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Overview of the Problem-Solving Mental Process

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

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

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

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Article • 7 min read

What Is Problem Solving?

By the Mind Tools Content Team

We all spend a lot of our time solving problems, both at work and in our personal lives.

Some problems are small, and we can quickly sort them out ourselves. But others are complex challenges that take collaboration, creativity, and a considerable amount of effort to solve.

At work, the types of problems we face depend largely on the organizations we're in and the jobs we do. A manager in a cleaning company, for example, might spend their day untangling staffing issues, resolving client complaints, and sorting out problems with equipment and supplies. An aircraft designer, on the other hand, might be grappling with a problem about aerodynamics, or trying to work out why a new safety feature isn't working. Meanwhile, a politician might be exploring solutions to racial injustice or climate change.

But whatever issues we face, there are some common ways to tackle them effectively. And we can all boost our confidence and ability to succeed by building a strong set of problem-solving skills.

Mind Tools offers a large collection of resources to help you do just that!

How Well Do You Solve Problems?

Start by taking an honest look at your existing skills. What's your current approach to solving problems, and how well is it working? Our quiz, How Good Is Your Problem Solving? lets you analyze your abilities, and signposts ways to address any areas of weakness.

Define Every Problem

The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem – not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work. However, if you look a bit deeper, the real issue might be a general lack of training, or an unreasonable workload across the team.

Tools like 5 Whys , Appreciation and Root Cause Analysis get you asking the right questions, and help you to work through the layers of a problem to uncover what's really going on.

However, defining a problem doesn't mean deciding how to solve it straightaway. It's important to look at the issue from a variety of perspectives. If you commit yourself too early, you can end up with a short-sighted solution. The CATWOE checklist provides a powerful reminder to look at many elements that may contribute to the problem, keeping you open to a variety of possible solutions.

Understanding Complexity

As you define your problem, you'll often discover just how complicated it is. There are likely several interrelated issues involved. That's why it's important to have ways to visualize, simplify and make sense of this tangled mess!

Affinity Diagrams are great for organizing many different pieces of information into common themes, and for understanding the relationships between them.

Another popular tool is the Cause-and-Effect Diagram . To generate viable solutions, you need a solid understanding of what's causing the problem.

When your problem occurs within a business process, creating a Flow Chart , Swim Lane Diagram or a Systems Diagram will help you to see how various activities and inputs fit together. This may well highlight a missing element or bottleneck that's causing your problem.

Quite often, what seems to be a single problem turns out to be a whole series of problems. The Drill Down technique prompts you to split your problem into smaller, more manageable parts.

General Problem-Solving Tools

When you understand the problem in front of you, you’re ready to start solving it. With your definition to guide you, you can generate several possible solutions, choose the best one, then put it into action. That's the four-step approach at the heart of good problem solving.

There are various problem-solving styles to use. For example:

• Constructive Controversy is a way of widening perspectives and energizing discussions.
• Inductive Reasoning makes the most of people’s experiences and know-how, and can speed up solution finding.
• Means-End Analysis can bring extra clarity to your thinking, and kick-start the process of implementing solutions.

Specific Problem-Solving Systems

Some particularly complicated or important problems call for a more comprehensive process. Again, Mind Tools has a range of approaches to try, including:

• Simplex , which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your organization.
• Appreciative Inquiry , which is a uniquely positive way of solving problems by examining what's working well in the areas surrounding them.
• Soft Systems Methodology , which takes you through four stages to uncover more details about what's creating your problem, and then define actions that will improve the situation.

Further Problem-Solving Strategies

Good problem solving requires a number of other skills – all of which are covered by Mind Tools.

For example, we have a large section of resources to improve your Creativity , so that you come up with a range of possible solutions.

By strengthening your Decision Making , you'll be better at evaluating the options, selecting the best ones, then choosing how to implement them.

And our Project Management collection has valuable advice for strengthening the whole problem-solving process. The resources there will help you to make effective changes – and then keep them working long term.

Problems are an inescapable part of life, both in and out of work. So we can all benefit from having strong problem-solving skills.

It's important to understand your current approach to problem solving, and to know where and how to improve.

Define every problem you encounter – and understand its complexity, rather than trying to solve it too soon.

There's a range of general problem-solving approaches, helping you to generate possible answers, choose the best ones, and then implement your solution.

Some complicated or serious problems require more specific problem-solving systems, especially when they relate to business processes.

By boosting your creativity, decision-making and project-management skills, you’ll become even better at solving all the problems you face.

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What is Problem Solving? A Complete Guide

Explore the essence of What is Problem Solving as we dissect this fundamental concept. From defining the very nature of problem-solving to understanding the intricate process it entails, this blog covers it all. Uncover the key skills essential for effective problem-solving and strategies to enhance your abilities in this critical skill.

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According to Statista , more than 50 per cent of IT Managers preferred candidates with effective Problem Solving skills. In this blog, you will learn what is Problem Solving, its process, key skills and strategies, along with tools and techniques to do so. 

Table of contents  

1) What is Problem Solving definition?  

2) The process of Problem Solving  

3) Key skills for effective Problem Solving  

4) Strategies for enhancing Problem Solving abilities  

5) Problem Solving tools and techniques  

6) Conclusion       

What is Problem Solving definition?  

The process of Problem Solving  

Understanding the problem   

The first step in Problem Solving is gaining a clear understanding of the issue at hand. Take the time to thoroughly analyse the problem and gather relevant information. Ask yourself questions like:  

1) What is the nature of the problem?  

2) What are the factors contributing to the problem?  

3) What are the desired outcomes?  

4) Are there any constraints or limitations to consider?  

By gaining a comprehensive understanding of the problem, you lay a solid foundation for finding an effective solution.  

Generating possible solutions   

Once you have a clear grasp of the problem, it's time to brainstorm potential solutions. Encourage creativity and think outside the box. Consider all possible options without judgment or criticism. The goal at this stage is to generate a variety of ideas and alternatives.  

Evaluating and selecting the best solution   

After generating a list of possible solutions, it's important to evaluate each option based on its feasibility, effectiveness, and alignment with the desired outcome. Consider the advantages and disadvantages of each and every solution. Assess its practicality and the resources required for implementation.  

Additionally, take into account the potential risks and benefits associated with each solution. Consider any potential consequences or impacts on other aspects. Based on this evaluation, select the solution that appears most viable and promising.  

Implementing the solution   

Once you have chosen the best solution, it's time to put it into action. Develop a detailed plan outlining the necessary steps and allocate the required resources. Determine responsibilities and deadlines to ensure a smooth implementation process.  

During implementation, monitor progress and make any necessary adjustments or adaptations. Stay proactive and address any challenges or obstacles that may arise along the way. Effective communication and collaboration with others involved in the process can greatly contribute to successful implementation.  

Assessing the results   

After implementing the solution, it's essential to assess the results. Evaluate whether the problem has been properly resolved or if further adjustments are required. Analyse the outcomes and compare them against the desired goals and expectations.  

Consider whether the chosen solution has brought about the intended benefits and if any unexpected consequences have emerged. Reflect on the overall effectiveness of the Problem Solving process and identify any lessons learned for future reference.  

Remember, Problem Solving is an iterative process, and it's not uncommon to revisit and refine solutions based on ongoing evaluation and feedback. Embrace a continuous improvement mindset and be open to seeking alternative approaches if necessary.  

By following this Problem Solving process, you can approach challenges systematically and increase your chances of finding effective solutions. Remember that practice and experience play a vital role in honing your skills. 

Master the art of solving problems and become a catalyst for innovation and success with our Problem Solving Training – Sign up now!  

Key skills for effective Problem Solving   

In order to become an effective problem solver, it is crucial to develop a set of key skills that enhance your Problem Solving abilities. These skills enable you to approach challenges with a strategic mindset and find innovative solutions. Let's look at some of these skills:  

Critical thinking   

Critical thinking involves analysing information objectively, considering different perspectives, and making logical judgments. It helps in evaluating problems accurately and identifying appropriate solutions.  

Creativity   

Creativity enables the generation of innovative and unconventional solutions. It involves thinking outside the box, exploring new possibilities, and approaching problems from different angles.  

Analytical skills   

Analytical skills are crucial for breaking down complex problems into smaller, more manageable parts. This ability aids in identifying patterns, relationships, and underlying causes. 

Decision-making   

Sound decision-making skills involve evaluating the pros and cons of each solution and selecting the best course of action. It requires considering the potential risks and benefits of different options.  

By honing these key skills, individuals can become more effective Problem Solvers and tackle challenges with confidence. 

Strategies for enhancing Problem Solving abilities  

Practice critical thinking   

Engage in activities that promote critical thinking, such as solving puzzles, engaging in thought-provoking discussions, and challenging assumptions. This helps sharpen your analytical skills and enhances your ability to think critically when faced with problems.  

Seek feedback and learn from experience   

Seek feedback from mentors, peers, or experts when solving problems. Reflect on past experiences to identify areas for improvement and learn from your successes and failures. Embrace every Problem Solving opportunity as a chance to grow and develop your skills.  

Embrace challenges   

Instead of avoiding challenges, embrace them as opportunities for growth. Approach difficult problems with a positive mindset, viewing them as chances to develop new strategies and expand your expertise in dealing with problems. Embracing challenges fosters resilience and strengthens your Problem Solving abilities.  

Collaborate with others   

Collaboration can enhance Problem Solving outcomes by bringing diverse perspectives and ideas to the table. Engage in group activities to discuss issues, seek input from others, and actively listen to different viewpoints. Collaborating with others broadens your knowledge of dealing with problems and promotes innovative thinking.  

Continuously learn and update knowledge   

Stay updated with the latest information and developments in areas relevant to your tasks. Read books, attend workshops or seminars, and leverage online resources to expand your knowledge base. Continuously learning equips you with a wider range of Problem Solving strategies and enhances your abilities.  

Think outside the box   

Encourage creative thinking by exploring unconventional ideas and solutions. Challenge assumptions and consider alternative approaches. This mindset shift can lead to innovative Problem Solving strategies and help you discover unique solutions to complex problems.  

Implementing these strategies can significantly enhance your Problem Solving abilities. Remember, practice, feedback, collaboration, continuous learning, and creativity are key to becoming a proficient problem solver. 

Problem Solving tools and techniques  

When faced with complex problems, utilising specific tools and techniques can help facilitate the solving process and lead to more effective solutions. Here are some commonly used Problem Solving tools and techniques:  

Root cause analysis   

Root cause analysis is a methodology used to detect the underlying causes of a problem. It involves investigating the problem's symptoms and tracing them back to their fundamental causes. By addressing the root causes, Problem Solvers can prevent the issue from recurring.  

