what is a problem solving means

At my current job as an operations analyst at XYZ Inc., my boss set a quarterly goal to cut contractor spending by 25% while maintaining the same level of production and moving more processes in-house. It turned out that achieving this goal required hiring an additional 6 full-time employees, which got stalled due to the pandemic. I suggested that we widen our net and hire remote employees after our initial applicant pool had no solid candidates. I ran the analysis on overhead costs and found that if even 4 of the 6 employees were remote, we’d save 16% annually compared to the contractors’ rates. In the end, all 6 employees we hired were fully remote, and we cut costs by 26% while production rose by a modest amount.

I try to step back and gather research as my first step. For instance, I had a client who needed a graphic designer to work with Crello, which I had never seen before, let alone used. After getting the project details straight, I began meticulously studying the program the YouTube tutorials, and the quick course Crello provides. I also reached out to coworkers who had worked on projects for this same client in the past. Once I felt comfortable with the software, I started work immediately. It was a slower process because I had to be more methodical in my approach, but by putting in some extra hours, I turned in the project ahead of schedule. The client was thrilled with my work and was shocked to hear me joke afterward that it was my first time using Crello.

As a digital marketer , website traffic and conversion rates are my ultimate metrics. However, I also track less visible metrics that can illuminate the story behind the results. For instance, using Google Analytics, I found that 78% of our referral traffic was coming from one affiliate, but that these referrals were only accounting for 5% of our conversions. Another affiliate, who only accounted for about 10% of our referral traffic, was responsible for upwards of 30% of our conversions. I investigated further and found that the second, more effective affiliate was essentially qualifying our leads for us before sending them our way, which made it easier for us to close. I figured out exactly how they were sending us better customers, and reached out to the first, more prolific but less effective affiliate with my understanding of the results. They were able to change their pages that were referring us traffic, and our conversions from that source tripled in just a month. It showed me the importance of digging below the “big picture” metrics to see the mechanics of how revenue was really being generated through digital marketing.

You can bring up your problem-solving skills in your resume summary statement , in your work experience , and under your education section , if you’re a recent graduate. The key is to include items on your resume that speak direclty to your ability to solve problems and generate results.

If you can, quantify your problem-solving accomplishments on your your resume . Hiring managers and recruiters are always more impressed with results that include numbers because they provide much-needed context.

This sample resume for a Customer Service Representative will give you an idea of how you can work problem solving into your resume.

Michelle Beattle 111 Millennial Parkway Chicago, IL 60007 (555) 987-6543 [email protected] Professional Summary Qualified Customer Services Representative with 3 years in a high-pressure customer service environment. Professional, personable, and a true problem solver. Work History ABC Store — Customer Service Representative 01/2015 — 12/2017 Managed in-person and phone relations with customers coming in to pick up purchases, return purchased products, helped find and order items not on store shelves, and explained details and care of merchandise. Became a key player in the customer service department and was promoted to team lead. XYZ Store — Customer Service Representative/Night Manager 01/2018 — 03/2020, released due to Covid-19 layoffs Worked as the night manager of the customer service department and filled in daytime hours when needed. Streamlined a process of moving customers to the right department through an app to ease the burden on the phone lines and reduce customer wait time by 50%. Was working on additional wait time problems when the Covid-19 pandemic caused our stores to close permanently. Education Chicago Tech 2014-2016 Earned an Associate’s Degree in Principles of Customer Care Skills Strong customer service skills Excellent customer complaint resolution Stock record management Order fulfillment New product information Cash register skills and proficiency Leader in problem solving initiatives

You can see how the resume gives you a chance to point out your problem-solving skills and to show where you used them a few times. Your cover letter is your chance to introduce yourself and list a few things that make you stand out from the crowd.

Michelle Beattle 111 Millennial Parkway Chicago, IL 60007 (555) 987-6543 [email protected] Dear Mary McDonald, I am writing in response to your ad on Zippia for a Customer Service Representative . Thank you for taking the time to consider me for this position. Many people believe that a job in customer service is simply listening to people complain all day. I see the job as much more than that. It’s an opportunity to help people solve problems, make their experience with your company more enjoyable, and turn them into life-long advocates of your brand. Through my years of experience and my educational background at Chicago Tech, where I earned an Associate’s Degree in the Principles of Customer Care, I have learned that the customers are the lifeline of the business and without good customer service representatives, a business will falter. I see it as my mission to make each and every customer I come in contact with a fan. I have more than five years of experience in the Customer Services industry and had advanced my role at my last job to Night Manager. I am eager to again prove myself as a hard worker, a dedicated people person, and a problem solver that can be relied upon. I have built a professional reputation as an employee that respects all other employees and customers, as a manager who gets the job done and finds solutions when necessary, and a worker who dives in to learn all she can about the business. Most of my customers have been very satisfied with my resolution ideas and have returned to do business with us again. I believe my expertise would make me a great match for LMNO Store. I have enclosed my resume for your review, and I would appreciate having the opportunity to meet with you to further discuss my qualifications. Thank you again for your time and consideration. Sincerely, Michelle Beattle

You’ve no doubt noticed that many of the skills listed in the problem-solving process are repeated. This is because having these abilities or talents is so important to the entire course of getting a problem solved.

In fact, they’re worthy of a little more attention. Many of them are similar, so we’ll pull them together and discuss how they’re important and how they work together.

Communication, active listening, and customer service skills. No matter where you are in the process of problem-solving, you need to be able to show that you’re listening and engaged and really hearing what the problem is or what a solution may be.

Obviously, the other part of this is being able to communicate effectively so people understand what you’re saying without confusion. Rolled into this are customer service skills , which really are all about listening and responding appropriately — it’s the ultimate in interpersonal communications.

Analysis (data and historical), research, and topic knowledge/understanding. This is how you intellectually grasp the issue and approach it. This can come from studying the topic and the process or it can come from knowledge you’ve gained after years in the business. But the best solutions come from people who thoroughly understand the problem.

