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What is analytical problem solving.

There are some very common misconceptions and myths about analytical problem solving. Most candidates simply skim over this phrase on consulting profiles without thinking about the meaning. This post will tell you what management consulting firms like McKinsey , Bain and BCG mean by analytical problem solving.

You would be surprised at how many people believe that analytical thinking is something that comes instinctively, letting you do data analysis and pinpoint relevant information to get the key takeaways from complex problems. The truth is, these analytical skills are, more often than not, hard skills that you acquire through years of problem solving and critical thinking. They’re problem-solving skills that help you go from coming up with easy solutions to coming up with creative solutions that go the extra mile.

This is important advice so it is worth reading carefully – we’ll also go over some analytical and problem solving skills examples to help you understand better.

What is analytical problem solving

To be an analytical thinker does not mean you must have a degree in science, engineering, finance, economics or any other quantitative subject. While some subjects, like those listed, imply you could be analytical in your thinking, not having quantitative background does not mean you cannot think analytically. Thousands of candidates with quantitative backgrounds fail to get offers from McKinsey, Bain and BCG every year. Therefore, having a quantitative background can be an advantage, but it does not guarantee analytical problem solving ability.

Being analytical refers to the way you think and not to the problem you solve. This is a very important statement. Lawyers, social scientists, linguists and historians can all be extremely analytical in their thinking. Yet, they are not solving quantitative problems. So the problem is not what determines if you are analytical, it is the way you solve the problem.

Good analyses are grounded in hypotheses. Can you develop hypotheses? It always surprises us how many people do not know what is a hypothesis. A hypothesis is not the problem. It is not a fact. It is not an opinion. It is a statement which captures the observed phenomenon as well as the likely cause of the phenomenon. Both must be present for it to be a hypothesis. A surprising number of candidates do not understand this.

Are you able to reason using only the facts provided? Analytical thinkers are not unemotional. No one is unemotional. However, analytical thinkers are able to separate their emotion from the situation and use the data provided to arrive at a conclusion. Analytical problem solving means reasoning using facts and logic. Past experience or opinions which cannot be substantiated are ignored.

Can you assemble data and facts to develop an argument or line of reasoning? Analytical thinkers can take pieces of information, compare them and decide what the information is saying. They can assemble the information to produce new insight into the problem rather than simply restating the information.

Analytical thinkers do not blurt out answers. Assuming your answer is even correct, the fact that you knew the answer means you did not need to analyse the facts. Therefore, your analytical problem solving skill could not be tested.

Logic has nothing to do with numbers. There is a misconception that if your reasoning lacks numbers then it must be incorrect. That is ridiculous. In many consulting case interviews, you will need to reason based on logical arguments and with very little numbers. Your line of reasoning is more important than your final answer.

Analytical thinkers can show you how they arrived at the answer. This should be obvious, right? After all, it is the foundation of the case interview method. If you followed a path of reasoning to arrive at an answer, you should be able to explain that path to someone. That is why the method is used. The interviewer is more interested in how you arrived at the answer than the answer you developed. How you arrived at the answer shows the strength of your analytical problem solving skill.

Logical thinkers apply MECE , even if they do not know it. I have some impressive friends in the legal profession. Watching them reason and debate is worth doing so. When you ask them how they arrived at an answer or why they eliminated an option, you realize they are applying the rules of MECE perfectly. Yet, they never heard of MECE. Reason and logic is not exclusive to management consulting but is it essential to management consulting.

You do not need to know anything about an income statement, balance sheet or cash-flow statement to develop analytical skills. I should not need to say this but I will say it anyway. The thought process is more important than the topic. You can learn accounting and financial concepts when you need them. It is not very difficult to do so.

Analytical and problem solving skills examples

Below we share with you some examples of analytical and problem solving skills and how analytical skills are being tested during consulting case interviews.

McKinsey case interview examples 

• Complex McKinsey Interviewer led profitability case in Pharma (by FIRMSconsulting.com) 
• Comprehensive McKinsey hypotheses based case interview example (by FIRMSconsulting.com)
• McKinsey cost-benefit approach complex profit case interview example (by FIRMSconsulting.com)

BCG case interview examples

• Comprehensive BCG interviewer led market entry case interview example (by FIRMSconsulting.com) 

General case interview examples

• A comprehensive approach to brainstorming in case interviews (by FIRMSconsulting.com)
• Framework for a Bain, McKinsey, BCG acquisition case (by FIRMSconsulting.com)

Structured case interview analytical and problem solving skills development is needed

If you would like to get help with developing your analytical and problem solving skills, and fast track your case interview preparation, we welcome you to enroll into Premium membership .

There is nowhere else in the world where you can see real candidates trained by former partners from major consulting firms to help them develop analytical and problem solving skills. You will see the candidate’s progression through each step of the case interview preparation process, and how their analytical and problem solving skills are being developed. And you will see candidates receiving real offers from major firms such as Deloitte, McKinsey, or BCG.

