, history, and language arts, try and point out to them that every STEM career can incorporate those subjects and their lessons. No topic in life is ever as cut and dry as it may seem on the surface. All subjects are important in making students well-rounded and active citizens in their communities, but STEM-oriented students simply choose to focus more of their attention to the areas of science, technology, engineering, and mathematics than in other areas.

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Cognitive Predictors of Everyday Problem Solving across the Lifespan

Center for Vital Longevity, School of Behavioral and Brain Sciences, University of Texas at Dallas

Christopher Hertzog

School of Psychology, Georgia Institute of Technology

Denise C. Park

An important aspect of successful aging is maintaining the ability to solve everyday problems encountered in daily life. The limited evidence today suggests that everyday problem solving ability increases from young adulthood to middle age, but decreases in older age.

The present study examined age differences in the relative contributions of fluid and crystallized abilities to solving problems on the Everyday Problems Test (EPT; [ 1 ]). We hypothesized that due to diminishing fluid resources available with advanced age, crystallized knowledge would become increasingly important in predicting everyday problem solving with greater age.

Two hundred and twenty-one healthy adults from the Dallas Lifespan Brain Study, aged 24–93 years, completed a cognitive battery that included measures of fluid ability (i.e., processing speed, working memory, inductive reasoning) and crystallized ability (i.e., multiple measures of vocabulary). These measures were used to predict performance on the Everyday Problems Test.

Everyday problem solving showed an increase in performance from young to early middle age, with performance beginning to decrease at about age of fifty. As hypothesized, fluid ability was the primary predictor of performance on everyday problem solving for young adults, but with increasing age, crystallized ability became the dominant predictor.

This study provides evidence that everyday problem solving ability differs with age, and, more importantly, that the processes underlying it differ with age as well. The findings indicate that older adults increasingly rely on knowledge to support everyday problem solving, whereas young adults rely almost exclusively on fluid intelligence.

An important aspect of successful aging is maintaining the ability to solve everyday problems encountered in daily life. Instrumental Activities of Daily Living (IADLs) represent one important domain of these problems. IADLs are complex behaviors required for independent management of one’s life, including adherence to complex medical regimens, ability to use increasingly complex communication devices, and management of financial resources [ 2 ]. Other everyday problems involve situations where a conflict is present or a goal cannot be reached without some inferential reasoning [ 3 ]. Cross-sectional data show that the practical ability to solve everyday problems increases from young adulthood until middle age [ 4 – 6 ], but that older age is characterized by diminishing performance[ 5 – 8 ].

One reason for peak performance during middle adulthood in everyday problem solving may be that middle-aged adults have the ideal balance of fluid and crystallized resources needed for everyday problem solving. Crystallized ability represents accumulated experience and knowledge of the world, and is typically measured by vocabulary and general knowledge. It does not decline, and may even grow, well into late adulthood [ 9 , 10 ]. In contrast, fluid ability – the ability to abstract and perform efficient mental operations – shows consistent age-related decline beginning in the 20s [ 10 ], but nevertheless, performance is still relatively high in middle-aged adults [ 11 ]. Fluid ability is best measured by different types of inductive and deductive reasoning tasks, and is closely related to the construct of processing resources [ 12 ] as operationalized by working memory [ 13 ].

Previous studies have found fluid ability to be an important predictor of everyday problem solving in healthy older adults [ 7 , 8 , 14 – 18 ]. Gross et al. [ 16 ] found that although memory, reasoning and processing speed were all significant predictors for everyday functioning and everyday problem solving, inductive reasoning (measured by Letter Series, Word Series, and Letter Sets tasks) independently accounted for the most variance in everyday functioning (measured by Everyday Problems Test, the Observed Tasks of Daily Living, and the Timed Instrumental Activities of Daily Living test). Willis et al. [ 19 ] also showed that older adults who underwent reasoning training showed less functional decline in IADLs than an untrained control group, indicating the importance of reasoning for everyday problem solving.

Everyday problem solving is also related to other aspects of fluid ability that decline with age, especially working memory and processing speed. Importantly, age-related decreases in working memory, using traditional measures that include Reading Span, Computation Span, and Operation Span tasks, have been strongly associated with lower performance on everyday problem solving tasks [ 14 , 20 ]. Age-related slowing in processing speed has also been associated with decreased everyday problem solving [ 8 , 21 ]. Rebok and colleagues [ 22 ] reported evidence that older adults who had extensive training on processing speed in the ACTIVE trial reported less difficulty in performing IADL’s ten years after training, suggesting that such an intervention confers protection in later life. In sum, there is little doubt that fluid ability plays an important role in everyday problem solving.

What is less certain is the role that crystallized ability and knowledge play in everyday problem solving. There have been a few studies that examined the joint contributions of both fluid ability and crystallized ability to everyday problem solving and all suggest an important role of fluid ability [ 7 , 14 , 15 , 17 , 21 , 23 , 24 ]. However, the importance of crystallized ability in everyday problem solving seems to be different depending on the age range of the sample included in the study. Three studies in older adults all found that both fluid and crystallized ability played very important roles in everyday problem solving. Diehl and colleagues [ 15 ] used structural equation modeling and found that both fluid and crystallized abilities had significant paths to everyday problem solving, measured by Observed Tasks of Daily Living (OTDL). In addition, the effects of memory and speed on OTDL were mediated by crystallized ability, indexed by vocabulary. Burton [ 21 ] used hierarchical regression and found that verbal ability, measured by verbal fluency and vocabulary tasks, predicted performance in Everyday Problems Test beyond the effect of fluid ability and demographic variables (e.g., age, education). Allaire and Marsiske [ 14 ] also found relationship between vocabulary and some domains of everyday problem solving, measured by Everyday Cognition Battery. However, studies including middle-aged adults yielded somewhat different conclusions on the role of crystallized ability in the relation to everyday problem solving. Kimbler [ 7 ] studied healthy middle-aged and older adults (age 50 to 92) and found no relationship between performance in vocabulary and Everyday Problems Test. Thornton and colleagues [ 24 ] reported that, although in a sample of healthy adults and chronic disease patients, crystallized ability (measured by ETS vocabulary) mediated age effects on performance in Everyday Problems Test, the relationship was not significant when the analysis was limited only to healthy adults.

These findings suggest that there is a discrepancy in the role of crystallized ability in predicting everyday problem solving across the adulthood lifespan. A potential explaination is that there may be an age-related shift in the contribution of fluid versus crystallized abilities in solving everyday problems. This shift can only be detected by using a lifespan sample with broader age range. We are aware of only two adult lifespan studies on the cognitive predictors of performance in everyday problem solving [ 6 , 23 ]. In both studies, the correlation of fluid and crystallized cognitive predictors to everyday problem solving (practical problem solving in [ 6 ]) was significant. However, when the effects of age and education on everyday problem solving were controlled, neither predictor was significant [ 6 ], limiting the understanding of their respective contribution. Moreover, we were unable to find any studies that include young, middle-age and older adults that examined how age affects the contribution of cognitive predictors to everyday problem solving. Therefore, the present study focuses on two important and unresolved issues. First, what are the strength of the contributions of fluid and crystallized abilities to everyday problem solving? And second, do these contributions shift in importance as a function of age?

Park has argued that older adults maintain performance on many cognitive tasks by increasingly relying on knowledge and experience to compensate for declines in fluid abilities [ 25 ]. Congruent with this perspective, Baltes also suggested that crystallized ability can compensate, to some extent, for age-related declines in processing efficiency with advanced age [ 26 ]. In support of this theorizing, Hedden et al. reported that performance on a verbal memory task was mediated by fluid abilities in young and middle-aged adults, but that older adults relied more on vocabulary (an index of crystallized ability) for optimal performance [ 27 ]. In the present study, we determine whether such an age-related shift occurs for everyday problem solving in an adult lifespan sample. We predicted that young adults who are rich in cognitive resources such as speed, working memory and reasoning would rely on fluid processing for success; however, as age increased, crystallized ability would play an increasingly important role in everyday problem solving.

Participants

A total of 221 healthy adults from the Dallas Lifespan Brain Study (DLBS; 148 women, 73 men, age range: 24–93 years, Mini-Mental Status Examination scores ≥ 26, mean = 28.37) were recruited locally from the community. All participants were right-handed with normal or corrected to normal vision. Participants with any of following conditions were excluded: history of major psychiatric or neurological disorder, history of prescription drug abuse/illegal drug use, and/or any head trauma. Participants were compensated fifteen dollars per hour for their participation. They completed two 2.5-hour sessions that are described below.

Each participant completed a battery of cognitive tests as well as the Everyday Problems Test (EPT) [ 1 ]. This comprehensive battery included both paper-and-pencil and computerized tasks. The cognitive constructs assessed and the tasks associated with each construct included the following:

Processing speed was measured by Digit Comparison [ 28 ], WAIS-III Digit Symbol [ 29 ] and Pattern Comparison task taken from NIH Toolbox Cognition Battery (NIHTB-CB) [ 30 ].

Working memory was measured by the Spatial Working Memory (SWM) task of Cambridge Neuropsychological Test Automated Battery (CANTAB) [ 31 ], WAIS-III Letter-Number Sequencing [ 29 ] and NIHTB-CB List Sorting [ 30 ].