Creativity, brainstorming, troubleshooting, and flexibility. All of you creative thinkers will like this area because it’s when your brain is at its best.

Coming up with ideas, collaborating with others, leaping over hurdles, and then being able to change courses immediately, if need be, are all essential. If you’re not creative by nature, then having a team of diverse thinkers can help you in this area.

Dependability, believability, trustworthiness, and follow-through. Think about it, these are all traits a person needs to have to make change happen and to make you comfortable taking that next step with them. Someone who is shifty and shady and never follows through, well, you’re simply not going to do what they ask, are you?

Leadership, teambuilding, decision-making, and project management. These are the skills that someone who is in charge is brimming with. These are the leaders you enjoy working for because you know they’re doing what they can to keep everything in working order. These skills can be learned but they’re often innate.

Prioritizing, prediction, forecasting, evaluating and weighing, and process flow. If you love flow charts, data analysis, prediction modeling, and all of that part of the equation, then you might have some great problem-solving abilities.

These are all great skills because they can help you weed out bad ideas, see flaws, and save massive amounts of time in trial and error.

What is a good example of problem-solving skills?

Good examples of porblem-solving skills include research, analysis, creativity, communciation, and decision-making. Each of these skills build off one another to contribute to the problem solving process. Research and analysis allow you to identify a problem.

Creativity and analysis help you consider different solutions. Meanwhile, communication and decision-making are key to working with others to solve a problem on a large scale.

What are 3 key attributes of a good problem solver?

3 key attributes of a good problem solver are persistence, intellegince, and empathy. Persistence is crucial to remain motivated to work through challenges. Inellegince is needed to make smart, informed choices. Empathy is crucial to maintain positive relationships with others as well as yourself.

What can I say instead of problem-solving skills?

Instead of saying problem-solving skills, you can say the following:

Critical thinker

Solutions-oriented

Engineering

Using different words is helpful, especially when writing your resume and cover letter.

What is problem-solving in the workplace?

Problem-solving in the workplace is the ability to work through any sort of challenge, conflict, or unexpected situation and still achieve business goals. Though it varies by profession, roblem-solving in the workplace is very important for almost any job, because probelms are inevitable. You need to have the appropriate level of problem-solving skills if you want to succeed in your career, whatever it may be.

Department of Labor – Problem Solving and Critical Thinking

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Kristin Kizer is an award-winning writer, television and documentary producer, and content specialist who has worked on a wide variety of written, broadcast, and electronic publications. A former writer/producer for The Discovery Channel, she is now a freelance writer and delighted to be sharing her talents and time with the wonderful Zippia audience.

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What Is Creative Problem-Solving & Why Is It Important?

Business team using creative problem-solving

01 Feb 2022

One of the biggest hindrances to innovation is complacency—it can be more comfortable to do what you know than venture into the unknown. Business leaders can overcome this barrier by mobilizing creative team members and providing space to innovate.

There are several tools you can use to encourage creativity in the workplace. Creative problem-solving is one of them, which facilitates the development of innovative solutions to difficult problems.

Here’s an overview of creative problem-solving and why it’s important in business.

What Is Creative Problem-Solving?

Research is necessary when solving a problem. But there are situations where a problem’s specific cause is difficult to pinpoint. This can occur when there’s not enough time to narrow down the problem’s source or there are differing opinions about its root cause.

In such cases, you can use creative problem-solving , which allows you to explore potential solutions regardless of whether a problem has been defined.

Creative problem-solving is less structured than other innovation processes and encourages exploring open-ended solutions. It also focuses on developing new perspectives and fostering creativity in the workplace . Its benefits include:

Design Thinking and Innovation | Uncover creative solutions to your business problems | Learn more

Creative problem-solving is traditionally based on the following key principles :

1. Balance Divergent and Convergent Thinking

Creative problem-solving uses two primary tools to find solutions: divergence and convergence. Divergence generates ideas in response to a problem, while convergence narrows them down to a shortlist. It balances these two practices and turns ideas into concrete solutions.

2. Reframe Problems as Questions

By framing problems as questions, you shift from focusing on obstacles to solutions. This provides the freedom to brainstorm potential ideas.

3. Defer Judgment of Ideas

When brainstorming, it can be natural to reject or accept ideas right away. Yet, immediate judgments interfere with the idea generation process. Even ideas that seem implausible can turn into outstanding innovations upon further exploration and development.

4. Focus on "Yes, And" Instead of "No, But"

Using negative words like "no" discourages creative thinking. Instead, use positive language to build and maintain an environment that fosters the development of creative and innovative ideas.

Creative Problem-Solving and Design Thinking

Whereas creative problem-solving facilitates developing innovative ideas through a less structured workflow, design thinking takes a far more organized approach.

Design thinking is a human-centered, solutions-based process that fosters the ideation and development of solutions. In the online course Design Thinking and Innovation , Harvard Business School Dean Srikant Datar leverages a four-phase framework to explain design thinking.

The four stages are:

The four stages of design thinking: clarify, ideate, develop, and implement

Creative problem-solving primarily operates in the ideate phase of design thinking but can be applied to others. This is because design thinking is an iterative process that moves between the stages as ideas are generated and pursued. This is normal and encouraged, as innovation requires exploring multiple ideas.

Creative Problem-Solving Tools

While there are many useful tools in the creative problem-solving process, here are three you should know:

Creating a Problem Story

One way to innovate is by creating a story about a problem to understand how it affects users and what solutions best fit their needs. Here are the steps you need to take to use this tool properly.

1. Identify a UDP

Create a problem story to identify the undesired phenomena (UDP). For example, consider a company that produces printers that overheat. In this case, the UDP is "our printers overheat."

2. Move Forward in Time

To move forward in time, ask: “Why is this a problem?” For example, minor damage could be one result of the machines overheating. In more extreme cases, printers may catch fire. Don't be afraid to create multiple problem stories if you think of more than one UDP.