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What is Analytical Thinking: An Introduction

Get introduced to "Analytical Thinking" with this comprehensive blog. Delve into the core concept of analytical thinking, exploring its characteristics such as curiosity, systematic approach, problem-solving aptitude and open-mindedness. By the end of this exploration, you'll have a clear understanding of what analytical thinking is and why it's a crucial skill.

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Table of Contents  

1) What is Analytical Thinking? 

2) Why is Analytical Thinking important? 

3) Important elements of Analytical Thinking 

4) How to master Analytical Thinking?

5) Conclusion 

What is Analytical Thinking ?    

Analytical Thinking is the cognitive process of dissecting intricate problems, data, or situations into smaller components to discern patterns, relationships, and underlying principles. It involves critical observation, logical reasoning, and systematic analysis to arrive at informed conclusions or solutions.   

Why is Analytical Thinking important?

Informed decision-making 

At its core, Analytical Thinking equips individuals with the tools to dissect intricate scenarios, distil pertinent information, and make informed decisions. From someone pondering a career move, considering a significant investment to someone deciding on a course of action, Analytical Thinking allows you to assess the pros and cons, identify potential pitfalls, and forecast outcomes.  

Innovative problem solving 

Innovation often springs from the ability to connect disparate dots and unearth hidden solutions. Analytical thinkers possess the capability for dissecting complex problems, breaking them into manageable components, and reassembling them in novel ways. This cognitive dexterity breeds innovation, as it enables individuals to envision alternative paths and approaches that might otherwise remain concealed. 

Precise communication 

Clear and effective communication is essential in all walks of life. Analytical Thinking fosters the capacity to organise thoughts logically, structure arguments coherently, and present ideas with precision. Regardless of whether you're explaining a concept to a colleague, delivering a persuasive pitch, or writing a research paper, the analytical thinker's ability to present complex ideas succinctly and comprehensibly is an invaluable asset. 

Strategic planning 

From business strategies to personal goals, strategic planning hinges on the ability to anticipate outcomes, devise contingencies, and adapt to changing circumstances. Analytical Thinking lends itself to strategic prowess by enabling individuals to assess multiple variables, foresee potential roadblocks, and chart a course that maximises the likelihood of success. 

Critical evaluation 

In a world rife with misinformation and biased narratives, the skill of critical evaluation is more crucial than ever. Analytical Thinking empowers individuals to sift through a barrage of information, discern credible sources, and separate fact from fiction. This aptitude for discernment is a bulwark against being swayed by superficial allure or baseless assertions. 

Continuous improvement 

Analytical thinkers possess an innate curiosity that propels them towards constant learning and growth. They see challenges not as insurmountable obstacles but as opportunities for enhancement. This drive for self-improvement extends beyond their capabilities; analytical thinkers often seek to refine processes, systems, and products, contributing to advancing their fields and industries.

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Important Elements of Analytical Thinking    

Now that you know the meaning of Analytical Thinking, let's explore its characteristics. Analytical Thinking is more than a mere mental exercise; it's a unique cognitive approach that involves a specific set of traits and habits. Those with these characteristics are adept at dissecting complexities, drawing insights from data, and arriving at well-reasoned conclusions. Here are the key attributes that define Analytical thinkers:  

Curiosity and inquisitiveness  

Analytical Thinkers exhibit a natural curiosity about the world around them. They possess an insatiable desire to understand how things work and why they are the way they are. This curiosity fuels their exploration of concepts, data, and problems, leading them to uncover hidden connections and unexpected insights. 

Attention to detail  

One of the hallmarks of Analytical Thinking is an unwavering attention to detail. Analytical individuals have a knack for spotting even the minutest discrepancies, anomalies, or patterns within data or scenarios that might go unnoticed by others. This acute attention to detail is instrumental in identifying potential issues and crafting precise solutions. 

Systematic approach  

Analytical Thinkers approach problems methodically. They break down complex issues into manageable parts, which allows them to analyse each component individually before synthesising a comprehensive understanding. This systematic approach enables them to unravel intricate challenges and address them step by logically. 

Logical reasoning  

Logical reasoning is the bedrock of Analytical Thinking . Those who possess this trait are skilled at constructing and deconstructing arguments, identifying flaws in reasoning, and evaluating the validity of information. This ability helps them sift through the noise and reach well-founded conclusions based on evidence and logic. 

Pattern recognition  

Analytical Thinkers excel at recognising patterns and trends across various data sets or scenarios. They have an innate ability to identify similarities and differences, allowing them to generalise principles from specific instances and apply them to broader contexts. 

Critical thinking  

Critical thinking is a cornerstone of Analytical Thinking . Individuals with this characteristic are not content with accepting information at face value; they question assumptions, challenge norms, and seek underlying reasons. This intellectual rigour ensures that their conclusions are well-substantiated and comprehensive. 

Problem-solving aptitude  

Analytical Thinkers thrive on solving complex problems. They approach challenges with a blend of creativity and logic, devising innovative solutions that address the root causes rather than merely treating symptoms. Their ability to dissect problems and explore multiple angles empowers them to tackle even the most daunting issues.  