Inductive reasoning was measured by Educational Testing Service (ETS) Letter Sets [ 32 ], Raven’s Progressive Matrices [ 33 ], and Stockings of Cambridge (SOC) of CANTAB [ 31 ].

Crystallized ability was measured by NIHTB-CB Picture Vocabulary [ 30 ], NIHTB-CB Oral Reading Recognition [ 30 ] and the ETS Advanced Vocabulary Scale [ 32 ]. Although the ETS Vocabulary task was timed, we made sure that no participants failed to complete the task because of the time limit so the performance on this task was not affected by their speed.

Everyday problem solving ability was measured by the Everyday Problems Test (EPT) [ 1 ]. It is a paper-pencil task that has 42 questions, which assesses the ability to solve tasks that are important to live independently in our society. The EPT is comprised of seven scales that include problems from domains of Health/Medications, Meal Preparation/Nutrition, Phone Usage, Consumer/Shopping, Financial Management, Household Management, and Transportation. For each of these seven scales, participants are presented with three sample stimuli (e.g., prescription drug label, bus schedule, catalog order form) and two questions about each stimulus. Figure 1 is an example of one EPT stimulus with two questions based on the stimulus. The performance on this task is measured as the total number of correct answers to the 42 questions. Compared to other neuropsychological tasks that assessed traditional problem solving ability, everyday problems test (EPT) was designed to be a better indicator of problem solving performance in real-life. Schmitter-Edgecombe and colleagues [ 34 ] found that EPT was strongly associated with directly observed everyday functioning performance in real world, and therefore considered to be a valid and useful measure for assessing everyday functioning in cognitively healthy older population.

a . Age-related differences in fluid ability. Fluid ability is comprised of the measures on processing speed, working memory and inductive reasoning. b . Age-related differences in crystallized ability. Crystallized ability is comprised of ETS Advanced Vocabulary Scale, NIHTB-CB Picture Vocabulary and NIHTB-CB Oral Reading Recognition. Figure 3c . Age-related differences in everyday problem solving. Everyday problem solving is measured by number of correct answers on the Everyday Problems Test (EPT).

Data Analyses

Altogether, there were 13 tasks subjected to analyses: three measures each for processing speed, working memory, inductive reasoning, crystallized ability, and a single measure of everyday problem solving. We created standard scores for the 12 cognitive measures that were used for further analyses. A confirmatory factor analyses (CFA) validated the expected factor structure of cognitive measures, Χ 2 (60) = 147.941, p < .001, CFI = .953, RMSEA = .081, SRMR = .076 (see Figure 2 ). The standardized scores for each crystallized and fluid test were averaged to produce composite crystallized and fluid scores in a standard-score (z-score) metric in the aggregate cross-sectional sample.

Confirmatory Factor Analysis of cognitive tasks, after controlling for age. Χ 2 (60)= 147.941, p < .001, CFI = .953, RMSEA = .081, SRMR = .076.

To test the hypothesis that crystallized intelligence would be a more potent predictor of everyday problem solving for older adults, relative to earlier ages, we conducted a hierarchical moderated regression analysis with age, fluid ability, and crystallized ability as predictors, using product variables to capture interactions. Prior to evaluating the interaction effects, we introduced quadratic age effects to test for possible curvilinearity in the relation of age and the variables to the EPT score. This approach was taken because curvilinear age relations were expected in abilities [ 35 ] and everyday problem solving performance, and because methodological studies have shown that failing to account for curvilinear relations of predictors to dependent variables in the context of moderated regression can create spurious product variable effects that are an artifact of curvilinear relations of both predictors to the dependent variable [ 36 ]. To foreshadow our results, we did detect curvilinear relations of age and abilities to EPS tests, requiring that moderated regression tests for age × ability interaction effects include quadratic terms for each predictor variable.

Linear predictor terms were first centered at the sample mean, and then squared predictors were computed to reduce collinearity issues in the multiple regression. Significant moderated regression effects were decomposed by computing simple slopes at the mean and at ± 1 SD of the predictor variables.

To further understand age differences in the predictive utility of fluid and crystallized abilities for everyday problem solving, we used bootstrapping to examine the regression coefficients for each of the three age groups (young, middle-aged, older). Finally, to assess the stability of the observed effects across individual problem solving domains, we examined the contributions of fluid and crystallized abilitites for each of the seven domains in everyday problem solving for young, middle-aged, and older adults.

Demographic Data and Age-related Differences

Demographic data are presented in Table 1 , broken down by 3 age groups (Young: 24–49 years old; Middle: 50–69 years old; Old: 70–93 years old). The three age groups differed on years of formal education, F (2, 218) = 6.16, p =.002, with young adults having somewhat higher levels than the other two age groups. Means and standard deviations of cognitive measures and EPT scores are also presented in Table 1 . For descriptive purposes, we presented age effects associated with fluid ability, crystallized ability and everyday problem solving score in scatter plots ( Figure 3 ). Figure 3a portrays a significant linear age-related decrease in fluid ability, R 2 = .626, R 2 adjusted = 625, F(1, 212) = 355.312, p < .001, and the quadratic relationship was also statistically significant, R 2 = .64, R 2 adjusted = .637, F(2, 211) = 187.72, p < .001. In contrast, crystallized ability ( Figure 3b ) did not have a significant linear relationship with age, p = .628. However, there was a significant quadratic relationship between crystallized ability and age, R 2 = .038, R 2 adjusted = .029, F(2, 217) = 4.258, p = .015, with increasing performance until about age 59. We also examined both linear and quadratic relationships between everyday problem solving ability and age. While the simple linear relationship showed significance, R 2 = .237, R 2 adjusted = .234, F(1, 219) = 68.091, p < .001, adding age 2 significantly improved the model, ΔR 2 = .105, ΔF = 34.810, p <.001, suggesting a quadratic relation with age was a better fit for everyday problem solving ability ( Figure 3c ), R 2 = .342, R 2 adjusted = .336, F (2, 218) = 56.707, p < .001, with the peak performance at 47.2 years of age.

Demographic and descriptive data.

Cognitive Predictors Across the Lifespan

We used hierarchical multiple regression to examine the role that fluid and crystallized abilities play in solving everyday problems. In the first model, we included years of education and linear and quadratic components for age. Then in the second model, we added fluid ability and crystallized ability as cognitive predictors. In the third model, we included quadratic components (crystallized 2 and fluid 2 ) to examine if there was a curvilinear relationship between cognitive predictors and everyday problem solving. In the fourth model, we added interactions among fluid ability, crystallized ability and age. Each of aforementioned steps improved the fit of the overall model significantly ( Table 2 ). We also examined a further model that included interactions between cognitive ability and age 2 , and found that it did not improve the model significantly. Therefore, the fourth model was chosen as the final model depicting the relationship between cognitive predictors and everyday problem solving across the lifespan. As shown in Table 2 , Model 4 explained a substantial amount of variance in everyday problem solving, R 2 = .683, R 2 Adjusted = 666. There was a main effect of age, age 2 , fluid ability, and crystallized ability on everyday problem solving. Although the quadratic terms of fluid ability and crystallized ability were not each statistically significant in the final model, adding quadratic terms of these predictors significantly improved the fit of the model. The partial residual plots of crystallized ability ( Figure 4a ) and fluid ability ( Figure 4b ) showed that these two predictors both evidenced a similar curvilinear pattern to everyday problem solving. Curvilinearity occurred because for lower ability participants compared to those of higher ability, cognitive ability had a stronger relationship to everyday problem solving.

a . Partial residual plot of crystallized ability. b . Partial residual plot of fluid ability. For both cognitive predictors, the effect of crystallized and fluid ability follows a similar curvilinear pattern regardless of age and the other cognitive level: for people who have lower cognitive ability, the level of cognitive ability has a strong effect on everyday problem solving, while for people who have high cognitive ability, higher cognitive ability does not affect everyday problem solving as much.

Hierarchical Multiple Regression.

Critically, we also found a significant Age × Crystallized ability interaction, b = 0.046, SEb = 0.016, t (201) = 2.943, β = .152, p = .004, 95% CI = [0.015, 0.076], indicating the relationship between crystallized ability and everyday problem solving differed across the lifespan. In order to better interpret the significant interaction, simple slopes (displayed in Figure 5 ) for the relationship between crystallized ability and everyday problem solving were tested for younger age (−1 SD below the mean), middle age (mean), and older age (+1 SD above the mean). Simple slope tests showed that the relationship of crystallized ability to everyday problem solving at a younger age was not significant, b = 0.708, SEb = 0.433, t (201) = 1.636, β = .125, p = .103, 95% CI = [−0.146, 1.562]. However, both the middle age model, b = 1.576, SEb = 0.292, t (201) = 5.391, β = .279, p < .001, 95% CI = [0.999, 2.152], and the older age model, b = 2.44, SEb = 0.397, t (201) = 6.141, β = .432, p < .001, 95% CI = [1.656, 3.223], revealed a significant positive association between crystallized ability and everyday problem solving. We then tested the difference between regression coefficients across models, and found that the effect of crystallized ability was stronger for both old ( z = −3.027, p = .001) and middle age ( z = −1.719, p = .043) compared to young, and that the effect was even stronger for the old age compared to middle, ( z = −1.753, p = .04), suggesting that crystallized ability played a continuously increasingly important role in solving everyday problems as age increased. Note that the interaction between fluid and crystallized ability was not significant ( p = .351), suggesting that the contribution of crystallized ability did not change across people with different fluid ability, after age-related effects taken into account.