3. Move Backward in Time

To move backward in time, ask: “What caused this UDP?” If you can't identify the root problem, think about what typically causes the UDP to occur. For the overheating printers, overuse could be a cause.

Following the three-step framework above helps illustrate a clear problem story:

You can extend the problem story in either direction if you think of additional cause-and-effect relationships.

4. Break the Chains

By this point, you’ll have multiple UDP storylines. Take two that are similar and focus on breaking the chains connecting them. This can be accomplished through inversion or neutralization.

Even if creating a problem story doesn't provide a solution, it can offer useful context to users’ problems and additional ideas to be explored. Given that divergence is one of the fundamental practices of creative problem-solving, it’s a good idea to incorporate it into each tool you use.

Brainstorming

Brainstorming is a tool that can be highly effective when guided by the iterative qualities of the design thinking process. It involves openly discussing and debating ideas and topics in a group setting. This facilitates idea generation and exploration as different team members consider the same concept from multiple perspectives.

Hosting brainstorming sessions can result in problems, such as groupthink or social loafing. To combat this, leverage a three-step brainstorming method involving divergence and convergence :

Alternate Worlds

The alternate worlds tool is an empathetic approach to creative problem-solving. It encourages you to consider how someone in another world would approach your situation.

For example, if you’re concerned that the printers you produce overheat and catch fire, consider how a different industry would approach the problem. How would an automotive expert solve it? How would a firefighter?

Be creative as you consider and research alternate worlds. The purpose is not to nail down a solution right away but to continue the ideation process through diverging and exploring ideas.

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If you're ready to develop your design thinking and creative problem-solving skills, explore Design Thinking and Innovation , one of our online entrepreneurship and innovation courses. If you aren't sure which course is the right fit, download our free course flowchart to determine which best aligns with your goals.

About the Author

How to Solve Problems

Laura Amico

To bring the best ideas forward, teams must build psychological safety.

Teams today aren’t just asked to execute tasks: They’re called upon to solve problems. You’d think that many brains working together would mean better solutions, but the reality is that too often problem-solving teams fall victim to inefficiency, conflict, and cautious conclusions. The two charts below will help your team think about how to collaborate better and come up with the best solutions for the thorniest challenges.

First, think of the last time you had to solve a problem. Maybe it was a big one: A major trade route is blocked and your product is time sensitive and must make it to market on time. Maybe it was a small one: A traffic jam on your way to work means you’re going to be late for your first meeting of the day. Whatever the size of the impact, in solving your problem you moved through five stages, according to “ Why Groups Struggle to Solve Problems Together ,” by Al Pittampalli.

Pittampalli finds that most of us, when working individually, move through these stages intuitively. It’s different when you’re working in a team, however. You need to stop and identify these different stages to make sure the group is aligned. For example, while one colleague might join a problem-solving discussion ready to evaluate assumptions (Stage 3), another might still be defining the problem (Stage 1). By defining each stage of your problem-solving explicitly, you increase the odds of your team coming to better solutions more smoothly.

This problem-solving technique gains extra power when applied to Alison Reynold’s and David Lewis’ research on problem-solving teams. In their article, “ The Two Traits of the Best Problem-Solving Teams ,” they find that highly effective teams typically have a pair of common features: They are cognitively diverse and they are psychologically safe. They also exhibit an array of characteristics associated with learning and confidence; these teammates tend to be curious, experimental, and nurturing, for example.

As you and your colleagues consider these ideas, think about the last problem you had to solve as a team. First, map out what you remember from each step of your problem-solving. Were all of you on the same page at each stage? What aspects of the problem did you consider — or might you have missed — as a result? What can you do differently the next time you have a problem to solve? Second, ask where your team sees themselves on the chart. What kinds of behaviors could your team adopt to help you move into that top-right quadrant?

Laura Amico is a senior editor at Harvard Business Review.

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What is Problem Solving Problem solving is the process of a problem analysis and resolving it in the best way possible for that situation.

This process contains analysing the problem ( root cause analysis ), defining countermeasures for the problem and implementing the right solution for that situation.

For problem solving, people need critical thinking and analytical skills . Everybody within a organization or company can benefit from having good skills because there are always problems.

There have been lots of scientific and practical studies from a learning point of view. Some of the techniques developed and used in artificial intelligence (AI), computer science, engineering, mathematics, or medicine are related to mental techniques studied in psychology.

What are the most known and used models and methods? What are their success stories and practical tips when you apply these? These posts are all about great tools and methods that can help you to achieve your goal or understand certain aspects that come with problem solving .

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A Complete Guide to know What is Problem Solving (Updated March 2023)

Everything happening in this world has its problems. This is because no system in this world has 100% efficiency. But this is not a big issue for the people who are prepared to deal with any kind of problem. The field that is heavily affected by the problems in the field of companies and organizations.

This is because a lot of employees are working in different departments under the same name. The problem for one employee or one department can cause issues for others. This is why the employees are given special problem-solving training. Here we will discuss what is problem-solving and some effective steps involved.

What is problem solving?

Problem-solving isa process of solving any kind of problem. This process is acted upon in some steps. These steps start from identifying the problem and determining the cause of the problem. After the problem and its cause are identified, the next step is to select alternatives for the solution and implement the solutions.

All of these steps are collectively known as a problem-solving process.

The basic steps involved in problem-solving.

As the problem-solving process comprises different steps that collectively help in getting id of the problem. So, here we will have a detailed discussion about the steps that are involved in problem-solving.

Defining the problem.

Defining the problem means that you are diagnosing the situation. This helps take the further steps for solving the problem. This is not just as simple as defining the problem. Here you take effective measures to keep track of the situation of the problem. Some of the most effective and easy to implement ways of defining the problem are listed below.

· Flowcharts of the process and the problem init.

· Cause and effect diagram.