Open-mindedness  

While Analytical Thinkers possess strong reasoning skills, they also embrace open-mindedness. They acknowledge that not all problems have linear solutions and are willing to explore unconventional ideas and viewpoints. This adaptability allows them to adapt their approach when encountering new and unexpected scenarios. 

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How to master Analytical Thinking? 

In order to master your Analytical Thinking skills, you can adapt the following skills: 

1) Analysing information involves thoroughly examining data or a situation to identify crucial elements, assess their strengths and weaknesses, and leverage this understanding to construct a compelling argument, offer recommendations, or address a problem effectively.

2) Breaking down problems simplifies significant challenges by dividing them into more minor, manageable issues that are easier to solve individually.

3) Gathering information requires asking pertinent questions of oneself and others to gain valuable insights, facilitating more informed decision-making when tackling problems.

4) Identifying issues and problems involves honing the skill of recognising underlying issues or challenges through analysing trends, associations, and cause-effect relationships within datasets.

5) Identifying the root cause is conducting a thorough analysis to pinpoint the fundamental cause of a problem, ensuring that efforts are focused on addressing the actual issue rather than just its symptoms.

6) Organising information entails systematically arranging and integrating all collected data to derive insights and generate ideas, laying the groundwork for potential solutions to the problems at hand.

Conclusion  

Analytical Thinking emerges as an invaluable beacon in a world demanding ever-greater insight and adaptability. Its ability to unravel complexity, innovate solutions, and foster critical evaluation empowers individuals across diverse domains. By cultivating a curious mind, attention to detail and logic, we can get started on a journey of continuous improvement. Hope we could answer all your queries about “What is Analytical Thinking”! 

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Frequently Asked Questions

Here's how you can enhance Analytical Thinking skills:

a) Practice regularly: Solve puzzles and engage in analytical games.

b) Read widely: Explore diverse topics for a broader perspective.

c) Critical reflection: Reflect on experiences and decisions critically.

d) Ask questions: Challenge information and seek underlying reasons.

e) Break down issues: Analyse complex problems by breaking them into parts.

f) Seek feedback: Discuss analyses with peers for valuable insights.

g) Learn from mistakes: Analyse failures for continuous improvement.

h) Data literacy: Understand and interpret data for informed decisions.

i) Stay curious: Cultivate curiosity to explore various problem angles.

j) Take on projects: Apply analytical skills in practical scenarios for hands-on experience.

Analytical Thinking is vital for career growth, enabling strategic decision-making and effective problem-solving. It empowers professionals to navigate challenges, make informed decisions, and drive innovation. Those skilled in Analytical Thinking excel in strategic planning, problem-solving, and efficient decision-making. They contribute to organisational success by optimising operations, fostering innovation, and exhibiting leadership qualities. This skill enhances adaptability in dynamic environments, encourages continuous learning, and improves communication with diverse stakeholders.

 Individuals with strong analytical skills can create detailed plans, identify critical milestones, and allocate resources efficiently by breaking down complex projects into manageable components. This approach allows setting of precise timelines and realistic goal-setting. Analytical thinkers excel at anticipating potential challenges, enabling proactive problem-solving and risk mitigation. They prioritise tasks based on strategic importance and resource availability, ensuring optimal time utilisation. Additionally, Analytical Thinking aids in assessing project progress through data analysis, facilitating informed adjustments when necessary.

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The Knowledge Academy offers various Leadership Courses , including Leadership Skills, Creative Leader Thinking and Creative and Analytical Thinking. These courses cater to different skill levels, providing comprehensive insights into Leadership Qualities    Our Leadership Training blogs covers a range of topics related to leadership and analytical thinking, offering valuable resources, best practices, and industry insights. Whether you are a beginner or looking to advance your Leadership skills, The Knowledge Academy's diverse courses and informative blogs have you covered.

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Analytical Thinking, Critical Analysis, and Problem Solving Guide

• Post author: Samir Saif
• Post published: September 5, 2023
• Post category: marketing skills
• Post comments: 4 Comments
• Post last modified: November 10, 2023
• Reading time: 9 mins read

Analytical thinking; is a mental process that entails dissecting an issue or situation into its constituent parts, investigating their relationships, and reaching conclusions based on facts and logic.

It is not about trusting instincts or making assumptions; rather, it is about studying details, recognizing patterns, and developing a full understanding. Whether you’re a seasoned professional, an aspiring entrepreneur, or a curious mind, improving analytical thinking can help you solve problems more effectively.

Table of Contents

Analytical Thinking’s Importance in Problem Solving

Certainly! Analytical thinking entails the capacity to gather pertinent information, critically assess evidence, and reach logical conclusions. It enables you to:

• Identify Root Causes: Analytical thinking allows you to delve deeper into a problem to find the underlying causes rather than just addressing surface-level symptoms.
• Reduce Risks: Analytical thinking can help discover potential risks and obstacles connected with various solutions. This kind of thinking encourages constant progress and the generation of new ideas.
• Improve Communication: Analytical thinking enables you to deliver clear and well-structured explanations while giving answers to others.
• Adaptability : Analytical thinking gives you a flexible attitude.
• Learning and Development: Analytical thinking improves your cognitive skills, allowing you to learn from prior experiences and apply those lessons to new situations.
• Problem Prevention: By examining previous difficulties, you can find trends and patterns.
• Analytical thinking is, in essence, the foundation of effective problem-solving. It enables you to approach problems methodically, make well-informed judgments, and eventually get better results.