Strengths, Weaknesses, Opportunities, Threats (SWOT) analysis   

SWOT analysis is a planning tool that strategically helps measure the weaknesses and internal strengths of a situation. Moreover, it can find external opportunities and threats. By assessing these factors, Problem Solvers can gain insights into the current state and make informed decisions about potential solutions.  

Fishbone diagrams   

Fishbone diagrams, also known as cause-and-effect diagrams or Ishikawa diagrams, visually represent the possible causes contributing to a problem. By organising causes into categories (such as people, process, equipment, and environment), Problem Solvers can systematically analyse the problem's potential sources.  

Decision matrices   

Decision matrices are used to evaluate and compare different options based on multiple criteria. This tool helps Problem Solvers weigh the importance of various factors and objectively assess each alternative, leading to an informed decision.  

Six Thinking Hats   

Six Thinking Hats is a technique initially developed by Edward de Bono that encourages parallel thinking by exploring different perspectives. Each "hat" represents a different thinking approach (e.g., logical, creative, emotional), allowing Problem Solvers to consider diverse viewpoints and generate innovative solutions.  

These are just a few examples of Problem Solving tools and techniques. Depending on the nature of the problem, other methods, such as brainstorming, mind mapping, flowcharts, or Pareto analysis, can also be applied. Choosing the appropriate tool or technique depends on the specific problem and the desired outcome. 

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Conclusion  

We hope you read and understand everything about What is Problem Solving. Developing effective skills is crucial for overcoming challenges, making informed decisions, and achieving success. By embracing problems as opportunities and applying strategic approaches, individuals can become proficient Problem Solvers in various domains of life. 

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48 Problem Solving

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

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

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

Definition of Problem Solving

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

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

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

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

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

Definition of Problem

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

Types of Problems

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

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

Cognitive Processes in Problem Solving

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

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

Knowledge for Problem Solving

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

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

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

Historical Approaches to Problem Solving

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

Early Conceptions

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

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

Associationism

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

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

Gestalt Psychology

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

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

Information Processing

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

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

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

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

Classic Issues in Problem Solving

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

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

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

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

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

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

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

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

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

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

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

Current and Future Issues in Problem Solving

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

Decision Making

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

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

Intelligence and Creativity

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

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

Teaching of Thinking Skills

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

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

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

Expert Problem Solving

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

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

Analogical Reasoning

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

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

Mathematical and Scientific Problem Solving

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

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

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

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

Everyday Thinking

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

Cognitive Neuroscience of Problem Solving

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

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

Future Directions

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

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Further Reading

Baron, J. ( 2008 ). Thinking and deciding (4th ed). New York: Cambridge University Press.

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Holyoak, K. J. , & Morrison, R. G. ( 2005 ). The Cambridge handbook of thinking and reasoning . New York: Cambridge University Press.

Mayer, R. E. , & Wittrock, M. C. ( 2006 ). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 287–304). Mahwah, NJ: Erlbaum.

Sternberg, R. J. , & Ben-Zeev, T. ( 2001 ). Complex cognition: The psychology of human thought . New York: Oxford University Press.

Weisberg, R. W. ( 2006 ). Creativity . New York: Wiley.

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Problem Solving Skills for the Digital Age

Lucid Content

Reading time: about 6 min

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?

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

Similar to pulling weeds from your garden, if you don’t get to the root of the problem, it’s bound to come back. A root cause analysis helps you figure out the root cause behind any disruption or problem, so you can take steps to correct the problem from recurring. The root cause analysis process involves defining the problem, collecting data, and identifying causal factors to pinpoint root causes and arrive at a solution.

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 .

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

Related articles

Sometimes you're faced with challenges that traditional problem solving can't fix. Creative problem solving encourages you to find new, creative ways of thinking that can help you overcome the issue at hand more quickly.

Root cause analysis refers to any problem-solving method used to trace an issue back to its origin. Learn how to complete a root cause analysis—we've even included templates to get you started.

Bring your bright ideas to life.

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Problem Solving

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Faculty of Economics and Behavioral Sciences, Department of Education, University of Freiburg, 79085, Freiburg, Germany

Norbert M. Seel

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Jonassen, D.H., Hung, W. (2012). Problem Solving. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_208

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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.

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Table of Contents

The problem-solving process, how to solve problems: 5 steps, train to solve problems with lean today, what is problem solving steps, techniques, & best practices explained.

Problem solving is the art of identifying problems and implementing the best possible solutions. Revisiting your problem-solving skills may be the missing piece to leveraging the performance of your business, achieving Lean success, or unlocking your professional potential. 

Ask any colleague if they’re an effective problem-solver and their likely answer will be, “Of course! I solve problems every day.” 

Problem solving is part of most job descriptions, sure. But not everyone can do it consistently. 

Problem solving is the process of defining a problem, identifying its root cause, prioritizing and selecting potential solutions, and implementing the chosen solution.

There’s no one-size-fits-all problem-solving process. Often, it’s a unique methodology that aligns your short- and long-term objectives with the resources at your disposal. Nonetheless, many paradigms center problem solving as a pathway for achieving one’s goals faster and smarter. 

One example is the Six Sigma framework , which emphasizes eliminating errors and refining the customer experience, thereby improving business outcomes. Developed originally by Motorola, the Six Sigma process identifies problems from the perspective of customer satisfaction and improving product delivery. 

Lean management, a similar method, is about streamlining company processes over time so they become “leaner” while producing better outcomes. 

Trendy business management lingo aside, both of these frameworks teach us that investing in your problem solving process for personal and professional arenas will bring better productivity.

1. Precisely Identify Problems

As obvious as it seems, identifying the problem is the first step in the problem-solving process. Pinpointing a problem at the beginning of the process will guide your research, collaboration, and solutions in the right direction. 

At this stage, your task is to identify the scope and substance of the problem. Ask yourself a series of questions: 

• What’s the problem? 
• How many subsets of issues are underneath this problem? 
• What subject areas, departments of work, or functions of business can best define this problem? 

Although some problems are naturally large in scope, precision is key. Write out the problems as statements in planning sheets . Should information or feedback during a later step alter the scope of your problem, revise the statements. 

Framing the problem at this stage will help you stay focused if distractions come up in later stages. Furthermore, how you frame a problem will aid your search for a solution. A strategy of building Lean success, for instance, will emphasize identifying and improving upon inefficient systems. 

2. Collect Information and Plan 

The second step is to collect information and plan the brainstorming process. This is another foundational step to road mapping your problem-solving process. Data, after all, is useful in identifying the scope and substance of your problems. 

Collecting information on the exact details of the problem, however, is done to narrow the brainstorming portion to help you evaluate the outcomes later. Don’t overwhelm yourself with unnecessary information — use the problem statements that you identified in step one as a north star in your research process. 

This stage should also include some planning. Ask yourself:

• What parties will ultimately decide a solution? 
• Whose voices and ideas should be heard in the brainstorming process? 
• What resources are at your disposal for implementing a solution? 

Establish a plan and timeline for steps 3-5. 

3. Brainstorm Solutions

Brainstorming solutions is the bread and butter of the problem-solving process. At this stage, focus on generating creative ideas. As long as the solution directly addresses the problem statements and achieves your goals, don’t immediately rule it out. 

Moreover, solutions are rarely a one-step answer and are more like a roadmap with a set of actions. As you brainstorm ideas, map out these solutions visually and include any relevant factors such as costs involved, action steps, and involved parties. 

With Lean success in mind, stay focused on solutions that minimize waste and improve the flow of business ecosystems. 

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4. Decide and Implement

The most critical stage is selecting a solution. Easier said than done. Consider the criteria that has arisen in previous steps as you decide on a solution that meets your needs. 

Once you select a course of action, implement it. 

Practicing due diligence in earlier stages of the process will ensure that your chosen course of action has been evaluated from all angles. Often, efficient implementation requires us to act correctly and successfully the first time, rather than being hurried and sloppy. Further compilations will create more problems, bringing you back to step 1. 

5. Evaluate

Exercise humility and evaluate your solution honestly. Did you achieve the results you hoped for? What would you do differently next time? 

As some experts note, formulating feedback channels into your evaluation helps solidify future success. A framework like Lean success, for example, will use certain key performance indicators (KPIs) like quality, delivery success, reducing errors, and more. Establish metrics aligned with company goals to assess your solutions.

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What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

• Identify the issue : Recognize the problem that needs to be solved.
• Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
• Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
• Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
• Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
• Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
• Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

• Brainstorming with others
• Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
• Analyzing cause and effect
• Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

• Creating a list of potential ideas to solve the problem
• Grouping and categorizing similar solutions
• Prioritizing potential solutions based on feasibility, cost, and resources required
• Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

• SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
• Decision-making matrices
• Pros and cons lists
• Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

• Communicating the solution to relevant parties
• Setting timelines and milestones
• Assigning tasks and responsibilities
• Monitoring the solution and making adjustments as necessary
• Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

• Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
• Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
• SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
• Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

• Generate a diverse range of solutions
• Encourage all team members to participate
• Foster creative thinking

When brainstorming, remember to:

• Reserve judgment until the session is over
• Encourage wild ideas
• Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

• 5 Whys : Ask “why” five times to get to the underlying cause.
• Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
• Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

• List your problem’s strengths, such as relevant resources or strong partnerships.
• Identify its weaknesses, such as knowledge gaps or limited resources.
• Explore opportunities, like trends or new technologies, that could help solve the problem.
• Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

• Write the problem in the center of a blank page.
• Draw branches from the central problem to related sub-problems or contributing factors.
• Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

• Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
• Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
• Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

• Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
• Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
• Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

• Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
• Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
• Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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What Is Problem Solving? How Software Engineers Approach Complex Challenges

From debugging an existing system to designing an entirely new software application, a day in the life of a software engineer is filled with various challenges and complexities. The one skill that glues these disparate tasks together and makes them manageable? Problem solving . 

Throughout this blog post, we’ll explore why problem-solving skills are so critical for software engineers, delve into the techniques they use to address complex challenges, and discuss how hiring managers can identify these skills during the hiring process. 

What Is Problem Solving?

But what exactly is problem solving in the context of software engineering? How does it work, and why is it so important?

Problem solving, in the simplest terms, is the process of identifying a problem, analyzing it, and finding the most effective solution to overcome it. For software engineers, this process is deeply embedded in their daily workflow. It could be something as simple as figuring out why a piece of code isn’t working as expected, or something as complex as designing the architecture for a new software system. 

In a world where technology is evolving at a blistering pace, the complexity and volume of problems that software engineers face are also growing. As such, the ability to tackle these issues head-on and find innovative solutions is not only a handy skill — it’s a necessity. 