With the help of these steps, you can easily identify the root causes of the problem. However, for these ways of defining the problem, you must involve the factual information and then compare the expectations to reality. Apart from this, you also need to stay focused on the root cause of the problem as eradicating this will be your main objective here.

To create a successful deduction for problem-solving in this step, you will first need to review different sectors of your system. Then you will have to evaluate things on the base of how something will affect the system.

Generating the alternatives.

Once you have gone through the first step, the next step will be to get the solution for the problem. It is in our psyche that once we think of an idea or solution, then we keep on thinking that it will be effective. But in reality, this will not happen every time and you will waste a lot of time coming up with another effective solution.

So, here the best thing to do is to come up with more than more solutions at a time. For this, you can do the following things.

· Take ideas from different employees.

· Mold your original idea according to different aspects of the problem.

· Think of other than one effective idea.

When you are going with a set of ideas for the backup, you will be very efficient in solving the problem. This is because if one idea fails, you can implement another one and this can be carried on until you have solved the problem.

Evaluating and selecting alternatives.

So, now you know that you have to come up with more than one idea, but how will you know if the ideas are effective or not. For this, you can easily evaluate the ideas that come up in your mind. This will help in filtering out only the best and the most effective ideas. Here is how this works.

· Will this solution be able to solve the specific problem without causing other problems in the system?

· Will all the people and stakeholders of the system accept the solution?

· Is the solution that I have come up with possible and easy to implement?

· Will the solution and the alternatives be in the constraints of the organization?

When you think of all the ideas and their alternatives, you will be very efficiently filtering out the ideas that do not seem to be working.

Implementing the solutions.

Now you are in the state where you have the ideas, the solutions, and the alternatives of these solutions. The only step left to get the problem solved is to implement the solution. This is also not a very simple step. Here are some things that you must include in this step to increase the efficiency of your solution.

· Involving others.

One of the best things to do is to involve others in the implementation of your solution. This will not only reduce the stress that you will have to bear. But this will also add other innovative ideas that come in their minds. This can be very helpful in making the solution to the problem better.

· Testing and expectations of the solution.

When you are implementing or you have implemented the solution, it is very important to keep constantly monitoring the solution and its working. For this, you can test the solutions’ working at different events. Testing the outcomes and comparing when with the expectations will also give you the idea of how well the solution is performing.

· Feedback system.

When you have implemented the solution, the role that you will play in the future will be lower than the role of other employees. So, you must take feedback after sometime. The feedback system will tell you about the feelings of people about your solution and its working. This will also help in improving the solution.

Some important things to consider in each of the problem-solving steps.

Above in the article, we discussed the significance of each step involved in problem-solving. Here we will discuss some additional things that you must be aware of. This is because they will not only make your problem-solving experience better, but they will also make your problem-solving techniques more efficient.

Knowing your problem in a good way:

If you are thinking about what is problem solving and how important it is to define the problem. Then we will tell you here the importance of defining the problem and some of the best ways to implement it. It is a must for solving any problem that you must know the real cause and the root of the problem.

This is because the smaller problems can be identified and solved easily. But when we are dealing with the problems on the level of different organizations, then it is very important to get rid of the problem from the start. This is because if the problem is not fully identified, then it will never be truly eradicated.

And this will keep on damaging the company in several ways. For the problem identifying methods we mentioned above, the initiative for any of the methods can be taken for different tools. Some of the tools are the 5 W’s, the root cause analysis, and appreciation. This is also very important that you consider each of them carefully from different perspectives.

This is because the cause of the problem could be an unreasonable workload or lack of training but if unidentified, this can be extremely bad.

Knowing about the complexity of the problem.

While you are solving any problem, you must understand that every problem will not have the same scope and the time required for every problem will be different. This is because the complexity of each problem is different. There are a lot of tools and methods to know about the complexity of the problem. Some of them are listed below.

After identifying different factors of the problem, you can implement any of these tools and this will tell you about the complexity of the problem. Sometimes a problem that seems to be a single problem is a collection of different smaller problems.

This is the point where the drill-down technique can be very helpful. It will easily and efficiently breakdown the problem into smaller parts.

Process of solving the problem.

So, there can be a case that the problem is very small, and it can easily be dealt with. But inmost of the cases, the problem is not that simple, and it is a collection of several complex problems related to different departments.

In this case, the head of the problem-solving team must take different members from different departments that will help in solving that problem using the tools, tricks methods, and tips we mentioned above.

With the increasing complexities in different organizations, many people are asking what is problem solving. If you are also uncertain about what is problem solving, then this will be the article that will tell you all about what is problem solving.

This is because it will not only tell you about some of the most effective techniques for solving different problems, but the tips, tools, and methods we mentioned here can also be very helpful for everyone in dealing with complex problems.

Want to discover more?

PROBLEM SOLVING

Problem solving is a process for individual's to overcome a specific problem. That process, simply, begins at a starting point and continues until a conclusion is reached. The process includes the higher mental functions and creative thinking . However, problem solving is also seen in the animal kingdom through the use of mazes and testing to obtain hidden rewards. Many animals display quite a range of problem solving strategies including win-stay.

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PRECONSCIOUS

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What Are Problem-Solving Skills? Definition and Examples

person sitting at desk with headphones thinking

Why do employers hire employees? To help them solve problems. Whether you’re a financial analyst deciding where to invest your firm’s money, or a marketer trying to figure out which channel to direct your efforts, companies hire people to help them find solutions. Problem-solving is an essential and marketable soft skill in the workplace.

So, how can you improve your problem-solving and show employers you have this valuable skill? In this guide, we’ll cover:

Problem-Solving Skills Definition

Why are problem-solving skills important, problem-solving skills examples, how to include problem-solving skills in a job application, how to improve problem-solving skills, problem-solving: the bottom line.

Problem-solving skills are the ability to identify problems, brainstorm and analyze answers, and implement the best solutions. An employee with good problem-solving skills is both a self-starter and a collaborative teammate; they are proactive in understanding the root of a problem and work with others to consider a wide range of solutions before deciding how to move forward.