Key Components of Analytical Thinking

Analytical thinking is a multifaceted process including a beautifully woven tapestry of observation, inquiry, and logic. Engage your curiosity as you approach a complex task and see patterns emerge, similar to stars in the night sky.

These patterns direct your thinking toward greater comprehension. Your understanding grows as you progress, and your analytical thinking becomes a light of clarity, guiding people through the fog of complexity.

Your tapestry is complete as you approach the shores of conclusion, a tribute to the power of analytical thinking. Embrace your curiosity, navigate the waters of observation, and let the stars of logic guide you. Remember that the art of analytical thinking is a magnificent journey that leads to enlightenment.

Using analytical reasoning in real-life situations

Absolutely! Let’s get started with analytical thinking! Consider yourself in a busy city, attempting to discover the shortest route to your goal. Instead than taking the first option that comes to mind, you take a moment to think about your possibilities.

This is the initial stage in analytical thinking: evaluating the situation. As you contemplate, you balance the advantages and disadvantages of each route, taking into account issues such as traffic, distance, and potential bypasses. This information gathering approach assists you in making an informed decision.

Breaking down the problem

Then you go to the second phase, which entails breaking the problem down into smaller portions. You break down the difficult job of navigating the city into manageable components, much like a puzzle.

This technique allows you to identify future difficulties and devise creative solutions. For example, you may observe a construction zone on one route but recall a shortcut that may save you time.

Read Also:  Goal Alignment: Key Strategies for Success

Analyzing the information

You employ critical thinking to assess the material you’ve received as you go. As you consider the significance of each component—time, distance, and traffic—patterns and connections emerge.

You begin to make connections and discover that, while a faster route may appear enticing, heavy traffic at certain times of day might make it a frustrating experience.

Make a decision

Making a decision in the last step necessitates a complete comprehension of the circumstance as well as critical analysis. Analytical thinking entails investigating alternatives, comprehending nuances, and making informed decisions.

This approach can lead to optimal, well-thought-out, and adaptable solutions, whether navigating a city, tackling a complex project, or making life decisions. Analytic thinking allows one to make informed judgments that benefit both the situation and the individual.

Strategies to Enhance Analytical Thinking Skills

Developing strong analytical thinking abilities is a journey that opens up new possibilities for comprehension and issue solving.

Consider yourself on an exciting mental journey where every challenge is an opportunity for improvement. Here’s a step-by-step guide to cultivating and improving your analytical thinking talents.

Accept curiosity

Begin by embracing your curiosity. Allow your thoughts to roam, pondering about the hows and whys of the world around you.

Allow yourself to immerse yourself completely in the complexities of a complex topic, such as climate change. “What are the underlying causes of this phenomenon?” Two decent places to start are “How do different variables interact to shape its outcomes?”.

Improve your observing abilities

Then, put your observation abilities to the test. Pay close attention to details that would otherwise go undetected. Instead of just gazing at the colors and shapes, try to figure out the brushstrokes, the play of light and shadow, and the feelings they create, as if you were studying a painting.

When analyzing data, look underneath the surface figures for trends, anomalies, and patterns that can reveal hidden insights.

Accept critical thinking

Learn to think critically as you progress. Examine your assumptions and look for alternative points of view. Assume you’re looking into a business problem, such as declining sales.

Instead than jumping to conclusions, investigate the matter from all angles. Consider changes in the sector, client preferences, and even internal corporate processes. This broader viewpoint can lead to creative solutions.

Read Also:  Business Development: Strategies and Tips for Success

Experiment with logical reasoning

Also, practice logical reasoning. Improve your ability to connect the dots and build logical chains of reasoning. As if you were assembling a jigsaw puzzle, each piece must fit snugly into the whole.

Consider how numerous variables such as population growth, infrastructure, and transportation systems logically interconnect when dealing with a complex issue such as urban congestion.

Improve your problem-solving skills

Develop your problem-solving abilities as well. For example, if you’re struggling with a personal issue, such as time management, break it down into smaller components. Analyze your daily routine to discover bottlenecks and develop a strategy to overcome them.

Foster continuous learning

Finally, encourage ongoing learning by broadening your knowledge base and investigating new domains. Imagine yourself as a discerning thinker analyzing the world’s intricacies and unraveling secrets.

Remember that progress, not perfection, is the goal. Every task, question, and conundrum you solve puts you one step closer to being an analytical juggernaut. Continue to explore and study to see your critical thinking skills soar to new heights.

Applying analytical reasoning to work

Assume you are a business owner who wants to boost client happiness. An analytical thinker would collect and analyze client input to uncover frequent pain issues.

You can adopt targeted adjustments that address the fundamental causes of unhappiness by detecting patterns in feedback data.

How can you demonstrate analytical skills on a resume?