The Importance of Problem-Solving Skills for Software Engineers

Problem-solving isn’t just another ability that software engineers pull out of their toolkits when they encounter a bug or a system failure. It’s a constant, ongoing process that’s intrinsic to every aspect of their work. Let’s break down why this skill is so critical.

Driving Development Forward

Without problem solving, software development would hit a standstill. Every new feature, every optimization, and every bug fix is a problem that needs solving. Whether it’s a performance issue that needs diagnosing or a user interface that needs improving, the capacity to tackle and solve these problems is what keeps the wheels of development turning.

It’s estimated that 60% of software development lifecycle costs are related to maintenance tasks, including debugging and problem solving. This highlights how pivotal this skill is to the everyday functioning and advancement of software systems.

Innovation and Optimization

The importance of problem solving isn’t confined to reactive scenarios; it also plays a major role in proactive, innovative initiatives . Software engineers often need to think outside the box to come up with creative solutions, whether it’s optimizing an algorithm to run faster or designing a new feature to meet customer needs. These are all forms of problem solving.

Consider the development of the modern smartphone. It wasn’t born out of a pre-existing issue but was a solution to a problem people didn’t realize they had — a device that combined communication, entertainment, and productivity into one handheld tool.

Increasing Efficiency and Productivity

Good problem-solving skills can save a lot of time and resources. Effective problem-solvers are adept at dissecting an issue to understand its root cause, thus reducing the time spent on trial and error. This efficiency means projects move faster, releases happen sooner, and businesses stay ahead of their competition.

Improving Software Quality

Problem solving also plays a significant role in enhancing the quality of the end product. By tackling the root causes of bugs and system failures, software engineers can deliver reliable, high-performing software. This is critical because, according to the Consortium for Information and Software Quality, poor quality software in the U.S. in 2022 cost at least $2.41 trillion in operational issues, wasted developer time, and other related problems.

Problem-Solving Techniques in Software Engineering

So how do software engineers go about tackling these complex challenges? Let’s explore some of the key problem-solving techniques, theories, and processes they commonly use.

Decomposition

Breaking down a problem into smaller, manageable parts is one of the first steps in the problem-solving process. It’s like dealing with a complicated puzzle. You don’t try to solve it all at once. Instead, you separate the pieces, group them based on similarities, and then start working on the smaller sets. This method allows software engineers to handle complex issues without being overwhelmed and makes it easier to identify where things might be going wrong.

Abstraction

In the realm of software engineering, abstraction means focusing on the necessary information only and ignoring irrelevant details. It is a way of simplifying complex systems to make them easier to understand and manage. For instance, a software engineer might ignore the details of how a database works to focus on the information it holds and how to retrieve or modify that information.

Algorithmic Thinking

At its core, software engineering is about creating algorithms — step-by-step procedures to solve a problem or accomplish a goal. Algorithmic thinking involves conceiving and expressing these procedures clearly and accurately and viewing every problem through an algorithmic lens. A well-designed algorithm not only solves the problem at hand but also does so efficiently, saving computational resources.

Parallel Thinking

Parallel thinking is a structured process where team members think in the same direction at the same time, allowing for more organized discussion and collaboration. It’s an approach popularized by Edward de Bono with the “ Six Thinking Hats ” technique, where each “hat” represents a different style of thinking.

In the context of software engineering, parallel thinking can be highly effective for problem solving. For instance, when dealing with a complex issue, the team can use the “White Hat” to focus solely on the data and facts about the problem, then the “Black Hat” to consider potential problems with a proposed solution, and so on. This structured approach can lead to more comprehensive analysis and more effective solutions, and it ensures that everyone’s perspectives are considered.

This is the process of identifying and fixing errors in code . Debugging involves carefully reviewing the code, reproducing and analyzing the error, and then making necessary modifications to rectify the problem. It’s a key part of maintaining and improving software quality.

Testing and Validation

Testing is an essential part of problem solving in software engineering. Engineers use a variety of tests to verify that their code works as expected and to uncover any potential issues. These range from unit tests that check individual components of the code to integration tests that ensure the pieces work well together. Validation, on the other hand, ensures that the solution not only works but also fulfills the intended requirements and objectives.

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Evaluating Problem-Solving Skills

We’ve examined the importance of problem-solving in the work of a software engineer and explored various techniques software engineers employ to approach complex challenges. Now, let’s delve into how hiring teams can identify and evaluate problem-solving skills during the hiring process.

Recognizing Problem-Solving Skills in Candidates

How can you tell if a candidate is a good problem solver? Look for these indicators:

• Previous Experience: A history of dealing with complex, challenging projects is often a good sign. Ask the candidate to discuss a difficult problem they faced in a previous role and how they solved it.
• Problem-Solving Questions: During interviews, pose hypothetical scenarios or present real problems your company has faced. Ask candidates to explain how they would tackle these issues. You’re not just looking for a correct solution but the thought process that led them there.
• Technical Tests: Coding challenges and other technical tests can provide insight into a candidate’s problem-solving abilities. Consider leveraging a platform for assessing these skills in a realistic, job-related context.

Assessing Problem-Solving Skills

Once you’ve identified potential problem solvers, here are a few ways you can assess their skills:

• Solution Effectiveness: Did the candidate solve the problem? How efficient and effective is their solution?
• Approach and Process: Go beyond whether or not they solved the problem and examine how they arrived at their solution. Did they break the problem down into manageable parts? Did they consider different perspectives and possibilities?
• Communication: A good problem solver can explain their thought process clearly. Can the candidate effectively communicate how they arrived at their solution and why they chose it?
• Adaptability: Problem-solving often involves a degree of trial and error. How does the candidate handle roadblocks? Do they adapt their approach based on new information or feedback?

Hiring managers play a crucial role in identifying and fostering problem-solving skills within their teams. By focusing on these abilities during the hiring process, companies can build teams that are more capable, innovative, and resilient.

Key Takeaways

As you can see, problem solving plays a pivotal role in software engineering. Far from being an occasional requirement, it is the lifeblood that drives development forward, catalyzes innovation, and delivers of quality software. 

By leveraging problem-solving techniques, software engineers employ a powerful suite of strategies to overcome complex challenges. But mastering these techniques isn’t simple feat. It requires a learning mindset, regular practice, collaboration, reflective thinking, resilience, and a commitment to staying updated with industry trends. 

For hiring managers and team leads, recognizing these skills and fostering a culture that values and nurtures problem solving is key. It’s this emphasis on problem solving that can differentiate an average team from a high-performing one and an ordinary product from an industry-leading one.

At the end of the day, software engineering is fundamentally about solving problems — problems that matter to businesses, to users, and to the wider society. And it’s the proficient problem solvers who stand at the forefront of this dynamic field, turning challenges into opportunities, and ideas into reality.

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What Is Problem Solving?

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches,…

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches, so why do people need to organize these drives? It’s evident that despite advertising and posting anti-littering messages, some of us don’t follow the rules.

Temporary food stalls and shops make it even more difficult to keep the beaches clean. Since people can’t ask the shopkeepers to relocate or prevent every single person from littering, the clean-up drive is needed.  This is an ideal example of problem-solving psychology in humans. ( 230-fifth.com ) So, what is problem-solving? Let’s find out.

What Is Problem-Solving?

At its simplest, the meaning of problem-solving is the process of defining a problem, determining its cause, and implementing a solution. The definition of problem-solving is rooted in the fact that as humans, we exert control over our environment through solutions. We move forward in life when we solve problems and make decisions. 

We can better define the problem-solving process through a series of important steps.

Identify The Problem: 

This step isn’t as simple as it sounds. Most times, we mistakenly identify the consequences of a problem rather than the problem itself. It’s important that we’re careful to identify the actual problem and not just its symptoms. 

Define The Problem: 

Once the problem has been identified correctly, you should define it. This step can help clarify what needs to be addressed and for what purpose.

Form A Strategy: 

Develop a strategy to solve your problem. Defining an approach will provide direction and clarity on the next steps. 

Organize The Information:  

Organizing information systematically will help you determine whether something is missing. The more information you have, the easier it’ll become for you to arrive at a solution.  

Allocate Resources:  

We may not always be armed with the necessary resources to solve a problem. Before you commit to implementing a solution for a problem, you should determine the availability of different resources—money, time and other costs.

Track Progress: 

The true meaning of problem-solving is to work towards an objective. If you measure your progress, you can evaluate whether you’re on track. You could revise your strategies if you don’t notice the desired level of progress. 

Evaluate The Results:  

After you spot a solution, evaluate the results to determine whether it’s the best possible solution. For example, you can evaluate the success of a fitness routine after several weeks of exercise.

Meaning Of Problem-Solving Skill

Now that we’ve established the definition of problem-solving psychology in humans, let’s look at how we utilize our problem-solving skills.  These skills help you determine the source of a problem and how to effectively determine the solution. Problem-solving skills aren’t innate and can be mastered over time. Here are some important skills that are beneficial for finding solutions.

Communication

Communication is a critical skill when you have to work in teams.  If you and your colleagues have to work on a project together, you’ll have to collaborate with each other. In case of differences of opinion, you should be able to listen attentively and respond respectfully in order to successfully arrive at a solution.

As a problem-solver, you need to be able to research and identify underlying causes. You should never treat a problem lightly. In-depth study is imperative because often people identify only the symptoms and not the actual problem.

Once you have researched and identified the factors causing a problem, start working towards developing solutions. Your analytical skills can help you differentiate between effective and ineffective solutions.

Decision-Making

You’ll have to make a decision after you’ve identified the source and methods of solving a problem. If you’ve done your research and applied your analytical skills effectively, it’ll become easier for you to take a call or a decision.

Organizations really value decisive problem-solvers. Harappa Education’s   Defining Problems course will guide you on the path to developing a problem-solving mindset. Learn how to identify the different types of problems using the Types of Problems framework. Additionally, the SMART framework, which is a five-point tool, will teach you to create specific and actionable objectives to address problem statements and arrive at solutions. 

Explore topics & skills such as Problem Solving Skills , PICK Chart , How to Solve Problems & Barriers to Problem Solving from our Harappa Diaries blog section and develop your skills.

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7 Thinking, Language, and Problem Solving

What is the best way to solve a problem? How does a person who has never seen or touched snow in real life develop an understanding of the concept of snow? How do young children acquire the ability to learn language with no formal instruction? Psychologists who study thinking explore questions like these and are called cognitive psychologists.

In other chapters, we discussed the cognitive processes of perception, learning, and memory. In this chapter, we will focus on high-level cognitive processes. As a part of this discussion, we will consider thinking and briefly explore the development and use of language. We will also discuss problem solving and creativity. After finishing this chapter, you will have a greater appreciation of the higher-level cognitive processes that contribute to our distinctiveness as a species.