Examples of using problem-solving skills in the workplace include:

Problem-solving skills are the most sought-after soft skill of 2022. In fact, 86% of employers look for problem-solving skills on student resumes, according to the National Association of Colleges and Employers Job Outlook 2022 survey .

It’s unsurprising why employers are looking for this skill: companies will always need people to help them find solutions to their problems. Someone proactive and successful at problem-solving is valuable to any team.

“Employers are looking for employees who can make decisions independently, especially with the prevalence of remote/hybrid work and the need to communicate asynchronously,” Eric Mochnacz, senior HR consultant at Red Clover, says. “Employers want to see individuals who can make well-informed decisions that mitigate risk, and they can do so without suffering from analysis paralysis.”

Problem-solving includes three main parts: identifying the problem, analyzing possible solutions, and deciding on the best course of action.

Research is the first step of problem-solving because it helps you understand the context of a problem. Researching a problem enables you to learn why the problem is happening. For example, is revenue down because of a new sales tactic? Or because of seasonality? Is there a problem with who the sales team is reaching out to?

Research broadens your scope to all possible reasons why the problem could be happening. Then once you figure it out, it helps you narrow your scope to start solving it.

Analysis is the next step of problem-solving. Now that you’ve identified the problem, analytical skills help you look at what potential solutions there might be.

“The goal of analysis isn’t to solve a problem, actually — it’s to better understand it because that’s where the real solution will be found,” Gretchen Skalka, owner of Career Insights Consulting, says. “Looking at a problem through the lens of impartiality is the only way to get a true understanding of it from all angles.”

Decision-Making

Once you’ve figured out where the problem is coming from and what solutions are, it’s time to decide on the best way to go forth. Decision-making skills help you determine what resources are available, what a feasible action plan entails, and what solution is likely to lead to success.

On a Resume

Employers looking for problem-solving skills might include the word “problem-solving” or other synonyms like “critical thinking” or “analytical skills” in the job description.

“I would add ‘buzzwords’ you can find from the job descriptions or LinkedIn endorsements section to filter into your resume to comply with the ATS,” Matthew Warzel, CPRW resume writer, advises. Warzel recommends including these skills on your resume but warns to “leave the soft skills as adjectives in the summary section. That is the only place soft skills should be mentioned.”

On the other hand, you can list hard skills separately in a skills section on your resume .

In a Cover Letter or an Interview

Explaining your problem-solving skills in an interview can seem daunting. You’re required to expand on your process — how you identified a problem, analyzed potential solutions, and made a choice. As long as you can explain your approach, it’s okay if that solution didn’t come from a professional work experience.

“Young professionals shortchange themselves by thinking only paid-for solutions matter to employers,” Skalka says. “People at the genesis of their careers don’t have a wealth of professional experience to pull from, but they do have relevant experience to share.”

Aaron Case, career counselor and CPRW at Resume Genius, agrees and encourages early professionals to share this skill. “If you don’t have any relevant work experience yet, you can still highlight your problem-solving skills in your cover letter,” he says. “Just showcase examples of problems you solved while completing your degree, working at internships, or volunteering. You can even pull examples from completely unrelated part-time jobs, as long as you make it clear how your problem-solving ability transfers to your new line of work.”

Learn How to Identify Problems

Problem-solving doesn’t just require finding solutions to problems that are already there. It’s also about being proactive when something isn’t working as you hoped it would. Practice questioning and getting curious about processes and activities in your everyday life. What could you improve? What would you do if you had more resources for this process? If you had fewer? Challenge yourself to challenge the world around you.

Think Digitally

“Employers in the modern workplace value digital problem-solving skills, like being able to find a technology solution to a traditional issue,” Case says. “For example, when I first started working as a marketing writer, my department didn’t have the budget to hire a professional voice actor for marketing video voiceovers. But I found a perfect solution to the problem with an AI voiceover service that cost a fraction of the price of an actor.”

Being comfortable with new technology — even ones you haven’t used before — is a valuable skill in an increasingly hybrid and remote world. Don’t be afraid to research new and innovative technologies to help automate processes or find a more efficient technological solution.

Collaborate

Problem-solving isn’t done in a silo, and it shouldn’t be. Use your collaboration skills to gather multiple perspectives, help eliminate bias, and listen to alternative solutions. Ask others where they think the problem is coming from and what solutions would help them with your workflow. From there, try to compromise on a solution that can benefit everyone.

If we’ve learned anything from the past few years, it’s that the world of work is constantly changing — which means it’s crucial to know how to adapt . Be comfortable narrowing down a solution, then changing your direction when a colleague provides a new piece of information. Challenge yourself to get out of your comfort zone, whether with your personal routine or trying a new system at work.

Put Yourself in the Middle of Tough Moments

Just like adapting requires you to challenge your routine and tradition, good problem-solving requires you to put yourself in challenging situations — especially ones where you don’t have relevant experience or expertise to find a solution. Because you won’t know how to tackle the problem, you’ll learn new problem-solving skills and how to navigate new challenges. Ask your manager or a peer if you can help them work on a complicated problem, and be proactive about asking them questions along the way.

Companies always need people to help them find solutions — especially proactive employees who have practical analytical skills and can collaborate to decide the best way to move forward. Whether or not you have experience solving problems in a professional workplace, illustrate your problem-solving skills by describing your research, analysis, and decision-making process — and make it clear that you’re the solution to the employer’s current problems.

Looking to learn more workplace professional skills? Check out Two Sigma’s Professional Skills Development Virtual Experience Program .

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26 January 2021

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Do your children have trouble solving their Maths homework?

Or, do they struggle to maintain friendships at school?

If your answer is ‘Yes,’ the issue might be related to your child’s problem-solving abilities. Whether your child often forgets his/her lunch at school or is lagging in his/her class, good problem-solving skills can be a major tool to help them manage their lives better.