Analytical skills on your CV can set you apart and leave a lasting impression on potential employers. Make your CV into a canvas, describing specific instances where your analytical skills were put to use.

Share how you methodically dissected a challenging topic or situation, revealing insights that aided your decision-making.

If you were tasked with optimizing a company’s supply chain, for example, dig further into data on inventory levels, production rates, and distribution deadlines.

Explain how your study found a bottleneck in the distribution network, leading to a realignment suggestion that saved the organization time and money.

Storytelling is key. Create a fascinating story about how your analytical abilities helped solve a tough problem, demonstrating your abilities and attracting the reader.

Your CV should read like a motivational trip through your analytical abilities, inspiring companies with your future contributions to their organization.

What is a case study of analytical thinking?

Absolutely! Let me give you an excellent example of analytical thinking that perfectly expresses its essence. Maya, a young scientist in this example, is dedicated to discovering a long-term solution for safe drinking water in rural areas.

She performs extensive research on water supplies, toxins, and local circumstances, looking for patterns and anomalies. She develops the concept that heavy rains increase runoff, resulting in higher levels of water contamination.

Maya designs controlled experiments in a lab setting to test her idea, acquiring quantifiable information through manipulation and observation.

Maya’s investigation continues, and she explores the big picture, imagining a multi-faceted solution that involves rainwater gathering, enhanced filtration systems, and community education.

She anticipates problems and works with engineers, social workers, and community leaders to refine her ideas and ensure their viability.

Her journey exemplifies how analytical thinking can lead to transformational solutions, and it motivates us to tackle complex challenges with curiosity, diligence, and the hope that careful analysis may design a better future.

Final Thoughts

Analytical thinking is more than just a cognitive skill; it’s a mindset that empowers you to unravel complexity, make informed choices, and navigate challenges with confidence.

You will be better able to handle the intricacies of the modern world as your analytical thinking skills increase, whether in business, academics, or daily life. Accept the power of analytical thinking, and your decision-making and problem-solving abilities will soar.

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What are analytical skills? Examples and how to level up

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What are analytical skills?

Why are analytical skills important, 9 analytical skills examples, how to improve analytical skills, how to show analytical skills in a job application, the benefits of an analytical mind.

With market forecasts, performance metrics, and KPIs, work throws a lot of information at you. 

If you want to stay ahead of the curve, not only do you have to make sense of the data that comes your way — you need to put it to good use. And that requires analytical skills.

You likely use analytical thinking skills every day without realizing it, like when you solve complex problems or prioritize tasks . But understanding the meaning of analysis skills in a job description, why you should include them in your professional development plan, and what makes them vital to every position can help advance your career.

Analytical skills, or analysis skills, are the ones you use to research and interpret information. Although you might associate them with data analysis, they help you think critically about an issue, make decisions , and solve problems in any context. That means anytime you’re brainstorming for a solution or reviewing a project that didn’t go smoothly, you’re analyzing information to find a conclusion. With so many applications, they’re relevant for nearly every job, making them a must-have on your resume.

Analytical skills help you think objectively about information and come to informed conclusions. Positions that consider these skills the most essential qualification grew by 92% between 1980 and 2018 , which shows just how in-demand they are. And according to Statista, global data creation will grow to more than 180 zettabytes by 2025 — a number with 21 zeros. That data informs every industry, from tech to marketing.

Even if you don’t interact with statistics and data on the job, you still need analytical skills to be successful. They’re incredibly valuable because:

• They’re transferable: You can use analysis skills in a variety of professional contexts and in different areas of your life, like making major decisions as a family or setting better long-term personal goals.
• They build agility: Whether you’re starting a new position or experiencing a workplace shift, analysis helps you understand and adapt quickly to changing conditions. 
• They foster innovation: Analytical skills can help you troubleshoot processes or operational improvements that increase productivity and profitability.
• They make you an attractive candidate: Companies are always looking for future leaders who can build company value. Developing a strong analytical skill set shows potential employers that you’re an intelligent, growth-oriented candidate.

If the thought of evaluating data feels unintuitive, or if math and statistics aren’t your strong suits, don’t stress. Many examples of analytical thinking skills don’t involve numbers. You can build your logic and analysis abilities through a variety of capacities, such as:

1. Brainstorming

Using the information in front of you to generate new ideas is a valuable transferable skill that helps you innovate at work . Developing your brainstorming techniques leads to better collaboration and organizational growth, whether you’re thinking of team bonding activities or troubleshooting a project roadblock. Related skills include benchmarking, diagnosis, and judgment to adequately assess situations and find solutions.

2. Communication

Becoming proficient at analysis is one thing, but you should also know how to communicate your findings to your audience — especially if they don’t have the same context or experience as you. Strong communication skills like public speaking , active listening , and storytelling can help you strategize the best ways to get the message out and collaborate with your team . And thinking critically about how to approach difficult conversations or persuade someone to see your point relies on these skills. 

3. Creativity

You might not associate analysis with your creativity skills, but if you want to find an innovative approach to an age-old problem, you’ll need to combine data with creative thinking . This can help you establish effective metrics, spot trends others miss, and see why the most obvious answer to a problem isn’t always the best. Skills that can help you to think outside the box include strategic planning, collaboration, and integration.