Simple slopes of Age × Crystallized ability. Simple slope was not significantly different from 0 at Age = 40 (1SD below mean), but was significant at Age = 59 (mean age) and Age = 78 (1SD above mean). Based on comparison using z-tests, the effect of crystallized ability was stronger at older age ( z = −3.027, p = .001) and middle age ( z = −1.719, p = .043), than at a younger age, and the effect was even stronger at a older age than middle, ( z = −1.753, p = .04).

Comparing Cognitive Predictors in Three Age-groups

To further examine which cognitive predictor – fluid or crystallized ability – was more important for everyday problem solving at different stages of the lifespan, we generated bootstrapped standard errors for regression coefficients in three age subgroups: younger adults (24–49 years old), middle-aged adults (50–69 years old), and older adults (70–93 years old). In each multiple regression, the predictor variables were age, fluid ability, crystallized ability, fluid 2 , crystallized 2 and the fluid × crystallized interaction. This model was derived from Model 4 used for the whole sample with first order age-related effects removed since this analysis was on each age group. We generated 95% confidence intervals (CI) using bias-corrected and accelerated (BCa) bootstrap (with 1000 iterations in each group) as presented in Table 3 . We then compared the BCa CI using a conservative rule by examining the overlap of confidence intervals [ 37 ]. Put simply, the rule assesses whether the 95% confidence intervals have less than 50% proportion overlap, expressed as a proportion of average margin of error. If the result is affirmative, the two estimates are significantly different ( p < .05). As shown in Figure 6 , for the young group, the lower end of 95% CI of the crystallized ability parameter was below zero, confirming its non-significance and that only the fluid ability value was predictive, as we found in simple slope analysis. For the middle age, the 95% CIs of fluid and crystallized abilities overlapped more than 50%, suggesting that both were predictive but not significantly different in middle-aged adults. Finally, for the older group, the predictive utility of crystallized ability was significantly larger than fluid ability, with the proportion overlap = 42.8%, p < .05. Hence, in middle-aged and older adults, everyday problem solving was associated with both fluid and crystallized abilities. Importantly for older adults, crystallized ability was a significantly stronger predictor compared to fluid ability (see Figure 6 ).

95% BCa CI for fluid and crystallized regression coefficients. In older adults, everyday problem solving was predicted more by crystallized ability than fluid ability, proportion overlap = 42.8%, p <.05.

Regression coefficient estimates and 95% BCa CI in three age groups.

We also note that we found no evidence for a Fluid × Crystallized interaction within any age group. The absence of the interaction suggests that fluid and crystallized ability made independent contributions to everyday problem solving, regardless of level of performance on either ability.

In a final analysis, we assessed the stability of the effects of fluid and crystallized ability for each of the seven problem-solving domains, within each age group, using the same bootstrapping approach. The main finding was that for older adults, crystallized ability played an important role for all EPT domains except meal preparation , which was marginally significant. In addition, fluid ability was significant for shopping, finance and meal preparation in older adults (see Table 4 ). Table 4 also shows that for young adults, fluid ability was significant for finance, household and transportation , and for finance, medication and transportation in middle-aged adults. Crystallized ability played no significant role for young adults, and significantly predicted only shopping in middle age.

Regression coefficient estimates and 95% BCa CI for seven EPT domains.

The main goal of this study was to understand how fluid and crystallized ability differ across the lifespan in predicting everyday problem solving. We hypothesized that due to diminished fluid resources with age, crystallized knowledge would become increasingly important in predicting everyday problem solving as a function of age. Congruent with this hypothesis, crystallized ability (measured by verbal knowledge in this study) played a more important role in predicting everyday problem solving as age increased. In contrast, fluid ability (measured by speed, working memory, and inductive reasoning) consistently explained variance for all age groups. This pattern of findings suggests that older adults are relying more on crystallized knowledge to solve everyday problems, whereas young adults rely more heavily on the efficiency of basic cognitive-mechanisms (e.g., processing speed, working memory, inductive reasoning) that comprise fluid ability.

Past studies have been inconclusive about the relative roles of crystallized versus fluid abilities in everyday problem solving at different ages, because none that have examined this issue have included a lifespan sample. The inclusion of the entire adult lifespan was an important feature of the present study, as it allowed us to begin to clarify when in the lifespan crystallized knowledge assumes importance in everyday problem solving. We began to observe a small contribution of crystallized ability to everyday problem solving in middle age, with a large contribution at older ages. The present findings provide clear evidence for the importance of including middle-aged samples in studies.

We also note that the present findings replicate a pattern reported by Hedden et al. [ 27 ] for a very different task—a verbal cued recall task that required participants to memorize associations between paired cues and target words. Hedden et al [ 27 ] used crystallized and fluid ability to predict performance on the verbal recall task. Just as reported in the present study, they found that crystallized ability (vocabulary scores) explained more variance for older compared to middle-aged and young adults. The similarity of the findings for these two very different tasks suggests that increasing reliance on crystallized ability may be a general characteristic of aging. Buttressing this conclusion, was the finding that crystallized ability accounted for significant variance in older adults in six of the seven EPT domains, suggesting that the breadth of the effect was reliable across domains. Moreover, the crystallized ability effect was nearly absent in the young and middle-aged adults, with only one significant effect for shopping in the middle-aged.

The notion that age differentially affects the type of cognitive ability drawn upon to perform everyday cognitive tasks has not received much attention in the literature. The present findings suggest that crystallized knowledge may help older adults maintain cognitive function in the face of declining fluid ability. Other studies of problem-solving support this interpretation. For example, older adults actually showed better problem-solving abilities than young and middle-aged adults when they were presented with problems associated with social conflict and interpersonal conflict. The solution to these types of problems rely more on wisdom and a broad range of social experiences rather than fluid ability [ 38 ]. Similarly, there is evidence that older adults develop adaptive, experience-based heuristics for solving everyday problems and make decisions that minimize the need to rely on fluid reasoning [ 39 ]. Conversely, there are also domains where crystallized ability makes a scant contribution, even for older adults. We suggest that these would be domains that require extensive on-line processing, such as constantly switching and updating information of different ingredients and procedures when cooking.

It is also important to recognize that everyday problem solving ability is a crucial skill that greatly affects older adults’ life quality, but few studies have examined the predictive utility of respondent-based, laboratory problem solivng tasks (such as the EPT) in the real world. In support of the use of such laboratory measures, there is a small body of evidence suggesting that the EPT explains substantial variance in every day functioning [ 17 , 34 , 40 ]; but much more research is needed. Moreover, the EPT consists of sets of questions that address well defined, but relatively narrow everyday problems. Real world problems are typically more complex, are more open-ended (ill-defined), and are comprised of many smaller interrelated problems that require different aspects of knowledge, skills and abilities. Thus, the EPT may not adequately mirror the complexity of real world problems. Additional investigation of ability predictors of everyday problem solving tasks would help to address this concern.

A limitation of this study is that crystallized ability was measured by vocabulary tasks, which have been traditionally considered as a proxy of knowledge and experience in cognitive psychology studies and everyday problem solving research. However, we acknowledge that a broader assessment of crystallized ability would incorporate experience and other types of world knowledge. Future research with more comprehensive assessment of knowledge and experience beyond measures of vocabulary may help to understand the individual differences in people’s utilization of cognition in solving everyday problems. One option might be to assess expertise and familiarity participants have in each problem solving domain in an effort to understand how life experiences asset problem solving. Similar strategies could be adapted to different problem solving paradigms.

We also recognize that it would be ideal to have longitudinal data on both cognitive and everyday problem solving so that the changing relationship between cognitive measures and everyday performance could be assessed as people grow and age. Cross-sectional designs are vulnerable to cohort differences and age × selection confounds. Finally, the compensatory role of crystallized ability may be maximized in high-functioning samples of older adults. Participants in this study were well-educated (mean years of education = 16.6); individuals with lower levels of educational attainment may not show the same degree of compensatory benefit (although we found no evidence of fluid × crystallized interactions in predicting EPS performance). It would therefore be useful to evaluate these relationships in a more representative sample of the population that included low-education individuals.

In conclusion, the present study suggests that young adults may solve everyday problems based on cognitive resources and mechanisms that are traditionally associated with effective problem solving. However, crystallized knowledge becomes a more predominant influence on everyday problem solving in older adults.

Example questions of the Everyday Problems Test.

Acknowledgments

This work was supported by National Institute on Aging at the National Institutes of Health (grant number 5R37AG006265-29 to D. C. P.).

Contributor Information

Xi Chen, Center for Vital Longevity, School of Behavioral and Brain Sciences, University of Texas at Dallas.

Christopher Hertzog, School of Psychology, Georgia Institute of Technology.