Children need to learn to solve problems on their own. Whether it is about dealing with academic difficulties or peer issues when children are equipped with necessary problem-solving skills they gain confidence and learn to make healthy decisions for themselves. So let us look at what is problem-solving, its benefits, and how to encourage your child to inculcate problem-solving abilities

Problem-solving skills can be defined as the ability to identify a problem, determine its cause, and figure out all possible solutions to solve the problem.

Trigonometric Problems

Problem Solving Skills: Meaning, Examples & Techniques

What is problem-solving, then? Problem-solving is the ability to use appropriate methods to tackle unexpected challenges in an organized manner. The ability to solve problems is considered a soft skill, meaning that it’s more of a personality trait than a skill you’ve learned at school, on-the-job, or through technical training. While your natural ability to tackle problems and solve them is something you were born with or began to hone early on, it doesn’t mean that you can’t work on it. This is a skill that can be cultivated and nurtured so you can become better at dealing with problems over time.

Problem Solving Skills: Meaning, Examples & Techniques are mentioned below in the Downloadable PDF.

Benefits of learning problem-solving skills

Promotes creative thinking and thinking outside the box.

Improves decision-making abilities.

Builds solid communication skills.

Develop the ability to learn from mistakes and avoid the repetition of mistakes.

Problem Solving as an ability is a life skill desired by everyone, as it is essential to manage our day-to-day lives. Whether you are at home, school, or work, life throws us curve balls at every single step of the way. And how do we resolve those? You guessed it right – Problem Solving.

Strengthening and nurturing problem-solving skills helps children cope with challenges and obstacles as they come. They can face and resolve a wide variety of problems efficiently and effectively without having a breakdown. Nurturing good problem-solving skills develop your child’s independence, allowing them to grow into confident, responsible adults.

Children enjoy experimenting with a wide variety of situations as they develop their problem-solving skills through trial and error. A child’s action of sprinkling and pouring sand on their hands while playing in the ground, then finally mixing it all to eliminate the stickiness shows how fast their little minds work.

Sometimes children become frustrated when an idea doesn't work according to their expectations, they may even walk away from their project. They often become focused on one particular solution, which may or may not work.

However, they can be encouraged to try other methods of problem-solving when given support by an adult. The adult may give hints or ask questions in ways that help the kids to formulate their solutions.

Encouraging Problem-Solving Skills in Kids

Practice problem solving through games.

Exposing kids to various riddles, mysteries, and treasure hunts, puzzles, and games not only enhances their critical thinking but is also an excellent bonding experience to create a lifetime of memories.

Create a safe environment for brainstorming

Welcome, all the ideas your child brings up to you. Children learn how to work together to solve a problem collectively when given the freedom and flexibility to come up with their solutions. This bout of encouragement instills in them the confidence to face obstacles bravely.

Invite children to expand their Learning capabilities

Whenever children experiment with an idea or problem, they test out their solutions in different settings. They apply their teachings to new situations and effectively receive and communicate ideas. They learn the ability to think abstractly and can learn to tackle any obstacle whether it is finding solutions to a math problem or navigating social interactions.

Problem-solving is the act of finding answers and solutions to complicated problems.

Developing problem-solving skills from an early age helps kids to navigate their life problems, whether academic or social more effectively and avoid mental and emotional turmoil.

Children learn to develop a future-oriented approach and view problems as challenges that can be easily overcome by exploring solutions.

About Cuemath

Cuemath, a student-friendly mathematics and coding platform, conducts regular Online Classes for academics and skill-development, and their Mental Math App, on both iOS and Android , is a one-stop solution for kids to develop multiple skills. Understand the Cuemath Fee structure and sign up for a free trial.

Frequently Asked Questions (FAQs)

How do you teach problem-solving skills.

Model a useful problem-solving method. Problem solving can be difficult and sometimes tedious. ... 1. Teach within a specific context. ... 2. Help students understand the problem. ... 3. Take enough time. ... 4. Ask questions and make suggestions. ... 5. Link errors to misconceptions.

What makes a good problem solver?

Excellent problem solvers build networks and know how to collaborate with other people and teams. They are skilled in bringing people together and sharing knowledge and information. A key skill for great problem solvers is that they are trusted by others.

What is ‘Developer Productivity’?

Providing a mental model that informs developers where to focus their time and energy to improve productivity.

⚠️ The definition of developer productivity is wide ranging, but some definitions are dangerous and outright harmful.

✅ Developer productivity is best when the creative process and analytical mind are allowed to coexist and mingle.

Developer Productivity != Assembly Line Productivity

There is an important distinction between developer productivity and assembly line productivity. It’s natural to pull from research in things like car manufacturing to form mental models about how software engineering should work. This can be useful at times, especially when considering the testing and release process, but can become quite counter productive when considering the R&D side of software engineering. Because of this, developer productivity ends up boiling down into two divergent mental models:

We create, we build (knowledge worker productivity model) ←THIS ONE! USE THIS ONE!!!

They think, we do (assembly line worker productivity model)

We create, we build

Developer Productivity is juiced up through maximizing human attention on solving problems creatively while letting the computers do things that can be automated.

When considering much of the literature on DevOps, especially the sections focused on CI/CD, it can be easy to fall into the trap of adopting the assembly line mode of thinking. Once peer review is complete and code has been merged to trunk, the process from there should absolutely resemble an assembly line.

The problem is that DevOps literature, especially Accelerate, DevOps Handbook, and the DORA metrics, are laser focused on the right side of the image above. This is not to say that these metrics aren’t useful or relevant, just that they are only part of the ‘developer productivity’ story.