Table of Contents

7.1 What is Cognition? 7.2 Language 7.3 Problem Solving

7.1 What is Cognition?

Learning Objectives

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

• Describe cognition
• Distinguish concepts and prototypes
• Explain the difference between natural and artificial concepts
• Describe how schemata are organized and constructed

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition . Simply put,  cognition  is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

Upon waking each morning, you begin thinking—contemplating the tasks that you must complete that day. In what order should you run your errands? Should you go to the bank, the cleaners, or the grocery store first? Can you get these things done before you head to class or will they need to wait until school is done? These thoughts are one example of cognition at work. Exceptionally complex, cognition is an essential feature of human consciousness, yet not all aspects of cognition are consciously experienced.

Cognitive psychology  is the field of psychology dedicated to examining how people think. It attempts to explain how and why we think the way we do by studying the interactions among human thinking, emotion, creativity, language, and problem solving, in addition to other cognitive processes. Cognitive psychologists strive to determine and measure different types of intelligence, why some people are better at problem solving than others, and how emotional intelligence affects success in the workplace, among countless other topics. They also sometimes focus on how we organize thoughts and information gathered from our environments into meaningful categories of thought, which will be discussed later.

Concepts and Prototypes

The human nervous system is capable of handling endless streams of information. The senses serve as the interface between the mind and the external environment, receiving stimuli and translating it into nervous impulses that are transmitted to the brain. The brain then processes this information and uses the relevant pieces to create thoughts, which can then be expressed through language or stored in memory for future use. To make this process more complex, the brain does not gather information from external environments only. When thoughts are formed, the mind synthesizes information from emotions and memories ( Figure 7.2 ). Emotion and memory are powerful influences on both our thoughts and behaviors.

Concepts are informed by our semantic memory (you will learn more about semantic memory in a later chapter) and are present in every aspect of our lives; however, one of the easiest places to notice concepts is inside a classroom, where they are discussed explicitly. When you study United States history, for example, you learn about more than just individual events that have happened in America’s past. You absorb a large quantity of information by listening to and participating in discussions, examining maps, and reading first-hand accounts of people’s lives. Your brain analyzes these details and develops an overall understanding of American history. In the process, your brain gathers details that inform and refine your understanding of related concepts like democracy, power, and freedom.

Concepts can be complex and abstract, like justice, or more concrete, like types of birds. Some concepts, like tolerance, are agreed upon by many people, because they have been used in various ways over many years. Other concepts, like the characteristics of your ideal friend or your family’s birthday traditions, are personal and individualized. In this way, concepts touch every aspect of our lives, from our many daily routines to the guiding principles behind the way governments function.

Another technique used by your brain to organize information is the identification of prototypes for the concepts you have developed. A  prototype  is the best example or representation of a concept. For example, what comes to your mind when you think of a dog? Most likely your early experiences with dogs will shape what you imagine. If your first pet was a Golden Retriever, there is a good chance that this would be your prototype for the category of dogs.

Natural and Artificial Concepts

In psychology, concepts can be divided into two categories, natural and artificial. Natural concepts  are created “naturally” through your experiences and can be developed from either direct or indirect experiences. For example, if you live in Essex Junction, Vermont, you have probably had a lot of direct experience with snow. You’ve watched it fall from the sky, you’ve seen lightly falling snow that barely covers the windshield of your car, and you’ve shoveled out 18 inches of fluffy white snow as you’ve thought, “This is perfect for skiing.” You’ve thrown snowballs at your best friend and gone sledding down the steepest hill in town. In short, you know snow. You know what it looks like, smells like, tastes like, and feels like. If, however, you’ve lived your whole life on the island of Saint Vincent in the Caribbean, you may never have actually seen snow, much less tasted, smelled, or touched it. You know snow from the indirect experience of seeing pictures of falling snow—or from watching films that feature snow as part of the setting. Either way, snow is a natural concept because you can construct an understanding of it through direct observations, experiences with snow, or indirect knowledge (such as from films or books) ( Figure 7.3 ).

An  artificial concept , on the other hand, is a concept that is defined by a specific set of characteristics. Various properties of geometric shapes, like squares and triangles, serve as useful examples of artificial concepts. A triangle always has three angles and three sides. A square always has four equal sides and four right angles. Mathematical formulas, like the equation for area (length × width) are artificial concepts defined by specific sets of characteristics that are always the same. Artificial concepts can enhance the understanding of a topic by building on one another. For example, before learning the concept of “area of a square” (and the formula to find it), you must understand what a square is. Once the concept of “area of a square” is understood, an understanding of area for other geometric shapes can be built upon the original understanding of area. The use of artificial concepts to define an idea is crucial to communicating with others and engaging in complex thought. According to Goldstone and Kersten (2003), concepts act as building blocks and can be connected in countless combinations to create complex thoughts.

A  schema (plural: schemata)  is a mental construct consisting of a cluster or collection of related concepts (Bartlett, 1932). There are many different types of schemata, and they all have one thing in common: schemata are a method of organizing information that allows the brain to work more efficiently. When a schema is activated, the brain makes immediate assumptions about the person or object being observed.

There are several types of schemata. A  role schema  makes assumptions about how individuals in certain roles will behave (Callero, 1994). For example, imagine you meet someone who introduces himself as a firefighter. When this happens, your brain automatically activates the “firefighter schema” and begins making assumptions that this person is brave, selfless, and community-oriented. Despite not knowing this person, already you have unknowingly made judgments about him. Schemata also help you fill in gaps in the information you receive from the world around you. While schemata allow for more efficient information processing, there can be problems with schemata, regardless of whether they are accurate: Perhaps this particular firefighter is not brave, he just works as a firefighter to pay the bills while studying to become a children’s librarian.

An  event schema , also known as a  cognitive script , is a set of behaviors that can feel like a routine. Think about what you do when you walk into an elevator ( Figure 7.4 ). First, the doors open and you wait to let exiting passengers leave the elevator car. Then, you step into the elevator and turn around to face the doors, looking for the correct button to push. You never face the back of the elevator, do you? And when you’re riding in a crowded elevator and you can’t face the front, it feels uncomfortable, doesn’t it? Interestingly, event schemata can vary widely among different cultures and countries. For example, while it is quite common for people to greet one another with a handshake in the United States, in Tibet, you greet someone by sticking your tongue out at them, and in Belize, you bump fists (Cairns Regional Council, n.d.)

Because event schemata are automatic, they can be difficult to change. Imagine that you are driving home from work or school. This event schema involves getting in the car, shutting the door, and buckling your seatbelt before putting the key in the ignition. You might perform this script two or three times each day. As you drive home, you hear your phone’s ring tone. Typically, the event schema that occurs when you hear your phone ringing involves locating the phone and answering it or responding to your latest text message. So without thinking, you reach for your phone, which could be in your pocket, in your bag, or on the passenger seat of the car. This powerful event schema is informed by your pattern of behavior and the pleasurable stimulation that a phone call or text message gives your brain. Because it is a schema, it is extremely challenging for us to stop reaching for the phone, even though we know that we endanger our own lives and the lives of others while we do it (Neyfakh, 2013) ( Figure 7.5 ).

Remember the elevator? It feels almost impossible to walk in and  not  face the door. Our powerful event schema dictates our behavior in the elevator, and it is no different with our phones. Current research suggests that it is the habit, or event schema, of checking our phones in many different situations that makes refraining from checking them while driving especially difficult (Bayer & Campbell, 2012). Because texting and driving has become a dangerous epidemic in recent years, psychologists are looking at ways to help people interrupt the “phone schema” while driving. Event schemata like these are the reason why many habits are difficult to break once they have been acquired. As we continue to examine thinking, keep in mind how powerful the forces of concepts and schemata are to our understanding of the world.

7.2 LAnguage

• Define language and demonstrate familiarity with the components of language
• Understand the development of language
• Explain the relationship between language and thinking

Language  is a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another. While language is a form of communication, not all communication is language. Many species communicate with one another through their postures, movements, odors, or vocalizations. This communication is crucial for species that need to interact and develop social relationships with their conspecifics. However, many people have asserted that it is language that makes humans unique among all of the animal species (Corballis & Suddendorf, 2007; Tomasello & Rakoczy, 2003). This section will focus on what distinguishes language as a special form of communication, how the use of language develops, and how language affects the way we think.

Components of Language

Language, be it spoken, signed, or written, has specific components: a lexicon and lexicon grammar .  Lexicon  refers to the words of a given language. Thus, lexicon is a language’s vocabulary.  Grammar  refers to the set of rules that are used to convey meaning through the use of the lexicon (Fernández & Cairns, 2011). For instance, English grammar dictates that most verbs receive an “-ed” at the end to indicate past tense.

Words are formed by combining the various phonemes that make up the language. A  phoneme  (e.g., the sounds “ah” vs. “eh”) is a basic sound unit of a given language, and different languages have different sets of phonemes. For example, the phoneme English speakers associate with the letter ‘L’ is not used in the Japanese language. Similarly, many Southern African languages use phonemes, sometimes referred to as ‘click consonants’ that are not used in English.

Phonemes are combined to form  morphemes , which are the smallest units of language that convey some type of meaning. Some words are morphemes, but not all morphemes are words.  For example, “-ed” is a morpheme used to convey the past-tense in English, but it is not a word. The word “review” contains two morphemes: re- (meaning to do something again) and view (to see). Finally, some words like “I” and “a” are both a phonemes and morphemes.

We use semantics and syntax to construct language. Semantics and syntax are part of a language’s grammar.  Semantics  refers to the process by which we derive meaning from morphemes and words by connecting those morphemes and words to stored concepts.  Syntax  refers to the way words are organized into sentences (Chomsky, 1965; Fernández & Cairns, 2011). For example, you would never say “the dog walked I today” to let someone know you took your dog for a walk–that sentence does not obey English syntax and is therefore difficult to make sense of.

We apply the rules of grammar to organize the lexicon in novel and creative ways, which allow us to communicate information about both concrete and abstract concepts. We can talk about our immediate and observable surroundings as well as the surface of unseen planets. We can share our innermost thoughts, our plans for the future, and debate the value of a college education. We can provide detailed instructions for cooking a meal, fixing a car, or building a fire. Through our use of words and language, we are able to form, organize, and express ideas, schema, and artificial concepts.