4. Critical thinking

Processing information and determining what’s valuable requires critical thinking skills . They help you avoid the cognitive biases that prevent innovation and growth, allowing you to see things as they really are and understand their relevance. Essential skills to turn yourself into a critical thinker are comparative analysis, business intelligence, and inference.

5. Data analytics

When it comes to large volumes of information, a skilled analytical thinker can sort the beneficial from the irrelevant. Data skills give you the tools to identify trends and patterns and visualize outcomes before they impact an organization or project’s performance. Some of the most common skills you can develop are prescriptive analysis and return on investment (ROI) analysis.

6. Forecasting

Predicting future business, market, and cultural trends better positions your organization to take advantage of new opportunities or prepare for downturns. Business forecasting requires a mix of research skills and predictive abilities, like statistical analysis and data visualization, and the ability to present your findings clearly.

7. Logical reasoning

Becoming a logical thinker means learning to observe and analyze situations to draw rational and objective conclusions. With logic, you can evaluate available facts, identify patterns or correlations, and use them to improve decision-making outcomes. If you’re looking to improve in this area, consider developing inductive and deductive reasoning skills.

8. Problem-solving

Problem-solving appears in all facets of your life — not just work. Effectively finding solutions to any issue takes analysis and logic, and you also need to take initiative with clear action plans . To improve your problem-solving skills , invest in developing visualization , collaboration, and goal-setting skills.

9. Research

Knowing how to locate information is just as valuable as understanding what to do with it. With research skills, you’ll recognize and collect data relevant to the problem you’re trying to solve or the initiative you’re trying to start. You can improve these skills by learning about data collection techniques, accuracy evaluation, and metrics.

You don’t need to earn a degree in data science to develop these skills. All it takes is time, practice, and commitment. Everything from work experience to hobbies can help you learn new things and make progress. Try a few of these ideas and stick with the ones you enjoy:

1. Document your skill set

The next time you encounter a problem and need to find solutions, take time to assess your process. Ask yourself:

• What facts are you considering?
• Do you ask for help or research on your own? What are your sources of advice?
• What does your brainstorming process look like?
• How do you make and execute a final decision?
• Do you reflect on the outcomes of your choices to identify lessons and opportunities for improvement?
• Are there any mistakes you find yourself making repeatedly?
• What problems do you constantly solve easily? 

These questions can give insight into your analytical strengths and weaknesses and point you toward opportunities for growth.

2. Take courses

Many online and in-person courses can expand your logical thinking and analysis skills. They don’t necessarily have to involve information sciences. Just choose something that trains your brain and fills in your skills gaps . 

Consider studying philosophy to learn how to develop your arguments or public speaking to better communicate the results of your research. You could also work on your hard skills with tools like Microsoft Excel and learn how to crunch numbers effectively. Whatever you choose, you can explore different online courses or certification programs to upskill. 

3. Analyze everything

Spend time consciously and critically evaluating everything — your surroundings, work processes, and even the way you interact with others. Integrating analysis into your day-to-day helps you practice. The analytical part of your brain is like a muscle, and the more you use it, the stronger it’ll become. 

After reading a book, listening to a podcast, or watching a movie, take some time to analyze what you watched. What were the messages? What did you learn? How was it delivered? Taking this approach to media will help you apply it to other scenarios in your life. 

If you’re giving a presentation at work or helping your team upskill , use the opportunity to flex the analytical side of your brain. For effective teaching, you’ll need to process and analyze the topic thoroughly, which requires skills like logic and communication. You also have to analyze others’ learning styles and adjust your teachings to match them. 

5. Play games

Spend your commute or weekends working on your skills in a way you enjoy. Try doing logic games like Sudoku and crossword puzzles during work breaks to foster critical thinking. And you can also integrate analytical skills into your existing hobbies. According to researcher Rakesh Ghildiyal, even team sports like soccer or hockey will stretch your capacity for analysis and strategic thinking . 

6. Ask questions

According to a study in Tr ends in Cognitive Sciences, being curious improves cognitive function , helping you develop problem-solving skills, retention, and memory. Start speaking up in meetings and questioning the why and how of different decisions around you. You’ll think more critically and even help your team find breakthrough solutions they otherwise wouldn’t.

7.Seek advice

If you’re unsure what analytical skills you need to develop, try asking your manager or colleagues for feedback . Their outside perspective offers insight you might not find within, like patterns in. And if you’re looking for more consistent guidance, talking to a coach can help you spot weaknesses and set goals for the long term.

8. Pursue opportunities

Speak to your manager about participating in special projects that could help you develop and flex your skills. If you’d like to learn about SEO or market research, ask to shadow someone in the ecommerce or marketing departments. If you’re interested in business forecasting, talk to the data analysis team. Taking initiative demonstrates a desire to learn and shows leadership that you’re eager to grow. 