Quote from DevOps Handbook and Accelerate that back up what I’m saying:

“For the remainder of this book, our attention will be on deployment lead time, a subset of the value stream described above” — The DevOps Handbook

“There are two parts to lead time: the time it takes to design and validate a product or feature, and the time to deliver the feature to customer.…We measure delivery lead time as the time it takes to go from code committed to code successfully running in production .” — Accelerate

The other part of the Developer Productivity story is creative problem solving. If you crack open Accelerate and check out Appendix A, you’ll find ‘Capabilities to drive improvement’. In other words, the assembly line metrics (ie DORA metrics) that are often used to measure developer productivity are impacted by team capabilities. Some of the capabilities include:

Product & Process Capabilities

Lean Mangement Capabilities

Cultural Capabilities

Architecture Capabilities

Technical Capabilities

If you want to improve productivity, you need to focus on improving capabilities, not the DORA metrics. In other words, the DORA metrics are the result, not the target.

They think, we do: Demoralization included!

Thinking of software engineers as factory line workers is demoralizing and self-defeating. Measuring software delivery like a factory works. Measuring software creation like a factory would be like measuring an artist’s output based on number of paintings produced.

If only Van Gough had assembly line metrics to guide his art!

The underlying assumption with a factory assembly line model is that each ‘piece’ of work is comparable (or better yet, exactly the same). To manage assembly line work, the goal is to limit variance. Each job role in the assembly line should be well defined to ensure interoperability of the labor force.

When you overlay this method of managing work on an innately creative process (in software development, each piece of work is by its very nature unique), it causes problems. Instead of developers using their creative efforts to push the envelope on what is feasible from an engineering standpoint, they are instead encouraged to stay within the predefined ‘box’ that others have imposed on them. In other words, it reduces innovation and continuous learning. It also results in estimates driving delivery expectations. Predicting when something that has never been done… will be done… is really an educated guess. Using these guesses in a complex system to drive scope estimates within an organization results in… undesirable effects.

How to think about developer productivity

Rapid feedback loops turbo charge learning and problem solving.

Developers should be getting feedback on their work multiple times a day. Whether it is feedback from their IDE or peer review, this feedback is the way developers improve their own personal capabilities to solve problems. The team should always be looking for ways to optimize their feedback loops.

Goldilocks zone of cognitive load

Human attention is a scarce resource. The areas we should be placing our attention should be the highest value arenas. Unnecessary complexity is the enemy of productivity. Reducing unnecessary complexity of things within your control will allow focus on more important problems. ‘Paper cut’ problems, when added up, reduce developer effectiveness. Take time to eliminate paper cut problems.

Optimal conditions for ‘Flow’

Achieving a state of ‘flow’ is something that can be engineered. When making calendar trade-offs, make sure flow time is prioritized. It is possible to enter a state of flow as a group in ensemble programming , so this doesn’t necessarily mean having blocked off ‘collaboration-free’ time.

Product Ownership over Product Owners

Building something that is desirable, viable, and valuable is everyone’s responsibility. Don’t outsource it to product management and designers. Developers should own the work they do and make sure they understand the problem their work is solving. If they don’t, they will probably be building something that doesn’t meet the original intent.

Some tactics that just seem to work

Successful technology delivery is difficult. Rather than setting up measures and target conditions, focus on the experience developers are having. Use these signals to focus capability improvement efforts.

More from Alex Herweyer

Working in industries spanning from government to software, Alex has driven transformational change working with people, process & technology.

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Problem Solving Skills for the Digital Age

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Let’s face it: Things don’t always go according to plan. Systems fail, wires get crossed, projects fall apart.

Problems are an inevitable part of life and work. They’re also an opportunity to think critically and find solutions. But knowing how to get to the root of unexpected situations or challenges can mean the difference between moving forward and spinning your wheels.

Here, we’ll break down the key elements of problem solving, some effective problem solving approaches, and a few effective tools to help you arrive at solutions more quickly.

So, what is problem solving?

Broadly defined, problem solving is the process of finding solutions to difficult or complex issues. But you already knew that. Understanding problem solving frameworks, however, requires a deeper dive.

Think about a recent problem you faced. Maybe it was an interpersonal issue. Or it could have been a major creative challenge you needed to solve for a client at work. How did you feel as you approached the issue? Stressed? Confused? Optimistic? Most importantly, which problem solving techniques did you use to tackle the situation head-on? How did you organize thoughts to arrive at the best possible solution?

The answers to these questions say a lot about your problem solving approach skills. But if you have trouble knowing the best way to approach a problem, you’re not alone. A report issued by the National Center for Education Statistics has found that American workers rank “dead last” out of 18 industrial nations when it comes to problem solving skills using technology.

Solve your problem-solving problem

Here’s the good news: Good problem solving skills can be learned. By its nature, problem solving doesn’t adhere to a clear set of do’s and don’ts—it requires flexibility, communication, and adaptation. However, most problems you face, at work or in life, can be tackled using four basic steps.

First, you must define the problem . This step sounds obvious, but often, you can notice that something is amiss in a project or process without really knowing where the core problem lies. The most challenging part of the problem solving process is uncovering where the problem originated.

Second, you work to generate alternatives to address the problem directly. This should be a collaborative process to ensure you’re considering every angle of the issue.

Third, you evaluate and test potential solutions to your problem. This step helps you fully understand the complexity of the issue and arrive at the best possible solution.

Finally, fourth, you select and implement the solution that best addresses the problem.

Following this basic four-step process will help you approach every problem you encounter with the same rigorous critical and strategic thinking process, recognize commonalities in new problems, and avoid repeating past mistakes.

In addition to these basic problem solving skills, there are several best practices that you should incorporate. These problem solving approaches can help you think more critically and creatively about any problem:

You may not feel like you have the right expertise to resolve a specific problem. Don’t let that stop you from tackling it. The best problem solvers become students of the problem at hand. Even if you don’t have particular expertise on a topic, your unique experience and perspective can lend itself to creative solutions.

Challenge the status quo

Standard problem solving methodologies and problem solving frameworks are a good starting point. But don’t be afraid to challenge assumptions and push boundaries. Good problem solvers find ways to apply existing best practices into innovative problem solving approaches.