Denise C. Park, Center for Vital Longevity, School of Behavioral and Brain Sciences, University of Texas at Dallas.

• For Parents

Math in Action: Problem Solving Skills for Everyday Life

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Author: BYJU’S Math Companion Tutor

How is math problem-solving commonly used in everyday life?

• Budgeting: Teach children how to manage allowances, savings, and expenses. Discussing budgeting strategies helps them make wise financial decisions.
• Cooking: Cooking involves precise measurements and conversions. Baking a cake, for instance, is a delicious way to apply math skills.
• Shopping: Explain how discounts, percentages, and sales tax work. Involve children in calculating discounts to make shopping both educational and fun.
• Travel planning: Planning a road trip requires understanding distance, time, and fuel consumption. Map reading and calculating travel expenses provide real-life math lessons.
• Time management: Teach children to use schedules and timetables. Managing their time effectively prepares them for future responsibilities.
• Problem-solving games: Encourage board games like chess, Sudoku, or logic puzzles. These games sharpen analytical thinking and math skills.

Math problem-solving skills that are essential for real-life challenges for children

• Critical thinking and analysis: Encourage children to dissect complex problems into smaller, manageable parts. This skill enables them to analyze situations, identify key variables, and approach challenges with clarity.
• Logical reasoning: Logical thinking helps your little one evaluate the relationships between different components of a problem. It guides them in determining cause-and-effect patterns and making informed decisions.
• Pattern recognition: Patterns are everywhere in our world, from nature’s symmetries to data trends. Teaching children to recognize and use patterns equips them with a powerful tool for problem-solving.
• Creative problem solving: Foster creativity by encouraging children to explore various approaches to a problem. This allows them to think outside the box and devise innovative solutions.
• Numerical fluency: Strong numerical skills are fundamental. Proficiency in addition, subtraction, multiplication, and division forms the basis for solving a wide range of everyday problems.
• Measurement and estimation: Understanding measurement units and making reasonable estimations are essential for tasks like cooking, DIY projects, and understanding sizes and quantities.
• Spatial awareness: Geometry plays a significant role in real-life situations, from arranging furniture to reading maps. Developing spatial skills enhances a child’s ability to navigate physical spaces efficiently.
• Time management: The skill of managing time effectively is essential for scheduling daily activities, setting goals, and adhering to deadlines.
• Probability and risk assessment: Understanding probability helps children assess risks and make decisions in uncertain situations, such as games of chance or investments.
• Measurement conversions: Being able to convert units, such as ounces to grams or miles to kilometers, is valuable in daily life.
• Algebraic thinking: Basic algebraic concepts can be applied to real-life situations, such as solving for an unknown variable in a recipe or a budget.

5 ways children use math in everyday life

• Money matters: Understanding and managing allowances, budgeting for spending, and calculating change while shopping.
• Time management: Reading clocks and calendars, scheduling activities, and tracking time spent on tasks.
• Homework and tests: Solving math problems for assignments and taking math tests and quizzes at school.
• Playing games : Board games, card games, and video games often involve counting, calculating scores, and making strategic moves.
• Sports and activities: Keeping score in sports, tracking statistics, and understanding game strategies that involve math.

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The Art of Problem Solving in Everyday Life in 7 Steps

• Post author: lesoned
• Post category: Life lessons
• Post comments: 0 Comments
• Post last modified: September 9, 2023

Everyday in our lives we face challenges and problems as they are some of the things that give purpose and meaning to our lives , they give us reason to wake up everyday and solve them so as to attain the things we want in life like being rich, having a successful business or a happy life which makes problem solving skills come hand in everyday life

Problem solving skills are also one of the most sought after job skills in the job world today because every business has problems and challenges to which critical thinkers and problem solvers are needed fix them.

As a matter of fact during a job interview you are very likely to be asked to give a work related situation in which you where able solve a problem or over came a challenge showcasing your ability to handle difficult or un expected situations.

Table of Contents

What is problem solving ?

Problem solving is the process of identifying a problem or a challenge then coming up with solutions to resolve the problem or challenge

Examples of problem solving skills include;

• Researching
• Decision making

Below are the 7 steps of problem solving process that you can use to solve problems in everyday life situations and all points are generalized and not customized to a particular problem.

1. Identifying What the problem is

This is the first step in problem solving process

This is where you identify a challenge, setback or problem to fix or find solutions for, for example the problem could be losses in a business, lack of friends as a person, or failure to get job as a person or any thing you feel needs to be resolved in your life.

2. Identify the cause of the problem

This is the core aspect of problem solving, failure to find the actual cause of a problem will result into the problem being persistent and never getting solved because you would be solving the wrong cause well as the actual cause is not touched, for example;

Let’s use a business that is not making profits, one of the causes of losses would be low demand of a product, or poor quality products or services, or lack of skilled labor or bad location for the business. So even if you improve the product and services, get the best employees when the cause of the problem is your location the problem will remain because it was never solved instead you solved something that wasn’t necessarily broken.

Improvement in all other aspects other than the core problem will show little to no growth as they aren’t the real problems in the first place.

Another real life example of problem solving was at a supermarket that was not making substantial profits. The owner, who was the actual problem, thought the cause of the problem was unskilled workers, so he increased the number of workers with specialized skills in different departments.

He also thought maybe the items were being sold cheaply so he increased the prices, set up promotional offers so as to attract clients, acquired some items on credit so that he can increase the variety of stock.

The results were mixed in that, increased prices chased away some clients who are price sensitive, especially considering the fact that the same location had other 5 supermarkets he was competing with

Increasing the labor force meant an increase in expenses that the company failed to handle in the long run since there weren’t enough profits made from the products and services they offered.

But amidst all those challenges, the core problem that was never touched and that was the owner of the business who took all the profits from the supermarket for his personal use and that’s the biggest problem with sole proprietor businesses. 

So the money that would have been reinvested in the business was all taken for personal use to the extent that paying electricity and water bills plus salaries was hard and neither could the company restock finished goods which led to low sales so the company could not break even.

So the solution was that the owner of the business had to separate personal income and finances from business finances and since everyone feared him, no one could stand up to him and tell him the ugly truth that stop taking out your business money for personal use and at least get a salary that should be paid to him and also set profits that should be paid out to him every month as a return on investment

More on business problem solving examples

Another always ignored perspective on business failing to find a solution is confusing signs and symptoms of a problem as a core problem for example, workers failing to perform to the expected standard may appear as the reason as to why a business is failing so you decide to get new workers when in reality the core problem is not the workers but delayed salaries

Most employers will ignore the fact that most employees work so that they can earn something for themselves and a livelihood not as volunteers. So failure to fix the actual problem of delayed salaries so as to motivate employees will result into fixing a wrong problem and the problem will persist well as you keep on insisting that workers these days are not good enough because even the new employees will be affected by the same problem

Another problem solving example would be treating a disease, for instance, HIV, typhoid and malaria have some similar signs and symptoms but unless you go for a blood test you might end up treating a wrong disease while the actual disease is killing you, so you might take malaria medicine whilst you are actually suffering typhoid and it will kill you because that’s the actual disease you suffering from and you are not treating it

In the same way failure to get the actual core cause of any problem or challenge will result into the problem never going away and always recurring

How to find the actual cause of a problem

This is another important part of problem solving and below are 4 ways you can use to identify the actual cause of a problem;

• Seeking advice from other successful people would be a great idea but one thing you should know is that something working out for you might not work out for another person because there could be lots of unforeseen factors that could have favored one person at that moment and might not favor you.
• As human beings we tend to see things from different perspective, seeking people’s different perspectives will give you different options to start with and this is like being open to criticism as people tend to see where others are wrong and how they can fix the problem
• Take feedback from people as way of identifying a problem, in case of a business, when people are unsatisfied they always offer feedback and that’s a great place to start and on a personal level when people are unhappy with you they could let you know  
• Put yourself in another person’s shoes, what would you do if you was them, this is not a fool proof solution as people act differently in different situations but it’s a good place to start for example would like going to a restaurant during day or later on at night after work thus you plan accordingly

3 . Generate solutions for the problem

After identifying what the cause of the problem is, for example staying indoors more often could be the cause of having no friends, then you might what to change a few things in your life style like maybe moving out more or if its a business failing then you need to come up with the right solutions to fix it.

4. Evaluate the solutions of the problem

Well this is like having multiple solutions a problem from which you will pick the most suitable one and if one doesn’t work then maybe another one could but also considering the capability of working on it for example sometimes you’re going to be busy with work and honestly won’t be able to go out regularly to meet new people certainly you will need an alternative solution as means of making friends

5. Select on the best option

Well since you’re having a couple of options to from choose after considering all possible circumstances then it’s time to pick the best solution that would work to attain the best results and not just good results, choose an option that is measurable and in line with your goals

6. Implement the solution

After picking the best solution that will work for you and is in line with your goals and objectives. its now time to put it into practice whilst you should be able to monitor progress all through out the implementation process

7. Evaluate the results

This is the last step of the problem solving process

After the solution has been implemented, you will need a reasonable time frame in which a solution should work and with in this period you should get different indicators that show your solution worked let alone being sustainable and consistent

Most actions have a time frame in which they are supposed to work, if something is not working with in a given time frame or you still get the same results even after a few changes then you either fixing the wrong problem or you’re fixing the problem wrongly.