Language Development

Given the remarkable complexity of a language, one might expect that mastering a language would be an especially arduous task; indeed, for those of us trying to learn a second language as adults, this might seem to be true. However, young children master language very quickly with relative ease. B. F.  Skinner  (1957) proposed that language is learned through reinforcement. Noam  Chomsky  (1965) criticized this behaviorist approach, asserting instead that the mechanisms underlying language acquisition are biologically determined. The use of language develops in the absence of formal instruction and appears to follow a very similar pattern in children from vastly different cultures and backgrounds. It would seem, therefore, that we are born with a biological predisposition to acquire a language (Chomsky, 1965; Fernández & Cairns, 2011). Moreover, it appears that there is a critical period for language acquisition, such that this proficiency at acquiring language is maximal early in life; generally, as people age, the ease with which they acquire and master new languages diminishes (Johnson & Newport, 1989; Lenneberg, 1967; Singleton, 1995).

Children begin to learn about language from a very early age ( Table 7.1 ). In fact, it appears that this is occurring even before we are born. Newborns show preference for their mother’s voice and appear to be able to discriminate between the language spoken by their mother and other languages. Babies are also attuned to the languages being used around them and show preferences for videos of faces that are moving in synchrony with the audio of spoken language versus videos that do not synchronize with the audio (Blossom & Morgan, 2006; Pickens, 1994; Spelke & Cortelyou, 1981).

DIG DEEPER: The Case of Genie

In the fall of 1970, a social worker in the Los Angeles area found a 13-year-old girl who was being raised in extremely neglectful and abusive conditions. The girl, who came to be known as Genie, had lived most of her life tied to a potty chair or confined to a crib in a small room that was kept closed with the curtains drawn. For a little over a decade, Genie had virtually no social interaction and no access to the outside world. As a result of these conditions, Genie was unable to stand up, chew solid food, or speak (Fromkin, Krashen, Curtiss, Rigler, & Rigler, 1974; Rymer, 1993). The police took Genie into protective custody.

Genie’s abilities improved dramatically following her removal from her abusive environment, and early on, it appeared she was acquiring language—much later than would be predicted by critical period hypotheses that had been posited at the time (Fromkin et al., 1974). Genie managed to amass an impressive vocabulary in a relatively short amount of time. However, she never developed a mastery of the grammatical aspects of language (Curtiss, 1981). Perhaps being deprived of the opportunity to learn language during a critical period impeded Genie’s ability to fully acquire and use language.

You may recall that each language has its own set of phonemes that are used to generate morphemes, words, and so on. Babies can discriminate among the sounds that make up a language (for example, they can tell the difference between the “s” in vision and the “ss” in fission); early on, they can differentiate between the sounds of all human languages, even those that do not occur in the languages that are used in their environments. However, by the time that they are about 1 year old, they can only discriminate among those phonemes that are used in the language or languages in their environments (Jensen, 2011; Werker & Lalonde, 1988; Werker & Tees, 1984).

After the first few months of life, babies enter what is known as the babbling stage, during which time they tend to produce single syllables that are repeated over and over. As time passes, more variations appear in the syllables that they produce. During this time, it is unlikely that the babies are trying to communicate; they are just as likely to babble when they are alone as when they are with their caregivers (Fernández & Cairns, 2011). Interestingly, babies who are raised in environments in which sign language is used will also begin to show babbling in the gestures of their hands during this stage (Petitto, Holowka, Sergio, Levy, & Ostry, 2004).

Generally, a child’s first word is uttered sometime between the ages of 1 year to 18 months, and for the next few months, the child will remain in the “one word” stage of language development. During this time, children know a number of words, but they only produce one-word utterances. The child’s early vocabulary is limited to familiar objects or events, often nouns. Although children in this stage only make one-word utterances, these words often carry larger meaning (Fernández & Cairns, 2011). So, for example, a child saying “cookie” could be identifying a cookie or asking for a cookie.

As a child’s lexicon grows, she begins to utter simple sentences and to acquire new vocabulary at a very rapid pace. In addition, children begin to demonstrate a clear understanding of the specific rules that apply to their language(s). Even the mistakes that children sometimes make provide evidence of just how much they understand about those rules. This is sometimes seen in the form of  overgeneralization . In this context, overgeneralization refers to an extension of a language rule to an exception to the rule. For example, in English, it is usually the case that an “s” is added to the end of a word to indicate plurality. For example, we speak of one dog versus two dogs. Young children will overgeneralize this rule to cases that are exceptions to the “add an s to the end of the word” rule and say things like “those two gooses” or “three mouses.” Clearly, the rules of the language are understood, even if the exceptions to the rules are still being learned (Moskowitz, 1978).

Language and Thought

When we speak one language, we agree that words are representations of ideas, people, places, and events. The given language that children learn is connected to their culture and surroundings. But can words themselves shape the way we think about things? Psychologists have long investigated the question of whether language shapes thoughts and actions, or whether our thoughts and beliefs shape our language. Two researchers, Edward Sapir and Benjamin Lee Whorf, began this investigation in the 1940s. They wanted to understand how the language habits of a community encourage members of that community to interpret language in a particular manner (Sapir, 1941/1964). Sapir and Whorf proposed that language determines thought. For example, in some languages there are many different words for love. However, in English we use the word love for all types of love. Does this affect how we think about love depending on the language that we speak (Whorf, 1956)? Researchers have since identified this view as too absolute, pointing out a lack of empiricism behind what Sapir and Whorf proposed (Abler, 2013; Boroditsky, 2011; van Troyer, 1994). Today, psychologists continue to study and debate the relationship between language and thought.

WHAT DO YOU THINK? The Meaning of Language

Think about what you know of other languages; perhaps you even speak multiple languages. Imagine for a moment that your closest friend fluently speaks more than one language. Do you think that friend thinks differently, depending on which language is being spoken? You may know a few words that are not translatable from their original language into English. For example, the Portuguese word  saudade  originated during the 15th century, when Portuguese sailors left home to explore the seas and travel to Africa or Asia. Those left behind described the emptiness and fondness they felt as  saudade  ( Figure 7.6 ) .  The word came to express many meanings, including loss, nostalgia, yearning, warm memories, and hope. There is no single word in English that includes all of those emotions in a single description. Do words such as  saudade  indicate that different languages produce different patterns of thought in people? What do you think??

One group of researchers who wanted to investigate how language influences thought compared how English speakers and the Dani people of Papua New Guinea think and speak about color. The Dani have two words for color: one word for  light  and one word for  dark . In contrast, the English language has 11 color words. Researchers hypothesized that the number of color terms could limit the ways that the Dani people conceptualized color. However, the Dani were able to distinguish colors with the same ability as English speakers, despite having fewer words at their disposal (Berlin & Kay, 1969). A recent review of research aimed at determining how language might affect something like color perception suggests that language can influence perceptual phenomena, especially in the left hemisphere of the brain. You may recall from earlier chapters that the left hemisphere is associated with language for most people. However, the right (less linguistic hemisphere) of the brain is less affected by linguistic influences on perception (Regier & Kay, 2009)

7.3 Problem Solving

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving and decision making

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.

Problem-Solving Strategies

When you 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.

A  problem-solving strategy  is a plan of action used to find a solution. Different strategies have different action plans associated with them ( Table 7.2 ). 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):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

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.

EVERYDAY CONNECTION: 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 ( Figure 7.7 ) 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.

Here is another popular type of puzzle ( Figure 7.8 ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

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. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to solve the problem ( Figure 7.10 ). 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  Table 7.3 .

Were you able to determine how many marbles are needed to balance the scales in  Figure 7.9 ? You need nine. Were you able to solve the problems in  Figure 7.7  and  Figure 7.8 ? Here are the answers ( Figure 7.11 ).

Chapter Summary

7.1 what is cognition.

In this section, you were introduced to cognitive psychology, which is the study of cognition, or the brain’s ability to think, perceive, plan, analyze, and remember. Concepts and their corresponding prototypes help us quickly organize our thinking by creating categories into which we can sort new information. We also develop schemata, which are clusters of related concepts. Some schemata involve routines of thought and behavior, and these help us function properly in various situations without having to “think twice” about them. Schemata show up in social situations and routines of daily behavior.

7.2 Language

Language is a communication system that has both a lexicon and a system of grammar. Language acquisition occurs naturally and effortlessly during the early stages of life, and this acquisition occurs in a predictable sequence for individuals around the world. Language has a strong influence on thought, and the concept of how language may influence cognition remains an area of study and debate in psychology.

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.

thinking; or, all of the processes associated with perception, knowledge, problem solving, judgement, language, and memory.

A modern school of psychological thought that empirically examines mental processes such as perception, memory, language, and judgement.

a category or grouping of linguistic information, images, ideas or memories, such as life experiences.

knowledge about words, concepts, and language-based knowledge and facts

the best example or representation of a concept, specific to an individual

concepts developed through direct or indirect experiences with the world

a concept defined by a specific set of characteristics.

a mental construct consisting of a cluster of related concepts

a set of ideas relating to how individuals in certain roles will behave.

also known as a cognitive script; a set of behaviors associated with a particular place or event

also known as an event schema; a set of behaviors associated with a particular place or event

a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another.

the words of a language

the rules of a language used to convey meaning through the use of the lexicon

the basic sounds that make up a language

the smallest unit of language that conveys meaning

the process by which we derive meaning from morphemes and words

the rules guiding the organization of morphemes into words and words into sentences.

Psychology 2e Copyright © 2020 by Openstax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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The Stuff of Problem Solving: Discovering Concepts and Applying Principles

Few would disagree that building critical thinking and creative problem solving skills is imperative for today's students. However, subject matter knowledge is equally important. The 21st Century Skills framework includes a Core Subjects section in addition to skills such as critical thinking and problem solving. The Framework for K-12 Science Education includes Core Ideas in addition to process skills.

You might say, "Of course! Everyone knows students need knowledge as well as skills. We have to teach content, too."

But what exactly IS content? Is it the stuff found in a textbook? Is it information? Is it the definitions, formulas and facts of a subject area?

The answer is: Yes -- but not really.

Understanding What Understanding Is

As an instructional designer, I constantly wrestle with figuring out what it means to really understand something. The answer to that question determines how I will design the instruction to help students build that understanding.

Consider what a person who really understands a subject matter does:

A definition isn't just a string of words to be memorized and repeated; it's an attempt to state the meaning of a concept. A formula isn't a string of variables; it's a relation between concepts -- a principle. Understanding a concept is not the same as recalling a definition, and knowing a principle is not the same as recalling a formula.

"Must Have" vs. "Can Have"

Think about a triangle, for example. If your kindergarten student told you that a triangle was a shape with three sides, would you be satisfied that she understood the concept? Maybe. But you would probably want some more evidence. For example, can she pick out the triangle when you show her a triangle, a square and a circle? Does she identify right triangles as triangles or only equilateral triangles? How about a triangle that isn't a closed figure -- something with three sides but not three angles? Does she call both a small line drawing and a big red felt cut-out "triangle"?