Shining a spotlight on your analytical skills can help you at any stage of your job search. But since they take many forms, it’s best to be specific and show potential employers exactly why and how they make you a better candidate. Here are a few ways you can showcase them to the fullest:

1. In your cover letter

Your cover letter crafts a narrative around your skills and work experience. Use it to tell a story about how you put your analytical skills to use to solve a problem or improve workflow. Make sure to include concrete details to explain your thought process and solution — just keep it concise. Relate it back to the job description to show the hiring manager or recruiter you have the qualifications necessary to succeed.

2. On your resume

Depending on the type of resume you’re writing, there are many opportunities to convey your analytical skills to a potential employer. You could include them in sections like: 

• Professional summary: If you decide to include a summary, describe yourself as an analytical person or a problem-solver, whichever relates best to the job posting. 
• Work experience: Describe all the ways your skill for analysis has helped you perform or go above and beyond your responsibilities. Be sure to include specific details about challenges and outcomes related to the role you’re applying for to show how you use those skills. 
• Skills section: If your resume has a skill-specific section, itemize the analytical abilities you’ve developed over your career. These can include hard analytical skills like predictive modeling as well as interpersonal skills like communication.

3. During a job interview

As part of your interview preparation , list your professional accomplishments and the skills that helped along the way, such as problem-solving, data literacy, or strategic thinking. Then, pull them together into confident answers to common interview questions using the STAR method to give the interviewer a holistic picture of your skill set.

Developing analytical skills isn’t only helpful in the workplace. It’s essential to life. You’ll use them daily whenever you read the news, make a major purchase, or interact with others. Learning to critically evaluate information can benefit your relationships and help you feel more confident in your decisions, whether you’re weighing your personal budget or making a big career change .

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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.

Get Advice From The Verywell Mind Podcast

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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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4 Ways to Improve Your Analytical Skills

• 07 Jan 2021

Data is ubiquitous. It’s collected at every purchase made, flight taken, ad clicked, and social media post liked—which means it’s never been more crucial to understand how to analyze it.

“Never before has so much data about so many different things been collected and stored every second of every day,” says Harvard Business School Professor Jan Hammond in the online course Business Analytics .

The volume of data you encounter can be overwhelming and raise several questions: Can I trust the data’s source? Is it structured in a way that makes sense? What story does it tell, and what actions does it prompt?

Data literacy and analytical skills can enable you to answer these questions and not only make sense of raw data, but use it to drive impactful change at your organization.

Here’s a look at what it means to be data literate and four ways to improve your analytical skills.

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What Is Data Literacy?

Data literacy is the ability to analyze, interpret, and question data. A dataset is made up of numerous data points that, when viewed together, tell a story.

Before conducting an analysis, it’s important to ensure your data’s quality and structure is in accordance with your organization’s needs.

“In order to transform data into actionable information, you first need to evaluate its quality,” says Professor Dustin Tingley in the Harvard Online course Data Science Principles . “But evaluating the quality of your data is just the first step. You’ll also need to structure your data. Without structure, it’s nearly impossible to extract any information.”

When you’re able to look at quality data, structure it, and analyze it, trends emerge. The next step is to reflect on your analysis and take action.

Tingley shares several questions to ask yourself once you’ve analyzed your dataset: “Did all the steps I took make sense? If so, how should I respond to my analysis? If not, what should I go back and improve?”

For example, you may track users who click a button to download an e-book from your website.

After ensuring your data’s quality and structuring it in a way that makes sense, you begin your analysis and find that a user’s age is positively correlated with their likelihood to click. What story does this trend tell? What does it say about your users, product offering, and business strategy?

To answer these questions, you need strong analytical skills, which you can develop in several ways.

Related: Business Analytics: What It Is & Why It’s Important

How to Improve Your Analytical Skills

Analysis is an important skill to have in any industry because it enables you to support decisions with data, learn more about your customers, and predict future trends.

Key analytical skills for business include:

• Visualizing data
• Determining the relationship between two or more variables
• Forming and testing hypotheses
• Performing regressions using statistical programs, such as Microsoft Excel
• Deriving actionable conclusions from data analysis

If you want to provide meaningful conclusions and data-based recommendations to your team, here are four ways to bolster your analytical skills.

Related: How to Learn Business Analytics Without A Business Background

1. Consider Opposing Viewpoints

While engaging with opposing viewpoints can help you expand your perspective, combat bias, and show your fellow employees their opinions are valued, it can also be a useful way to practice analytical skills.

When analyzing data, it’s crucial to consider all possible interpretations and avoid getting stuck in one way of thinking.

For instance, revisit the example of tracking users who click a button on your site to download an e-book. The data shows that the user’s age is positively correlated with their likelihood to click the button; as age increases, downloads increase, too. At first glance, you may interpret this trend to mean that a user chooses to download the e-book because of their age.

This conclusion, however, doesn’t take into consideration the vast number of variables that change with age. For instance, perhaps the real reason your older users are more likely to download the e-book is their higher level of responsibility at work, higher average income, or higher likelihood of being parents.

This example illustrates the need to consider multiple interpretations of data, and specifically shows the difference between correlation (the trending of two or more variables in the same direction) and causation (when a trend in one variable causes a trend to occur in one or more other variables).