This can further be sorted with key performance indicators (KPIs) that can help track the performance of a given action in solving a problem

Be realistic, it’s one thing to set goals it’s another to set achievable goals. Setting unrealistic goals will make you think a certain solution is not working

The failure to get step one of problem solving right which is identifying the actual problem and step two which is the cause of the problem will give results accordingly but the problem intended to be solved will not be solved if the initial stage is got wrong as it’s the main determinant part in the art of getting a problem solved 

Sometimes nothing is wrong and you just have unrealistic goals and expectations and you think something is wrong when in reality everything is okay and is going as it should hence you end up trying to fix something that is not broken due lack of adequate knowledge or misinformation.

Thus you need make realistic and attainable solutions to actual problems and challenges not assumptions after collecting all possible data about a problem and analyzing it

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A model approach to solving problems

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Use models in your teaching to help students learn how to find solutions

Source: © Tobatron

Models help students solve problems in the science classroom, a skill they will take into the wider world

In science, as in everyday life, there are many problems to solve. As science teachers, we use models all the time in our lessons, not just because they are explicitly mentioned in exam board specifications, but also because they help make abstract concepts more concrete. How do we help our students use models to problem solve in their science education?

Problem solving in everyday life

As a starting point, we can link models and problem solving to everyday life. In class, a student can successfully neutralise an acid using an alkali. We can gain student buy-in by applying this to situations outside the classroom, for example the need to brush our teeth.

Introduce routines around problem solving to motivate students

Taking it further, we can use their classroom experience of models when thinking about future careers. We can emphasise that problem solving is a fundamental skill in all jobs. We can embed the idea that problem solving isn’t simply something being learned in the classroom. Rather, it is a skill that will help them be successful in their later lives. To help them understand this concept, ask students to name a job and then explain how problem solving would be successfully used in that job.

Introduce routines around problem solving to motivate students into believing they have a strategy to attempt a task. Teach your students to use a textbook if they’re stuck. Teach them how to use the contents and index pages. This reinforces a skill that encourages independence and will benefit them if they run out of mobile data.

Promote engagement with students needing more encouragement by using a simple rhyme and choral response: ‘What do we do if we’re stuck?’ – ‘We look in a textbook’. If students find a task too hard and can’t solve the problem, motivation will fall and possibly lead to behavioural issues. While this approach needs a big input of teacher direction to begin with, over time the skill will embed.

Download this

Evaluate multiple models activity, for age range 14–16

Enhance your learners' skills interpreting and evaluating models with this set of examples showing a hydrogen molecule.

Download the teacher notes as MS Word or pdf , slides as PowerPoint or pdf and student worksheet as MS Word or pdf.

Multiple-models activity, for age range 14–16 years

Enhance your learners’ skills interpreting and evaluating models with this set of examples showing a hydrogen molecule, including classroom slides and a worksheet.

Download the activity from the Education in Chemistry website: rsc.li/3x7j2KW

Using models

While models are scattered throughout the curriculum, there are some best bets of where they routinely apply. When discussing JJ Thomson’s plum pudding model, students could choose a different model that represents the same idea, for example, a chocolate chip cookie. After a chromatography practical, students can be encouraged to identify an unknown substance based on different Rf values.

Acronyms are a useful model that students can learn to apply to similar questions. For example, to aid students in successfully drawing covalent bonding , introduce them to GROSO:

• g roup number
• r equired shared pairs
• o verlap circles
• s hared pairs drawn in
• o ther outer electrons

Acronyms are a useful model that students can learn to apply to similar questions. For example, to aid students in successfully drawing covalent bonding, introduce them to GROSO:  g roup number;  r equired shared pairs;  o verlap circles;  s hared pairs drawn in;  o ther outer electrons.

Initially, this would need lots of practice and quick checks using mini whiteboards. Once the routine is embedded though, students can take this model and apply it to other covalent questions.

Worked examples also support students by providing a scaffold of how to answer a question. By referencing a completed question, students can attempt a question by following the steps.

More recommended resources

• Use Johnstone’s triangle to help learners of all ages and stages model their thinking.
• Our online Problem solving tutor  will help your 16–18 learners to structure and develop their problem solving skills in quantitative chemistry.
• Find out how to use post-16 models to inform 14–16 understanding .
• Show your students how models can help to predict reactions and influence the taste and texture of chocolate and biscuits, by sharing a profile of food scientist, Robert .
• Use Johnstone’s triangle to help learners of all ages and stages model their thinking: rsc.li/3mLA282
• Our online Problem solving tutor will help your 16–18 learners to structure and develop their problem solving skills in quantitative chemistry: rsc.li/3DJRJtG
• Find out how to use post-16 models to inform 14–16 understanding: rsc.li/3HYxHy6
• Show your students how models can help to predict reactions and influence the taste and texture of chocolate and biscuits, by sharing a profile of food scientist, Robert: rsc.li/3RCMMZl

Focusing on problem solving is also a brilliant opportunity to work with other departments. If multiple departments are using the same routine, students are more likely to commit this to long-term memory, thus reducing cognitive load.

The Ofsted research review into science contains a section on coherence between the mathematics and science departments describing how to share similar language around tackling equations. If students can problem solve in maths, we can show them how to carry that skill across by using the same method in science. Many maths departments teach the balance method to solve equations. You can apply this to many chemistry calculations, such as titration.

The Ofsted research review into science contains a section on coherence between the mathematics and science departments describing how to share similar language around tackling equations (rsc.li/3Yx4yjf). If students can problem solve in maths, we can show them how to carry that skill across by using the same method in science. Many maths departments teach the balance method to solve equations. You can apply this to many chemistry calculations, such as titration.

By using these strategies and questions with our students, we can teach them the importance of problem solving. These are skills, once learned, that students can carry with them for future success.

This article is part of our Teaching science skills series, bringing together strategies and classroom activities to help your learners develop essential scientific skills, from literacy to risk assessment and more.

More from Holly Walsh

Using multiple models in science | 14–16 years

Atoms, molecules and compounds quiz | 11–14 years

How is carbon cycled? | 11–14 years

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Ideas Made to Matter

How to use algorithms to solve everyday problems

Kara Baskin

May 8, 2017

How can I navigate the grocery store quickly? Why doesn’t anyone like my Facebook status? How can I alphabetize my bookshelves in a hurry? Apple data visualizer and MIT System Design and Management graduate Ali Almossawi solves these common dilemmas and more in his new book, “ Bad Choices: How Algorithms Can Help You Think Smarter and Live Happier ,” a quirky, illustrated guide to algorithmic thinking. 

For the uninitiated: What is an algorithm? And how can algorithms help us to think smarter?

An algorithm is a process with unambiguous steps that has a beginning and an end, and does something useful.

Algorithmic thinking is taking a step back and asking, “If it’s the case that algorithms are so useful in computing to achieve predictability, might they also be useful in everyday life, when it comes to, say, deciding between alternative ways of solving a problem or completing a task?” In all cases, we optimize for efficiency: We care about time or space.

Note the mention of “deciding between.” Computer scientists do that all the time, and I was convinced that the tools they use to evaluate competing algorithms would be of interest to a broad audience.

Why did you write this book, and who can benefit from it?

All the books I came across that tried to introduce computer science involved coding. My approach to making algorithms compelling was focusing on comparisons. I take algorithms and put them in a scene from everyday life, such as matching socks from a pile, putting books on a shelf, remembering things, driving from one point to another, or cutting an onion. These activities can be mapped to one or more fundamental algorithms, which form the basis for the field of computing and have far-reaching applications and uses.

I wrote the book with two audiences in mind. One, anyone, be it a learner or an educator, who is interested in computer science and wants an engaging and lighthearted, but not a dumbed-down, introduction to the field. Two, anyone who is already familiar with the field and wants to experience a way of explaining some of the fundamental concepts in computer science differently than how they’re taught.

I’m going to the grocery store and only have 15 minutes. What do I do?

Do you know what the grocery store looks like ahead of time? If you know what it looks like, it determines your list. How do you prioritize things on your list? Order the items in a way that allows you to avoid walking down the same aisles twice.

For me, the intriguing thing is that the grocery store is a scene from everyday life that I can use as a launch pad to talk about various related topics, like priority queues and graphs and hashing. For instance, what is the most efficient way for a machine to store a prioritized list, and what happens when the equivalent of you scratching an item from a list happens in the machine’s list? How is a store analogous to a graph (an abstraction in computer science and mathematics that defines how things are connected), and how is navigating the aisles in a store analogous to traversing a graph?

Nobody follows me on Instagram. How do I get more followers?

The concept of links and networks, which I cover in Chapter 6, is relevant here. It’s much easier to get to people whom you might be interested in and who might be interested in you if you can start within the ball of links that connects those people, rather than starting at a random spot.

You mention Instagram: There, the hashtag is one way to enter that ball of links. Tag your photos, engage with users who tag their photos with the same hashtags, and you should be on your way to stardom.

What are the secret ingredients of a successful Facebook post?