A concept like "triangle" really refers to a category of things. There are some features that it "must have" in order to be placed in that category. A triangle "must have" three sides, and it must be a closed figure. But the sides can be different lengths, the angles can be different sizes, and it can be any color or made out of any material. These are some of the "can haves" -- the features that vary across examples of the category. 2

Part of "understanding" a concept, then, is to classify it -- paying attention to the "must haves" across a variety of "can haves."

Given this, how should concepts be taught?

Analyzing Your Concept

First, analyze your concept. Figure out what the "must have" features are. Think of a typical example and then change one of its features. Is it still an example? If so, then that feature is a "can have." Is it now an example of something else? If so, then the feature you just changed is a "must have."

Next, figure out what kind of variety your concept has. What are all the different "can haves"? Change all of them and see how different two examples can be from each other and still be examples of the concept.

Teaching Your Concept

First, make the "must haves" obvious. See if you can find an example and a non-example that share all of the same "can haves" and vary in just one "must have." The single difference between the example and non-example will allow your students to infer the critical must-have feature. Or, better yet, help them discover a concept and practice thinking skills at the same time by taking them through the process of analysis. Change a variable and ask, "Is it still x ?"

Then extend across the range of "can haves" by asking students to identify a variety of examples with widely different features. You might assign them to look for the most "far out" or different example they can that's still an example of the concept.

Concepts and Principles: The Stuff of Problem Solving

When we look at a new phenomenon, we're comparing it to what we already know -- the classes of things and the relations of things already discovered. We might classify it as another example of an already established category, or we might invent a whole new classification system to incorporate it. We might discover a relation between concepts and recognize it as the application of an already known principle, or we might discover a new principle by analogy to what's already known.

Content is important, but it's more than the definitions and formulas found in a textbook. Content is made up of the concepts and principles of our world. Teaching concepts and principles with examples and non-examples can go a long way in helping students develop true understanding. In doing so, we offer our students more than something to be memorized. We offer them the "stuff" they need for problem solving.

1 Markle, S. M. & Tiemann, P. W. (1970). "Behavioral" analysis of "cognitive" content. Educational Technology, 10, 41–45.

2 Thanks to Joe Layng for coming up with the terms "must have" and "can have" for necessary and variable features, respectively.

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Fluency, Reasoning and Problem Solving: What This Looks Like In Every Math Lesson

Neil almond.

Fluency, reasoning and problem solving are central strands of mathematical competency, as recognized by the National Council of Teachers of Mathematics (NCTM) and the National Research Council’s report ‘Adding It Up’.

They are key components to the Standards of Mathematical Practice, standards that are interwoven into every mathematics lesson. Here we look at how these three approaches or elements of math can be interwoven in a child’s math education through elementary and middle school.

We look at what fluency, reasoning and problem solving are, how to teach them, and how to know how a child is progressing in each – as well as what to do when they’re not, and what to avoid.

The hope is that this blog will help elementary and middle school teachers think carefully about their practice and the pedagogical choices they make around the teaching of what the common core refers to as ‘mathematical practices’, and reasoning and problem solving in particular.

Before we can think about what this would look like in Common Core math examples and other state-specific math frameworks, we need to understand the background to these terms.

What is fluency in math?

What is reasoning in math, what is problem solving in math, mathematical problem solving is a learned skill, performance vs learning: what to avoid when teaching fluency, reasoning, and problem solving.

• What IS ‘performance vs learning’?
• Teaching to “cover the curriculum” hinders development of strong problem solving skills.
• Fluency and reasoning – Best practice in a lesson, a unit, and a semester

Best practice for problem solving in a lesson, a unit, and a semester 

Fluency, reasoning and problem solving should not be taught by rote , the ultimate guide to problem solving techniques.

Develop problem solving skills in the classroom with this free, downloadable worksheet

Fluency in math is a fairly broad concept. The basics of mathematical fluency – as defined by the Common Core State Standards for math – involve knowing key mathematical skills and being able to carry them out flexibly, accurately and efficiently.

But true fluency in math (at least up to middle school) means being able to apply the same skill to multiple contexts, and being able to choose the most appropriate method for a particular task.

Fluency in math lessons means we teach the content using a range of representations, to ensure that all students understand and have sufficient time to practice what is taught.

Read more: How the best schools develop math fluency

Reasoning in math is the process of applying logical thinking to a situation to derive the correct problem solving strategy for a given question, and using this method to develop and describe a solution.

Put more simply, mathematical reasoning is the bridge between fluency and problem solving. It allows students to use the former to accurately carry out the latter.

Read more: Developing math reasoning: the mathematical skills required and how to teach them .

It’s sometimes easier to start off with what problem solving is not. Problem solving is not necessarily just about answering word problems in math. If a child already has a readily available method to solve this sort of problem, problem solving has not occurred. Problem solving in math is finding a way to apply knowledge and skills you have to answer unfamiliar types of problems.

Read more: Math problem solving: strategies and resources for primary school teachers .

We are all problem solvers

First off, problem solving should not be seen as something that some students can do and some cannot. Every single person is born with an innate level of problem-solving ability.

Early on as a species on this planet, we solved problems like recognizing faces we know, protecting ourselves against other species, and as babies the problem of getting food (by crying relentlessly until we were fed).

All these scenarios are a form of what the evolutionary psychologist David Geary (1995) calls biologically primary knowledge. We have been solving these problems for millennia and they are so ingrained in our DNA that we learn them without any specific instruction.

Why then, if we have this innate ability, does actually teaching problem solving seem so hard?

As you might have guessed, the domain of mathematics is far from innate. Math doesn’t just happen to us; we need to learn it. It needs to be passed down from experts that have the knowledge to novices who do not.

This is what Geary calls biologically secondary knowledge. Solving problems (within the domain of math) is a mixture of both primary and secondary knowledge.

The issue is that problem solving in domains that are classified as biologically secondary knowledge (like math) can only be improved by practicing elements of that domain.

So there is no generic problem-solving skill that can be taught in isolation and transferred to other areas.

This will have important ramifications for pedagogical choices, which I will go into more detail about later on in this blog.

The educationalist Dylan Wiliam had this to say on the matter: ‘for…problem solving, the idea that students can learn these skills in one context and apply them in another is essentially wrong.’ (Wiliam, 2018) So what is the best method of teaching problem solving to elementary and middle school math students?

The answer is that we teach them plenty of domain specific biological secondary knowledge – in this case, math. Our ability to successfully problem solve requires us to have a deep understanding of content and fluency of facts and mathematical procedures.

Here is what cognitive psychologist Daniel Willingham (2010) has to say:

‘Data from the last thirty years leads to a conclusion that is not scientifically challengeable: thinking well requires knowing facts, and that’s true not simply because you need something to think about.

The very processes that teachers care about most—critical thinking processes such as reasoning and problem solving—are intimately intertwined with factual knowledge that is stored in long-term memory (not just found in the environment).’

Colin Foster (2019), a reader in Mathematics Education in the Mathematics Education Center at Loughborough University, UK, says, ‘I think of fluency and mathematical reasoning, not as ends in themselves, but as means to support students in the most important goal of all: solving problems.’

In that paper he produces this pyramid:

This is important for two reasons:

1)    It splits up reasoning skills and problem solving into two different entities

2)    It demonstrates that fluency is not something to be rushed through to get to the ‘problem solving’ stage but is rather the foundation of problem solving.

In my own work I adapt this model and turn it into a cone shape, as education seems to have a problem with pyramids and gross misinterpretation of them (think Bloom’s taxonomy).

Notice how we need plenty of fluency of facts, concepts, procedures and mathematical language.

Having this fluency will help with improving logical reasoning skills, which will then lend themselves to solving mathematical problems – but only if it is truly learnt and there is systematic retrieval of this information carefully planned across the curriculum.

I mean to make no sweeping generalization here; this was my experience both at university when training and from working in schools.

At some point, schools become obsessed with the ridiculous notion of moving students through content at an accelerated rate. I have heard it used in all manner of educational contexts while training and being a teacher. ‘You will need to show ‘accelerated progress in math’ in this lesson,’ ‘School officials will be looking for ‘accelerated progress’ etc.

I have no doubt that all of this came from a good place and from those wanting the best possible outcomes – but it is misguided.

I remember being told that we needed to get students onto the problem solving questions as soon as possible to demonstrate this mystical ‘accelerated progress’.

This makes sense; you have a group of students and you have taken them from not knowing something to working out pretty sophisticated 2-step or multi-step word problems within an hour. How is that not ‘accelerated progress?’

This was a frequent feature of my lessons up until last academic year: teach a mathematical procedure; get the students to do about 10 of them in their books; mark these and if the majority were correct, model some reasoning/problem solving questions from the same content as the fluency content; give the students some reasoning and word problem questions and that was it.

I wondered if I was the only one who had been taught this while at university so I did a quick poll on Twitter and found that was not the case.

I know these numbers won’t be big enough for a representative sample but it still shows that others are familiar with this approach.

The issue with the lesson framework I mentioned above is that it does not take into account ‘performance vs learning.’

What IS ‘performance vs learning’?

The premise is that performance in a lesson is not a good proxy for learning.

Yes, those students were performing well after I had modeled a mathematical procedure for them, and managed to get questions correct.

But if problem solving depends on a deep knowledge of mathematics, this approach to lesson structure is going to be very ineffective.

As mentioned earlier, the reasoning and problem solving questions were based on the same math content as the fluency exercises, making it more likely that students would solve problems correctly whether they fully understood them or not.

Chances are that all they’d need to do is find the numbers in the questions and use the same method they used in the fluency section to get their answers (a process referred to as “number plucking”) – not exactly high level problem solving skills.

Teaching to “cover the curriculum” hinders development of strong problem solving skills.

This is one of my worries with ‘math mastery schemes’ that block content so that, in some circumstances, it is not looked at again until the following year (and with new objectives).

The pressure for teachers to ‘get through the curriculum’ results in many opportunities to revisit content being missed in the classroom.

Students are unintentionally forced to skip ahead in the fluency, reasoning, problem solving chain without proper consolidation of the earlier processes.

As David Didau (2019) puts it, ‘When novices face a problem for which they do not have a conveniently stored solution, they have to rely on the costlier means-end analysis.

This is likely to lead to cognitive overload because it involves trying to work through and hold in mind multiple possible solutions.

It’s a bit like trying to juggle five objects at once without previous practice. Solving problems is an inefficient way to get better at problem solving.’