Think broadly about and visualize the issue

Sometimes it’s hard to see a problem, even if it’s right in front of you. Clear answers could be buried in rows of spreadsheet data or lost in miscommunication. Use visualization as a problem solving tool to break down problems to their core elements. Visuals can help you see bottlenecks in the context of the whole process and more clearly organize your thoughts as you define the problem.

Hypothesize, test, and try again

It might be cliche, but there’s truth in the old adage that 99% of inspiration is perspiration. The best problem solvers ask why, test, fail, and ask why again. Whether it takes one or 1,000 iterations to solve a problem, the important part—and the part that everyone remembers—is the solution.

Consider other viewpoints

Today’s problems are more complex, more difficult to solve, and they often involve multiple disciplines. They require group expertise and knowledge. Being open to others’ expertise increases your ability to be a great problem solver. Great solutions come from integrating your ideas with those of others to find a better solution. Excellent problem solvers build networks and know how to collaborate with other people and teams. They are skilled in bringing people together and sharing knowledge and information.

4 effective problem solving tools

As you work through the problem solving steps, try these tools to better define the issue and find the appropriate solution.

Root cause analysis

Less structured than other more traditional problem solving methods, the 5 Whys is simply what it sounds like: asking why over and over to get to the root of an obstacle or setback. This technique encourages an open dialogue that can trigger new ideas about a problem, whether done individually or with a group. Each why piggybacks off the answer to the previous why. Get started with the template below—both flowcharts and fishbone diagrams can also help you track your answers to the 5 Whys.

Brainstorming

A meeting of the minds, a brain dump, a mind meld, a jam session. Whatever you call it, collaborative brainstorming can help surface previously unseen issues, root causes, and alternative solutions. Create and share a mind map with your team members to fuel your brainstorming session.

Gap analysis

Sometimes you don’t know where the problem is until you determine where it isn’t. Gap filling helps you analyze inadequacies that are preventing you from reaching an optimized state or end goal. For example, a content gap analysis can help a content marketer determine where holes exist in messaging or the customer experience. Gap analysis is especially helpful when it comes to problem solving because it requires you to find workable solutions. A SWOT analysis chart that looks at a problem through the lens of strengths, opportunities, opportunities, and threats can be a helpful problem solving framework as you start your analysis.

A better way to problem solve

Beyond these practical tips and tools, there are myriad methodical and creative approaches to move a project forward or resolve a conflict. The right approach will depend on the scope of the issue and your desired outcome.

Depending on the problem, Lucidchart offers several templates and diagrams that could help you identify the cause of the issue and map out a plan to resolve it. Learn more about how Lucidchart can help you take control of your problem solving process .

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How You Can Use Creative Problem Solving at Work

Solve issues faster with the root cause analysis process

7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage (1990) suggesting that while collecting data for what would later be his book The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground. Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

2. Solving the Tower of Hanoi problem tends to utilize a ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm: problem-solving strategy characterized by a specific set of instructions

anchoring bias: faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic: faulty heuristic in which you make a decision based on information readily available to you

confirmation bias: faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness: inability to see an object as useful for any other use other than the one for which it was intended

heuristic: mental shortcut that saves time when solving a problem

hindsight bias: belief that the event just experienced was predictable, even though it really wasn’t

mental set: continually using an old solution to a problem without results

problem-solving strategy: method for solving problems

representative bias: faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error: problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards: heuristic in which you begin to solve a problem by focusing on the end result

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Is there a public key encryption scheme that is based on an NP-hard problem, where breaking the encryption is equivalent to solving the problem and vice versa?

I know that RSA does not satisfy this requirement because efficiently solving factorization means breaking RSA, but breaking RSA does not mean having an efficient way to factor a large number. These two problems are not the same.

Some sources say that creating a public key encryption scheme that satisfies this requirement is equivalent to building a one-way function. However, we cannot prove that this one-way function actually exists.

Some say that the question of its existence is equivalent to the P=NP question.

This is a great question. You're basically asking about basing cryptography on NP-hardness.

First off, even within cryptography, there is a hierarchy of primitives, with OWF/PRF/PRG/symmetric key encryption at the bottom, then key exchange/PKE somewhere in the middle, then some more advanced stuff at the top like IBE/FHE/FE/etc. We have proven some black-box separations between them, so we know it is a strict-ish hierarchy.

I don't know where you are getting your "some sources". Ask an academic and they'll give you two answers: one which is things that we know how to prove, and one which is things we believe but don't yet know how to prove.

Theorem (trivial): Breaking factoring automatically breaks RSA.

Belief: Breaking RSA might not break factoring, but they are closely related enough that one would believe this is morally close.

Theorem (trivial): Existence of a PKE implies the existence of a OWF.

Theorem (difficult, from the famous work of Impagliazzo-Rudich89): Existence of a OWF does not automatically imply the existence of a PKE, in the sense that there is a black-box separation between OWF and CPA-secure PKE

Belief: OWF and PKE both exist.

Theorem (trivial): Existence of a OWF implies that P is not NP.

Gap: Even if P is not NP, OWF might not exist. Read about Impagliazzo's worlds: https://blog.computationalcomplexity.org/2004/06/impagliazzos-five-worlds.html

Gap: Even if P is not NP and OWF exists, PKE might not exist.

Finally, to answer your original question:

Belief: It is difficult to base cryptography on NP-hardness. We've tried, especially in the realm of lattice-based ones which have the closest hope of actually being NP-hard. There are signature schemes that rely on knapsack-like problems, but in special cases.

Now on to some controversial things.

Belief: P is not NP, but there are things in NP that are not NP-complete (aka not NP-hard).

Belief: Factoring and RSA are quite possibly in NP but are not NP-hard.

Thank you for providing such a clear answer. I mentioned earlier that I have been referring to some sources, most of which are from the book "Introduction to Modern Cryptography". However, it's possible that I may have overlooked some details while reading through the text.

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