I’ve posted things on social media that have died a sad death and then posted the same thing at a later date that somehow did great. Again, if we think of it in terms that are relevant to algorithms, we’d say that the challenge with making something go viral is really getting that first spark. And to get that first spark, a person who is connected to the largest number of people who are likely to engage with that post, needs to share it.

With [my first book], “Bad Arguments,” I spent a month pouring close to $5,000 into advertising for that project with moderate results. And then one science journalist with a large audience wrote about it, and the project took off and hasn’t stopped since.

What problems do you wish you could solve via algorithm but can’t?

When we care about efficiency, thinking in terms of algorithms is useful. There are cases when that’s not the quality we want to optimize for — for instance, learning or love. I walk for several miles every day, all throughout the city, as I find it relaxing. I’ve never asked myself, “What’s the most efficient way I can traverse the streets of San Francisco?” It’s not relevant to my objective.

Algorithms are a great way of thinking about efficiency, but the question has to be, “What approach can you optimize for that objective?” That’s what worries me about self-help: Books give you a silver bullet for doing everything “right” but leave out all the nuances that make us different. What works for you might not work for me.

Which companies use algorithms well?

When you read that the overwhelming majority of the shows that users of, say, Netflix, watch are due to Netflix’s recommendation engine, you know they’re doing something right.

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

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

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Problem solving skills are invaluable in any job. But all too often, we jump to find solutions to a problem without taking time to really understand the dilemma we face, according to Thomas Wedell-Wedellsborg , an expert in innovation and the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

In this episode, you’ll learn how to reframe tough problems by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for just one root cause can be misleading.

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

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

• Listen to the original HBR IdeaCast episode: The Secret to Better Problem Solving (2016)
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HANNAH BATES: Welcome to HBR on Leadership , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock the best in those around you.

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

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

He’s an expert in innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

  In this episode, you’ll learn how to reframe tough problems, by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for one root cause can be misleading. And you’ll learn how to use experimentation and rapid prototyping as problem-solving tools.

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

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

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

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

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

THOMAS WEDELL-WEDELLSBORG: Thanks for inviting me.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

SARAH GREEN CARMICHAEL: That is a really good question.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

THOMAS WEDELL-WEDELLSBORG: Completely, completely hypothetical.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

SARAH GREEN CARMICHAEL: We got take-out.

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

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

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

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

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

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

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

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

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

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

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

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

THOMAS WEDELL-WEDELLSBORG: Thank you, Sarah.  

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

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

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

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

See you next week.

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A Guide to Using the Scientific Method in Everyday Life

The  scientific method —the process used by scientists to understand the natural world—has the merit of investigating natural phenomena in a rigorous manner. Working from hypotheses, scientists draw conclusions based on empirical data. These data are validated on large-scale numbers and take into consideration the intrinsic variability of the real world. For people unfamiliar with its intrinsic jargon and formalities, science may seem esoteric. And this is a huge problem: science invites criticism because it is not easily understood. So why is it important, then, that every person understand how science is done?

Because the scientific method is, first of all, a matter of logical reasoning and only afterwards, a procedure to be applied in a laboratory.

Individuals without training in logical reasoning are more easily victims of distorted perspectives about themselves and the world. An example is represented by the so-called “ cognitive biases ”—systematic mistakes that individuals make when they try to think rationally, and which lead to erroneous or inaccurate conclusions. People can easily  overestimate the relevance  of their own behaviors and choices. They can  lack the ability to self-estimate the quality of their performances and thoughts . Unconsciously, they could even end up selecting only the arguments  that support their hypothesis or beliefs . This is why the scientific framework should be conceived not only as a mechanism for understanding the natural world, but also as a framework for engaging in logical reasoning and discussion.

A brief history of the scientific method

The scientific method has its roots in the sixteenth and seventeenth centuries. Philosophers Francis Bacon and René Descartes are often credited with formalizing the scientific method because they contrasted the idea that research should be guided by metaphysical pre-conceived concepts of the nature of reality—a position that, at the time,  was highly supported by their colleagues . In essence, Bacon thought that  inductive reasoning based on empirical observation was critical to the formulation of hypotheses  and the  generation of new understanding : general or universal principles describing how nature works are derived only from observations of recurring phenomena and data recorded from them. The inductive method was used, for example, by the scientist Rudolf Virchow to formulate the third principle of the notorious  cell theory , according to which every cell derives from a pre-existing one. The rationale behind this conclusion is that because all observations of cell behavior show that cells are only derived from other cells, this assertion must be always true. 

Inductive reasoning, however, is not immune to mistakes and limitations. Referring back to cell theory, there may be rare occasions in which a cell does not arise from a pre-existing one, even though we haven’t observed it yet—our observations on cell behavior, although numerous, can still benefit from additional observations to either refute or support the conclusion that all cells arise from pre-existing ones. And this is where limited observations can lead to erroneous conclusions reasoned inductively. In another example, if one never has seen a swan that is not white, they might conclude that all swans are white, even when we know that black swans do exist, however rare they may be.  

The universally accepted scientific method, as it is used in science laboratories today, is grounded in  hypothetico-deductive reasoning . Research progresses via iterative empirical testing of formulated, testable hypotheses (formulated through inductive reasoning). A testable hypothesis is one that can be rejected (falsified) by empirical observations, a concept known as the  principle of falsification . Initially, ideas and conjectures are formulated. Experiments are then performed to test them. If the body of evidence fails to reject the hypothesis, the hypothesis stands. It stands however until and unless another (even singular) empirical observation falsifies it. However, just as with inductive reasoning, hypothetico-deductive reasoning is not immune to pitfalls—assumptions built into hypotheses can be shown to be false, thereby nullifying previously unrejected hypotheses. The bottom line is that science does not work to prove anything about the natural world. Instead, it builds hypotheses that explain the natural world and then attempts to find the hole in the reasoning (i.e., it works to disprove things about the natural world).

How do scientists test hypotheses?

Controlled experiments

The word “experiment” can be misleading because it implies a lack of control over the process. Therefore, it is important to understand that science uses controlled experiments in order to test hypotheses and contribute new knowledge. So what exactly is a controlled experiment, then? 

Let us take a practical example. Our starting hypothesis is the following: we have a novel drug that we think inhibits the division of cells, meaning that it prevents one cell from dividing into two cells (recall the description of cell theory above). To test this hypothesis, we could treat some cells with the drug on a plate that contains nutrients and fuel required for their survival and division (a standard cell biology assay). If the drug works as expected, the cells should stop dividing. This type of drug might be useful, for example, in treating cancers because slowing or stopping the division of cells would result in the slowing or stopping of tumor growth.

Although this experiment is relatively easy to do, the mere process of doing science means that several experimental variables (like temperature of the cells or drug, dosage, and so on) could play a major role in the experiment. This could result in a failed experiment when the drug actually does work, or it could give the appearance that the drug is working when it is not. Given that these variables cannot be eliminated, scientists always run control experiments in parallel to the real ones, so that the effects of these other variables can be determined.  Control experiments  are designed so that all variables, with the exception of the one under investigation, are kept constant. In simple terms, the conditions must be identical between the control and the actual experiment.     

Coming back to our example, when a drug is administered it is not pure. Often, it is dissolved in a solvent like water or oil. Therefore, the perfect control to the actual experiment would be to administer pure solvent (without the added drug) at the same time and with the same tools, where all other experimental variables (like temperature, as mentioned above) are the same between the two (Figure 1). Any difference in effect on cell division in the actual experiment here can be attributed to an effect of the drug because the effects of the solvent were controlled.

In order to provide evidence of the quality of a single, specific experiment, it needs to be performed multiple times in the same experimental conditions. We call these multiple experiments “replicates” of the experiment (Figure 2). The more replicates of the same experiment, the more confident the scientist can be about the conclusions of that experiment under the given conditions. However, multiple replicates under the same experimental conditions  are of no help  when scientists aim at acquiring more empirical evidence to support their hypothesis. Instead, they need  independent experiments  (Figure 3), in their own lab and in other labs across the world, to validate their results. 

Often times, especially when a given experiment has been repeated and its outcome is not fully clear, it is better  to find alternative experimental assays  to test the hypothesis. 

Applying the scientific approach to everyday life

So, what can we take from the scientific approach to apply to our everyday lives?

A few weeks ago, I had an agitated conversation with a bunch of friends concerning the following question: What is the definition of intelligence?

Defining “intelligence” is not easy. At the beginning of the conversation, everybody had a different, “personal” conception of intelligence in mind, which – tacitly – implied that the conversation could have taken several different directions. We realized rather soon that someone thought that an intelligent person is whoever is able to adapt faster to new situations; someone else thought that an intelligent person is whoever is able to deal with other people and empathize with them. Personally, I thought that an intelligent person is whoever displays high cognitive skills, especially in abstract reasoning. 

The scientific method has the merit of providing a reference system, with precise protocols and rules to follow. Remember: experiments must be reproducible, which means that an independent scientists in a different laboratory, when provided with the same equipment and protocols, should get comparable results.  Fruitful conversations as well need precise language, a kind of reference vocabulary everybody should agree upon, in order to discuss about the same “content”. This is something we often forget, something that was somehow missing at the opening of the aforementioned conversation: even among friends, we should always agree on premises, and define them in a rigorous manner, so that they are the same for everybody. When speaking about “intelligence”, we must all make sure we understand meaning and context of the vocabulary adopted in the debate (Figure 4, point 1).  This is the first step of “controlling” a conversation.