Fluency and reasoning – Best practice in a lesson, a unit, and a semester

By now I hope you have realized that when it comes to problem solving, fluency is king. As such we should look to mastery math based teaching to ensure that the fluency that students need is there.

The answer to what fluency looks like will obviously depend on many factors, including the content being taught and the grade you find yourself teaching.

But we should not consider rushing them on to problem solving or logical reasoning in the early stages of this new content as it has not been learnt, only performed.

I would say that in the early stages of learning, content that requires the end goal of being fluent should take up the majority of lesson time – approximately 60%. The rest of the time should be spent rehearsing and retrieving other knowledge that is at risk of being forgotten about.

This blog on mental math strategies students should learn at each grade level is a good place to start when thinking about the core aspects of fluency that students should achieve.

Little and often is a good mantra when we think about fluency, particularly when revisiting the key mathematical skills of number bond fluency or multiplication fluency. So when it comes to what fluency could look like throughout the day, consider all the opportunities to get students practicing.

They could chant multiplication facts when transitioning. If a lesson in another subject has finished earlier than expected, use that time to quiz students on number bonds. Have fluency exercises as part of the morning work.

Read more: How to teach multiplication for instant recall

What about best practice over a longer period?

Thinking about what fluency could look like across a unit of work would again depend on the unit itself.

Look at this unit below from a popular scheme of work.

They recommend 20 days to cover 9 objectives. One of these specifically mentions problem solving so I will forget about that one at the moment – so that gives 8 objectives.

I would recommend that the fluency of this unit look something like this:

This type of structure is heavily borrowed from Mark McCourt’s phased learning idea from his book ‘Teaching for Mastery.’

This should not be seen as something set in stone; it would greatly depend on the needs of the class in front of you. But it gives an idea of what fluency could look like across a unit of lessons – though not necessarily all math lessons.

When we think about a semester, we can draw on similar ideas to the one above except that your lessons could also pull on content from previous units from that semester.

So lesson one may focus 60% on the new unit and 40% on what was learnt in the previous unit.

The structure could then follow a similar pattern to the one above.

When an adult first learns something new, we cannot solve a problem with it straight away. We need to become familiar with the idea and practice before we can make connections, reason and problem solve with it.

The same is true for students. Indeed, it could take up to two years ‘between the mathematics a student can use in imitative exercises and that they have sufficiently absorbed and connected to use autonomously in non-routine problem solving.’ (Burkhardt, 2017).

Practice with facts that are secure

So when we plan for reasoning and problem solving, we need to be looking at content from 2 years ago to base these questions on.

You could get students in 3rd grade to solve complicated place value problems with the numbers they should know from 1st or 2nd grade. This would lessen the cognitive load , freeing up valuable working memory so they can actually focus on solving the problems using content they are familiar with.

Increase complexity gradually

Once they practice solving these types of problems, they can draw on this knowledge later when solving problems with more difficult numbers.

This is what Mark McCourt calls the ‘Behave’ phase. In his book he writes:

‘Many teachers find it an uncomfortable – perhaps even illogical – process to plan the ‘Behave’ phase as one that relates to much earlier learning rather than the new idea, but it is crucial to do so if we want to bring about optimal gains in learning, understanding and long term recall.’  (Mark McCourt, 2019)

This just shows the fallacy of ‘accelerated progress’; in the space of 20 minutes some teachers are taught to move students from fluency through to non-routine problem solving, or we are somehow not catering to the needs of the child.

When considering what problem solving lessons could look like, here’s an example structure based on the objectives above.

It is important to reiterate that this is not something that should be set in stone. Key to getting the most out of this teaching for mastery approach is ensuring your students (across abilities) are interested and engaged in their work.

Depending on the previous attainment and abilities of the children in your class, you may find that a few have come across some of the mathematical ideas you have been teaching, and so they are able to problem solve effectively with these ideas.

Equally likely is encountering students on the opposite side of the spectrum, who may not have fully grasped the concept of place value and will need to go further back than 2 years and solve even simpler problems.

In order to have the greatest impact on class performance, you will have to account for these varying experiences in your lessons.

Read more: 

• Math Mastery Toolkit : A Practical Guide To Mastery Teaching And Learning
• Problem Solving and Reasoning Questions and Answers
• Get to Grips with Math Problem Solving For Elementary Students
• Mixed Ability Teaching for Mastery: Classroom How To
• 21 Math Challenges To Really Stretch Your More Able Students
• Why You Should Be Incorporating Stem Sentences Into Your Elementary Math Teaching

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The content in this article was originally written by primary school lead teacher Neil Almond and has since been revised and adapted for US schools by elementary math teacher Jaclyn Wassell.

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A Crash Course in Critical Thinking

What you need to know—and read—about one of the essential skills needed today..

Posted April 8, 2024 | Reviewed by Michelle Quirk

• In research for "A More Beautiful Question," I did a deep dive into the current crisis in critical thinking.
• Many people may think of themselves as critical thinkers, but they actually are not.
• Here is a series of questions you can ask yourself to try to ensure that you are thinking critically.

Conspiracy theories. Inability to distinguish facts from falsehoods. Widespread confusion about who and what to believe.

These are some of the hallmarks of the current crisis in critical thinking—which just might be the issue of our times. Because if people aren’t willing or able to think critically as they choose potential leaders, they’re apt to choose bad ones. And if they can’t judge whether the information they’re receiving is sound, they may follow faulty advice while ignoring recommendations that are science-based and solid (and perhaps life-saving).

Moreover, as a society, if we can’t think critically about the many serious challenges we face, it becomes more difficult to agree on what those challenges are—much less solve them.

On a personal level, critical thinking can enable you to make better everyday decisions. It can help you make sense of an increasingly complex and confusing world.

In the new expanded edition of my book A More Beautiful Question ( AMBQ ), I took a deep dive into critical thinking. Here are a few key things I learned.

First off, before you can get better at critical thinking, you should understand what it is. It’s not just about being a skeptic. When thinking critically, we are thoughtfully reasoning, evaluating, and making decisions based on evidence and logic. And—perhaps most important—while doing this, a critical thinker always strives to be open-minded and fair-minded . That’s not easy: It demands that you constantly question your assumptions and biases and that you always remain open to considering opposing views.

In today’s polarized environment, many people think of themselves as critical thinkers simply because they ask skeptical questions—often directed at, say, certain government policies or ideas espoused by those on the “other side” of the political divide. The problem is, they may not be asking these questions with an open mind or a willingness to fairly consider opposing views.

When people do this, they’re engaging in “weak-sense critical thinking”—a term popularized by the late Richard Paul, a co-founder of The Foundation for Critical Thinking . “Weak-sense critical thinking” means applying the tools and practices of critical thinking—questioning, investigating, evaluating—but with the sole purpose of confirming one’s own bias or serving an agenda.

In AMBQ , I lay out a series of questions you can ask yourself to try to ensure that you’re thinking critically. Here are some of the questions to consider:

• Why do I believe what I believe?
• Are my views based on evidence?
• Have I fairly and thoughtfully considered differing viewpoints?
• Am I truly open to changing my mind?

Of course, becoming a better critical thinker is not as simple as just asking yourself a few questions. Critical thinking is a habit of mind that must be developed and strengthened over time. In effect, you must train yourself to think in a manner that is more effortful, aware, grounded, and balanced.

For those interested in giving themselves a crash course in critical thinking—something I did myself, as I was working on my book—I thought it might be helpful to share a list of some of the books that have shaped my own thinking on this subject. As a self-interested author, I naturally would suggest that you start with the new 10th-anniversary edition of A More Beautiful Question , but beyond that, here are the top eight critical-thinking books I’d recommend.

The Demon-Haunted World: Science as a Candle in the Dark , by Carl Sagan

This book simply must top the list, because the late scientist and author Carl Sagan continues to be such a bright shining light in the critical thinking universe. Chapter 12 includes the details on Sagan’s famous “baloney detection kit,” a collection of lessons and tips on how to deal with bogus arguments and logical fallacies.

Clear Thinking: Turning Ordinary Moments Into Extraordinary Results , by Shane Parrish

The creator of the Farnham Street website and host of the “Knowledge Project” podcast explains how to contend with biases and unconscious reactions so you can make better everyday decisions. It contains insights from many of the brilliant thinkers Shane has studied.

Good Thinking: Why Flawed Logic Puts Us All at Risk and How Critical Thinking Can Save the World , by David Robert Grimes

A brilliant, comprehensive 2021 book on critical thinking that, to my mind, hasn’t received nearly enough attention . The scientist Grimes dissects bad thinking, shows why it persists, and offers the tools to defeat it.

Think Again: The Power of Knowing What You Don't Know , by Adam Grant

Intellectual humility—being willing to admit that you might be wrong—is what this book is primarily about. But Adam, the renowned Wharton psychology professor and bestselling author, takes the reader on a mind-opening journey with colorful stories and characters.

Think Like a Detective: A Kid's Guide to Critical Thinking , by David Pakman

The popular YouTuber and podcast host Pakman—normally known for talking politics —has written a terrific primer on critical thinking for children. The illustrated book presents critical thinking as a “superpower” that enables kids to unlock mysteries and dig for truth. (I also recommend Pakman’s second kids’ book called Think Like a Scientist .)

Rationality: What It Is, Why It Seems Scarce, Why It Matters , by Steven Pinker

The Harvard psychology professor Pinker tackles conspiracy theories head-on but also explores concepts involving risk/reward, probability and randomness, and correlation/causation. And if that strikes you as daunting, be assured that Pinker makes it lively and accessible.

How Minds Change: The Surprising Science of Belief, Opinion and Persuasion , by David McRaney

David is a science writer who hosts the popular podcast “You Are Not So Smart” (and his ideas are featured in A More Beautiful Question ). His well-written book looks at ways you can actually get through to people who see the world very differently than you (hint: bludgeoning them with facts definitely won’t work).

A Healthy Democracy's Best Hope: Building the Critical Thinking Habit , by M Neil Browne and Chelsea Kulhanek

Neil Browne, author of the seminal Asking the Right Questions: A Guide to Critical Thinking, has been a pioneer in presenting critical thinking as a question-based approach to making sense of the world around us. His newest book, co-authored with Chelsea Kulhanek, breaks down critical thinking into “11 explosive questions”—including the “priors question” (which challenges us to question assumptions), the “evidence question” (focusing on how to evaluate and weigh evidence), and the “humility question” (which reminds us that a critical thinker must be humble enough to consider the possibility of being wrong).

Warren Berger is a longtime journalist and author of A More Beautiful Question .

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A Complete Guide to know What is Problem Solving (Updated April 2024)

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.

·       Affinity diagrams.

·       Swim Lane diagram.

·       System diagram.

·       Flow charts.

·       Bottleneck method.

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.

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

• 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.

Access your free e-book today.

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:

• Finding creative solutions to complex problems : User research can insufficiently illustrate a situation’s complexity. While other innovation processes rely on this information, creative problem-solving can yield solutions without it.
• Adapting to change : Business is constantly changing, and business leaders need to adapt. Creative problem-solving helps overcome unforeseen challenges and find solutions to unconventional problems.
• Fueling innovation and growth : In addition to solutions, creative problem-solving can spark innovative ideas that drive company growth. These ideas can lead to new product lines, services, or a modified operations structure that improves efficiency.

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:

• Clarify: The clarification stage allows you to empathize with the user and identify problems. Observations and insights are informed by thorough research. Findings are then reframed as problem statements or questions.
• Ideate: Ideation is the process of coming up with innovative ideas. The divergence of ideas involved with creative problem-solving is a major focus.
• Develop: In the development stage, ideas evolve into experiments and tests. Ideas converge and are explored through prototyping and open critique.
• Implement: Implementation involves continuing to test and experiment to refine the solution and encourage its adoption.

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:

• The printer is overused.
• The printer overheats.
• The printer breaks down.

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.

• Inversion: Inversion changes the relationship between two UDPs so the cause is the same but the effect is the opposite. For example, if the UDP is "the more X happens, the more likely Y is to happen," inversion changes the equation to "the more X happens, the less likely Y is to happen." Using the printer example, inversion would consider: "What if the more a printer is used, the less likely it’s going to overheat?" Innovation requires an open mind. Just because a solution initially seems unlikely doesn't mean it can't be pursued further or spark additional ideas.
• Neutralization: Neutralization completely eliminates the cause-and-effect relationship between X and Y. This changes the above equation to "the more or less X happens has no effect on Y." In the case of the printers, neutralization would rephrase the relationship to "the more or less a printer is used has no effect on whether it overheats."

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 :

• Have each group member come up with as many ideas as possible and write them down to ensure the brainstorming session is productive.
• Continue the divergence of ideas by collectively sharing and exploring each idea as a group. The goal is to create a setting where new ideas are inspired by open discussion.
• Begin the convergence of ideas by narrowing them down to a few explorable options. There’s no "right number of ideas." Don't be afraid to consider exploring all of them, as long as you have the resources to do so.

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.

Continue Developing Your Skills

Whether you’re an entrepreneur, marketer, or business leader, learning the ropes of design thinking can be an effective way to build your skills and foster creativity and innovation in any setting.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

THOMAS WEDELL-WEDELLSBORG: Thanks for inviting me.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

SARAH GREEN CARMICHAEL: That is a really good question.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

THOMAS WEDELL-WEDELLSBORG: Completely, completely hypothetical.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

SARAH GREEN CARMICHAEL: We got take-out.

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

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

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

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

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

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

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

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

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

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

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

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

THOMAS WEDELL-WEDELLSBORG: Thank you, Sarah.  

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

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

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

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

See you next week.

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What is the Concept of Problem-Solving?

Concept of Problem-Solving

Problem-solving is a cognitive process that involves discovering, analyzing, and solving problems. It’s a critical skill that individuals use to overcome challenges, achieve goals, and make decisions. The concept of problem-solving can be applied to various aspects of life. Including personal, professional, and academic domains.

Key elements of the concept of problem-solving include:

Identification of a problem:                             .

• The process begins with recognizing that a problem exists. This may involve understanding a discrepancy between the current state and the desired state.

Definition and Analysis of the Problem:

• Once a problem is identified, it needs to be clearly defined and understood. This may involve breaking down the problem into smaller components, analyzing its causes and effects, and gathering relevant information.

Goal Setting:

• Establishing specific, measurable, achievable, relevant, and time-bound (SMART) goals is crucial. These goals guide the problem-solving process and help in measuring success.

Generation of Possible Solutions:

• Brainstorming and generating a variety of potential solutions to the problem is a key step. Creativity and critical thinking play important roles in this phase.

Evaluation of Solutions:

• Assessing the pros and cons of each potential solution is essential. Consideration of feasibility, effectiveness, and potential consequences helps in selecting the most appropriate solution.

Decision-Making:

• Based on the evaluation, a decision is made regarding the best course of action. This may involve choosing one solution or a combination of solutions.

Implementation of the Chosen Solution:

• Putting the chosen solution into action. This may require planning, coordination, and execution.

Monitoring and Evaluation:

• After implementation, it’s important to assess the effectiveness of the solution. Monitoring allows for adjustments. and improvements to be made if necessary.

Reflection and Learning:

• Reflecting on the problem-solving process provides insights into what worked well and what could be improved. This learning contributes to an individual’s problem-solving skills for future challenges.

Problem-solving is not a linear process, and individuals may revisit certain steps as needed. It involves a combination of analytical thinking, creativity, adaptability, and effective decision-making. Developing strong problem-solving skills is beneficial in various aspects of life, including personal development, academic success, and professional advancement.

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MSU Extension Child & Family Development

Parenting the preschooler: intellectual development.

April 4, 2024 - Kylie Rymanowicz, Vivian Washington <[email protected]> and Kevin Zoromski <[email protected]> , Michigan State University Extension

Ages & Stages

Preschooler A child who is 3 to 5 years of age.

Young child A child who is 0 to 8 years of age.

Minding Our Language

In this series we have chosen to use the inclusive words they , their , and them as singular, nongendered pronouns.

Families and parents come in all shapes, sizes, and styles. A family may include people who are related by blood, by marriage, and by choice. Parents may be biological, step-, foster, adoptive, legally appointed, or something else. When we use the words family and parent in these materials, we do so inclusively and with great respect for all adults who care for and work with young people.

For preschool-aged children, intellectual development (also called cognitive or thinking development) occurs mostly through play. Playing with objects that are different shapes, colors, and textures gives them a chance to learn how things are the same and how things are different. They can learn about spatial relationships by manipulating blocks or learn about time through daily activities. Opportunities to explore different objects, participate in dramatic play, and observe the world around them are also important parts of intellectual development.

This unit of Parenting the Preschooler focuses on the range of thinking skills and knowledge that children need to be prepared for school. The concept sheets in this unit offer information that will help you help your child learn:

• Concrete information about shapes, colors, numbers, and other knowledge of objects
• Problem-solving skills
• How things work
• About the physical and social world they live in

Playing, having fun, and trying new things are also vital to your child’s brain and thinking development, and to their school readiness. Therefore, the unit offers tips on creating opportunities for new experiences for your child and helping them build on their previous experiences.

Intellectual Development Concept Sheets

Brain development.

• 01-Scaffolding— How do you help your child learn?
• 02-General Brain Development— How do you help boost your child’s brain development?
• 03-Types of Intelligence— What does your child do well?
• 04-School Readiness— How are you preparing your child for school?
• 05-Playing to Learn— How do you make play time fun for your preschooler?
• 06-Colors and Shapes— How do you help your child learn about colors and shapes?
• 07-Time— How do you help your child learn about time?
• 08-Math— How do you make learning math fun for your child?
• 09-Spatial Relations— How do you help your child see things from different perspectives?
• 10-Learning From the Environment— How do you interest your child in the things around them?

Find Out More

MSU Extension provides the following resources for parents and caregivers of preschoolers and young children at no or low cost. Be sure to check out these and other MSU Extension resources available at www.extension.msu.edu .

• Extension Extras ( https://bit.ly/2LC2vdX )—These compilations of news articles, activities, parenting tips, and advice are published online Monday through Friday. The resources are designed for parents and caregivers of young children who are home all day during the novel coronavirus pandemic. Each day has a theme: Mindful Mondays, Tips on Tuesday, Working Wednesdays, Thinking Thursday, and Fun Fridays.
• Extension Extras Enrichment Kits ( https://bit.ly/35QAplQ )—These kits feature five or six early childhood activities with learning goals focused in areas such as social and emotional health, literacy, and STEM; a supply list; suggested children’s books; introduction letters explaining how to use the materials; and an evaluation. The kits are available as free downloads.
• Early Childhood Videos ( https://bit.ly/3ioyEkS )—These short videos offer parents and caregivers of young children information on parenting topics. Titles include “Perspective Taking,” “Family Movies,” “Goals of Misbehavior,” “Using Thinking and Feeling Words,” “The Waiting Game,” and “When Siblings Fight.”
• Building Early Emotional Skills (BEES) in Young Children ( https://bit.ly/38XW4KI )—This page provides links to a variety of free online parenting courses, workshops, and events offered by MSU Extension for parents and caregivers of young children aged 0 to 3.
• Mindfulness A to Z: An Alphabet of Fun & Calming Activities ( https://bit.ly/3iMLWtA )—The “Mindfulness A to Z” book and activity cards include 26 fun, delightfully illustrated mindfulness activities for children ages 3 to 12. From A (Alpaca Breathing) to Z (Zipper Stretches), children learn to slow down, calm down, and relax so they can focus and feel better. The book and activity cards are available for sale from shop.msu.edu .

This is a revised edition of the Parenting the Preschooler curriculum that was originally published by Michigan State University Extension in 2006. The authors of this edition would like to thank the authors of the first edition for leading the way.

Parenting the Preschooler: Intellectual Development Overview © 2022 Michigan State University. These concept sheets may be copied for purposes of 4-H and other nonprofit educational programs and for individual use with credit to Michigan State University Extension. 1R-1P-Web-04:2022-RM/CFD WCAG 2.0 AA

Tags: brain development , child development , childhood , cognitive development , co-parenting , creativity , critical thinking , decision making , early childhood development , emotional intelligence , emotional skills , emotions , imagination , independence , intellectual development , learning styles , msu extension , parenting , parenting the preschooler , play , pp intellectual development , preschoolers , problem solving , responsibility , school readiness , social skills , well-being

Vivian Washington [email protected]

Kevin Zoromski [email protected]

new - method size: 1 - Random key: 0, method: personalized - key: 0

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Accessibility Questions:

For questions about accessibility and/or if you need additional accommodations for a specific document, please send an email to ANR Communications & Marketing at [email protected] .

• brain development,
• child development,
• cognitive development,
• co-parenting,
• creativity,
• critical thinking,
• decision making,
• early childhood development,
• emotional intelligence,
• emotional skills,
• imagination,
• independence,
• intellectual development,
• learning styles,
• msu extension,
• parenting the preschooler,
• pp intellectual development,
• preschoolers,
• problem solving,
• responsibility,
• school readiness,
• social skills,
• well-being,
• child & family development