There is another downside that a discussion well-grounded in a scientific framework would avoid. The mistake is not structuring the debate so that all its elements, except for the one under investigation, are kept constant (Figure 4, point 2). This is particularly true when people aim at making comparisons between groups to support their claim. For example, they may try to define what intelligence is by comparing the  achievements in life of different individuals: “Stephen Hawking is a brilliant example of intelligence because of his great contribution to the physics of black holes”. This statement does not help to define what intelligence is, simply because it compares Stephen Hawking, a famous and exceptional physicist, to any other person, who statistically speaking, knows nothing about physics. Hawking first went to the University of Oxford, then he moved to the University of Cambridge. He was in contact with the most influential physicists on Earth. Other people were not. All of this, of course, does not disprove Hawking’s intelligence; but from a logical and methodological point of view, given the multitude of variables included in this comparison, it cannot prove it. Thus, the sentence “Stephen Hawking is a brilliant example of intelligence because of his great contribution to the physics of black holes” is not a valid argument to describe what intelligence is. If we really intend to approximate a definition of intelligence, Steven Hawking should be compared to other physicists, even better if they were Hawking’s classmates at the time of college, and colleagues afterwards during years of academic research. 

In simple terms, as scientists do in the lab, while debating we should try to compare groups of elements that display identical, or highly similar, features. As previously mentioned, all variables – except for the one under investigation – must be kept constant.

This insightful piece  presents a detailed analysis of how and why science can help to develop critical thinking.

In a nutshell

Here is how to approach a daily conversation in a rigorous, scientific manner:

• First discuss about the reference vocabulary, then discuss about the content of the discussion.  Think about a researcher who is writing down an experimental protocol that will be used by thousands of other scientists in varying continents. If the protocol is rigorously written, all scientists using it should get comparable experimental outcomes. In science this means reproducible knowledge, in daily life this means fruitful conversations in which individuals are on the same page. 
• Adopt “controlled” arguments to support your claims.  When making comparisons between groups, visualize two blank scenarios. As you start to add details to both of them, you have two options. If your aim is to hide a specific detail, the better is to design the two scenarios in a completely different manner—it is to increase the variables. But if your intention is to help the observer to isolate a specific detail, the better is to design identical scenarios, with the exception of the intended detail—it is therefore to keep most of the variables constant. This is precisely how scientists ideate adequate experiments to isolate new pieces of knowledge, and how individuals should orchestrate their thoughts in order to test them and facilitate their comprehension to others.   

Not only the scientific method should offer individuals an elitist way to investigate reality, but also an accessible tool to properly reason and discuss about it.

Edited by Jason Organ, PhD, Indiana University School of Medicine.

Simone is a molecular biologist on the verge of obtaining a doctoral title at the University of Ulm, Germany. He is Vice-Director at Culturico (https://culturico.com/), where his writings span from Literature to Sociology, from Philosophy to Science. His writings recently appeared in Psychology Today, openDemocracy, Splice Today, Merion West, Uncommon Ground and The Society Pages. Follow Simone on Twitter: @simredaelli

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This has to be the best article I have ever read on Scientific Thinking. I am presently writing a treatise on how Scientific thinking can be adopted to entreat all situations.And how, a 4 year old child can be taught to adopt Scientific thinking, so that, the child can look at situations that bothers her and she could try to think about that situation by formulating the right questions. She may not have the tools to find right answers? But, forming questions by using right technique ? May just make her find a way to put her mind to rest even at that level. That is why, 4 year olds are often “eerily: (!)intelligent, I have iften been intimidated and plain embarrassed to see an intelligent and well spoken 4 year old deal with celibrity ! Of course, there are a lot of variables that have to be kept in mind in order to train children in such controlled thinking environment, as the screenplay of little Sheldon shows. Thanking the author with all my heart – #ershadspeak #wearescience #weareallscientists Ershad Khandker

Simone, thank you for this article. I have the idea that I want to apply what I learned in Biology to everyday life. You addressed this issue, and have given some basic steps in using the scientific method.

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How is Algebra Used in Real Life – 10 Practical Examples Explained

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The Role of Algebra in Everyday Life

Role of algebra in budgeting and expenses, role of algebra in managing loans and interest rates, role of algebra in investment and profits, role of algebra in construction and engineering, role of algebra in travel planning and scheduling, role of algebra in computer programming and technology, role of algebra in logical thinking and critical analysis, role of algebra in patterns, formulas, and rules, role of algebra in gaming, sports, and hobbies, role of algebra in cooking, crafting, and interior decorating.

To use algebra in real life , I first grasp the fundamental concepts of variables and equations. Algebra stretches far beyond the walls of my classroom, seamlessly integrating into my daily routines and responsibilities. It’s the silent partner in my budgeting, where balancing expenses becomes a balancing act of numbers.

In my career, algebra unlocks a deeper understanding of various systems . For example, robotics use algebraic geometry to study the motion of robots with multidimensional search spaces. By applying algebra , I can model and solve problems with an array of possible outcomes and constraints. 

Algebra is a cornerstone of mathematics that pops up in numerous daily activities , often without my even noticing. From budgeting to cooking, the use of variables , equations , and the algebraic expressions simplifies complex tasks.

Knowing how to manipulate these allows me to solve practical problems effectively. Here’s how I apply algebra in real life:

Budgeting : Crafting a monthly budget requires balancing income and expenses . Variables represent the amounts, while equations make sure everything adds up. For example, if my income is $I$ and my monthly expenses are a sum of individual costs $c_1, c_2, …, c_n$, the algebraic expression looks like this: $I = c_1 + c_2 + … + c_n$.

Cooking : Modifying a recipe based on servings involves ratios and proportions , which are algebraic concepts. For a recipe that serves $4$ and I need it for $6$, I’ll use a simple formula : Multiply each ingredient quantity by $\frac{6}{4}$.

Shopping Discounts : When I’m out shopping and there’s a $20%$ sale, I calculate the discounted price using the original price $P$. The sale price $S$ is $S = P – (0.20 \times P)$ or simply $S = 0.80P$.

Fitness Tracking : Keeping up with my fitness regimen involves calculating calories and exercise durations. If a workout burns $C$ calories per minute and I exercise for $t$ minutes, the total calories burned is $Ct$.

Here’s a quick table summarizing the use of algebra in everyday situations:

Algebra is not just an abstract tool; it is a vital part of managing finances in my everyday life. When I sit down to create a budget, I’m essentially using algebraic equations to plan my spending, savings, and investments.

For example, when planning monthly expenses, I might use a simple equation:

 $\text{Income} – \text{Expenses} = \text{Savings}$

Here’s how algebra becomes practical:

• Income : I calculate my total income from different sources, such as my salary, freelance work, and any other passive income.
• Expenses : I then sum up my monthly bills, groceries, transport, and other known costs.
• Savings : What I aim to save is the variable I need to solve for in the equation.

I use algebra to calculate my monthly payments using the formula for an ordinary annuity, which is:

$M = P \frac{r(1 + r)^n}{(1 + r)^n – 1}$

• ( M ) is the monthly payment,
• ( P ) is the principal loan amount,
• ( r ) is the monthly interest rate (annual rate divided by 12 months),
• ( n ) is the number of payments (loan term in years multiplied by 12 months).

By plugging in the values, I can budget my monthly expenses effectively, ensuring I don’t overspend and land myself in financial hot water.

When I assess the impact of an interest rate on my loan, I recognize that a lower rate can significantly reduce the total amount of interest I’ll pay over time. For instance, if I consider two loans with different interest rates, algebra helps me determine which is more cost-effective for my budget and long-term financial goals.

Here’s a quick comparison of two different interest rates on a $10,000 car loan over 5 years:

Investing is a financial strategy I use to grow my income and savings over time. To make informed decisions, I rely heavily on algebra to predict potential profits and manage my investments. For instance, when considering the future value of an investment, I calculate compound interest using the formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Here’s a breakdown of this equation:

• ( A ) is the amount of money accumulated after ( n ) years, including interest.
• ( P ) is the principal amount (the initial money I put in).
• ( r ) is the annual interest rate (decimal).
• ( n ) is the number of times that interest is compounded per year.
• ( t ) is the time in years.

When planning my budget, algebra aids me in balancing my income, expenses, and savings. The basic structure of a budget can be summarized by:

$\text{Income} – \text{Expenses} = \text{Savings}$

I also assess loans and manage finances by understanding the interest rates and calculating monthly payments using amortization formulas.

The formula for figuring out the monthly payment (( PMT )) on a loan is:

$PMT = \frac{P \times \frac{r}{n}}{1 – (1 + r)^{-n}}$

Calculating taxes is another essential use of algebra. To find out my after-tax income, I subtract the tax, which is a percentage of my income, as follows:

$\text{After-Tax Income} = \text{Income} – (\text{Income} \times \text{Tax Rate}) $

By mastering these algebraic operations , I ensure my investments are profitable and my financial future secure.

In my career as a construction engineer, I’ve constantly engaged with algebra. It’s vital for creating stable structures and ensuring buildings can withstand stress. For example, calculating loads involves algebraic equations, so I can determine if a beam will support the weight using the formula:

$$ Load = \frac{Weight}{Area} $$

In the realm of construction scheduling, I integrate algebra to manage timelines efficiently. By establishing critical paths and resource allocations, I can pinpoint areas that need attention, making sure that my projects stay on track.

In my approach to technology and computer programming, I’ve also noticed a strong reliance on algebra. Whether it’s algorithm development or designing complex structures through Computer-Aided Design (CAD) software, algebraic concepts are crucial. Let me give you a brief glimpse at how algebra intersects across various applications:

When I plan a trip, algebra becomes a trusty companion, particularly in managing schedules and budgets. The use of algebra in travel planning is not just theoretical; it’s a practical tool that helps me make the most of my time and money.

To start with, creating a travel schedule can often feel like a puzzle. I use algebra to calculate travel times between destinations, accounting for layovers and connections. For example, if my flight from A to B takes 3 hours and my layover in B before flying to C is 2 hours, I can figure out my total travel time with a simple algebraic expression, ($ t_{\text{total}} = t_{\text{A to B}} + t_{\text{layover}} + t_{\text{B to C}}$ ).

In budgeting, I list all expenses such as transportation, accommodation, and activities. Then I sum them up, letting algebra help me keep a tight rein on spending. Here’s a small table I might create:

The application of algebra extends to more complex scenarios in engineering and construction , where it assists in optimizing project schedules and resource allocations. In computer science , algorithms for scheduling are embedded in various applications, using algebraic formulas to automate and enhance the planning process.

Algebra is a cornerstone in the realm of computer programming and technology. I often see it as the hidden hero in various applications spanning from simple software to complex engineering systems. It forms the backbone of algorithms, which are the step-by-step instructions I follow when writing code for anything from sorting data to encrypting information.

In computer science, I leverage algebraic structures to optimize code and solve computational problems. For example, the boolean algebra helps me in creating logic circuits and program decision-making capabilities in software. Here’s how algebraic concepts are applied:

Binary Operations : These allow me to perform tasks in programming languages, using operators such as $+$, $-$, $\times$, and $\div$.

Linear Algebra : It’s crucial in the construction of 3D graphics and animations, which are essential in video games and simulations.

Matrices : I use these for data organization and to perform multiple calculations at once, which is integral in image processing and machine learning tasks.

Algebra has its applications in scheduling and optimization algorithms too. Whether it’s assigning resources efficiently or finding the quickest routes for travel, algebra provides me with methods to compute optimal solutions.

Let me give you an example: when I’m dealing with robotics, I apply algebraic geometry to study the dynamics of robotic mechanisms. This involves handling a myriad of dimensional states and motions—something that is made manageable through algebraic principles.

In technology-enhanced education, algebra facilitates better learning tools, offering both visually engaging and interactive ways for students to grasp mathematical concepts. This contributes to a deeper understanding, heightened interest, and improved proficiency in mathematics.

Algebra is much more than just manipulating symbols and solving equations for me. It’s the backbone of my logical thinking and critical analysis skills. When I tackle an algebraic problem, I’m engaging with an entire system of logic and patterns that help build my reasoning abilities. 

For instance, consider the simple algebraic formula for solving for ( x ) in a linear equation: ( ax + b = c ). This equation might represent a real-life problem, like calculating the price after a discount (where ( x ) is the original price). Stringently following algebraic rules, I rearrange the formula to ( x = $\frac{c – b}{a}$ ), a process that reinforces my understanding of operations and the order in which they should be conducted.

Algebra strengthens my critical thinking by requiring me to apply sets of rules—properties of operations, for example—to various problems. These formulas and rules are not arbitrary; they are logical structures that I can rely on to find clarity in confusion.

Algebra serves as the foundation for problem-solving in various everyday scenarios. When I encounter patterns , algebra helps me to recognize and understand the structure behind these arrangements. For instance, a simple pattern like an increasing sequence of odd numbers can be represented algebraically as (2n + 1), where n represents the position in the sequence. This aids in predicting subsequent numbers, demonstrating a relationship ruled by algebra.

In my daily life, I use formulas to calculate things like interest rates or to determine the distance I travel. This use of formulas represents a set of rules that guide my critical thinking and enable accurate problem-solving. Here’s a snapshot of how I might use a formula:

Logic and reasoning intersect with algebra when I face a problem requiring a structured approach. Algebraic expressions give me a powerful language to describe relationships and solve problems methodically. This intersection fosters my critical thinking , which becomes instrumental when I’m trying to discover a rule through an observed pattern. It’s exciting to deduce a formula from scattered information, and algebra is my go-to toolkit for doing just that.

In gaming, I often find algebra underlying the design and development of many video games, particularly when programming movements or scoring systems. For instance, in a platformer, the character’s jump might be calculated using the formula ( s = ut + $\frac{1}{2}at^2$ ), where ( s ) is displacement, ( u ) is the initial velocity, ( a ) is the acceleration due to gravity, and ( t ) is time.

Sports analytics use algebra to enhance team performance and strategy. Take basketball, where player efficiency is often computed using a complex algebraic formula to analyze performance statistics.

As for cooking, algebra helps in scaling recipes. If I want to double a recipe, I apply proportional reasoning, a fundamental algebraic concept, to adjust ingredient quantities. With crafting and art, algebra assists in planning layouts and dimensions, ensuring symmetrical designs or patterns.

For children’s education and hobbies, algebra fosters problem-solving skills. It might be as simple as figuring out the right amount of paint for a color mix, calculated by a ratio or equation.

Cooking: When preparing a meal, algebra helps me adjust recipes. For instance, if a recipe calls for 4 cups of flour to serve 8 people, and I only need to serve 2, I use the algebraic equation ($ \text{required flour} = \frac{4}{8} \times 2 $) to determine that I need 1 cup of flour.

• Original servings: ( $s_1$ )
• Desired servings: ( $s_2$)
• Original ingredient amount: ( $a_1 $)
• New ingredient amount: ($ a_2 = \frac{a_1 \times s_2}{s_1}$ )

Crafting: Algebra aids me in creating and executing my designs accurately. If I’m designing a quilt, the number of squares (( q )) I need will depend on the size of the quilt and the size of each square. The equation ($ q = \frac{\text{total area of quilt}}{\text{area of one square}} $) saves time and materials.

• Total area of project: ( $A_t $)
• Area per piece: ($A_p$ )
• Pieces required: ( P =$ \frac{A_t}{A_p}$ )

Interior Decorating: When redecorating my living space, algebra helps me maximize the area and aesthetics. If I need to cover a wall with wallpaper, I need to know how many rolls to purchase. I’ll use the equation ($ \text{rolls needed} = \frac{\text{wall area}}{\text{coverage per roll}} $) to get the right quantity.

In exploring the intersection of algebra and daily life , I’ve highlighted its undeniable presence in the routines and decisions we navigate. From managing personal finances to interpreting data trends in work settings, algebra is not confined to textbooks—it thrives in the world around us.

I’ve found that recognizing variables and constants, denoted as $x$ and $c$ respectively, equips us with the insight to forecast outcomes. In doing so, we harness the capability to plan and strategize more effectively. Whether we’re considering the purchase of a new home, conserving gas based on our vehicle’s efficiency, or baking with precision, algebraic principles guide us.

Appreciating that a formula such as $distance = speed \times time$ can determine travel details, or that calculating an unknown expenditure with $income – expenses = savings$, is practical algebra at play. My experiences have shown that algebra isn’t just about solving equations; it’s a toolkit for problem-solving.

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Everyday problem solving across the adult life span: solution diversity and efficacy

Affiliation.

• 1 Center for the Study of Lifespan Development, Psychology Department, Western Kentucky University, Bowling Green, Kentucky, USA. [email protected]
• PMID: 22023569
• PMCID: PMC3746011
• DOI: 10.1111/j.1749-6632.2011.06207.x

Everyday problem solving involves examining the solutions that individuals generate when faced with problems that take place in their everyday experiences. Problems can range from medication adherence and meal preparation to disagreeing with a physician over a recommended medical procedure or compromising with extended family members over where to host Thanksgiving dinner. Across the life span, research has demonstrated divergent patterns of change in performance based on the type of everyday problems used as well as based on the way that problem-solving efficacy is operationally defined. Advancing age is associated with worsening performance when tasks involve single-solution or fluency-based definitions of effectiveness. However, when efficacy is defined in terms of the diversity of strategies used, as well as by the social and emotional impact of solution choice on the individual, performance is remarkably stable and sometimes even improves in the latter half of life. This article discusses how both of these approaches to everyday problem solving inform research on the influence that aging has on everyday functioning.

© 2011 New York Academy of Sciences.

Publication types

• Aging / physiology
• Aging / psychology*
• Choice Behavior
• Life Expectancy*
• Problem Solving / physiology*

Grants and funding

• R24 AG039350/AG/NIA NIH HHS/United States