“Data science is built on a foundation of critical thinking,” Tingley says in Data Science Principles . “From the first step of determining the quality of a data source to determining the accuracy of an algorithm, critical thinking is at the heart of every decision data scientists—and those who work with them—make.”

To practice this skill, challenge yourself to question your assumptions and ask others for their opinions. The more you actively engage with different viewpoints, the less likely you are to get stuck in a one-track mindset when analyzing data.

2. Play Games or Brain Teasers

If you’re looking to sharpen your skills on a daily basis, there are many simple, enjoyable ways to do so.

Games, puzzles, and stories that require visualizing relationships between variables, examining situations from multiple angles, and drawing conclusions from known data points can help you build the skills necessary to analyze data.

Some fun ways to practice analytical thinking include:

• Crossword puzzles
• Mystery novels
• Logic puzzles
• Strategic board games or card games

These options can supplement your analytics coursework and on-the-job experience. Some of them also allow you to spend time with friends or family. Try engaging with one each day to hone your analytical mindset.

Related: 3 Examples of Business Analytics in Action

3. Take an Online Analytics Course

Whether you want to learn the basics, brush up on your skills, or expand your knowledge, taking an analytics course is an effective way to improve. A course can enable you to focus on the content you want to learn, engage with the material presented by a professional in the field, and network and interact with others in the data analytics space.

For a beginner, courses like Harvard Online's Data Science Principles can provide a foundation in the language of data. A more advanced course, like Harvard Online's Data Science for Business , may be a fit if you’re looking to explore specific facets of analytics, such as forecasting and machine learning. If you’re interested in hands-on applications of analytical formulas, a course like HBS Online's Business Analytics could be right for you. The key is to understand what skills you hope to gain, then find a course that best fits your needs.

If you’re balancing a full-time job with your analytics education, an online format may be a good choice . It offers the flexibility to engage with course content whenever and wherever is most convenient for you.

An online course may also present the opportunity to network and build relationships with other professionals devoted to strengthening their analytical skills. A community of like-minded learners can prove to be an invaluable resource as you learn and advance your career.

Related: Is An Online Business Analytics Course Worth It?

4. Engage With Data

Once you have a solid understanding of data science concepts and formulas, the next step is to practice. Like any skill, analytical skills improve the more you use them.

Mock datasets—which you can find online or create yourself—present a low-risk option for putting your skills to the test. Import the data into Microsoft Excel, then explore: make mistakes, try that formula you’re unsure of, and ask big questions of your dataset. By testing out different analyses, you can gain confidence in your knowledge.

Once you’re comfortable, engage with your organization’s data. Because these datasets have inherent meaning to your business's financial health, growth, and strategic direction, analyzing them can produce evidence and insights that support your decisions and drive change at your organization.

Investing in Your Data Literacy

As data continues to be one of businesses’ most valuable resources, taking the time and effort to build and bolster your analytical skill set is vital.

“Much more data are going to be available; we’re only seeing the beginning now,” Hammond says in a previous article . “If you don’t use the data, you’re going to fall behind. People that have those capabilities—as well as an understanding of business contexts—are going to be the ones that will add the most value and have the greatest impact.”

Are you interested in furthering your data literacy? Download our Beginner’s Guide to Data & Analytics to learn how you can leverage the power of data for professional and organizational success.

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What Are Analytical Skills? (Definition, Examples, And Resume Tips)

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Summary. Analytical skills are used to assess situations and make plans to overcome obstacles, usually in structured, logical ways.

There are a few skill sets that are important to hone no matter what industry you work in, and analytical skills are one of those.

In this article, you’ll learn about several different types of analytical skills, how to highlight them when applying for a job, and how to improve your analytical skills.

Key Takeaways

Analytical skills are necessary for figuring out how to overcome obstacles and make wise decisions.

Some examples of analytical skills are data analysis, research, critical thinking, communication, problem-solving, visualization, and creativity.

You should highlight your analytical skills on your resume , in your cover letter , and during your interviews.

It’s important to work to grow your analytical skills throughout your career.

Types of Analytical Skills

Additional analytical skills, examples of how to showcase your analytical skills, examples of resumes that showcase analytical skills, example of analytical skills in a cover letter, examples of analytical skills in a job interview, examples of analytical skills on the job, how to improve your analytical skills, analytical skills faqs, final thoughts.

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Analytical skills are the qualities you possess that help you to assess situations rationally, create effective plans, and overcome obstacles. Analytical thinkers can separate themselves from their emotions in order to work effectively. They usually utilize a process to break down large problems into smaller issues to tackle.

There are a variety of traits and abilities that fall under the heading of strong analytical skills. Drawing attention to your strengths in analytical thinking can grab an employer’s attention, and land you an interview or a promotion.

Some analytical skills may be more relevant to your field than others. Take some time to consider which qualities will be the most valuable to your potential employers. Below are some great examples of important analytical thinking that hiring managers look for on your resume .

Data analysis. Taking in information, making sense of it logically, and using it to the best of your abilities is an important step in making calculated decisions.

Having impressive skills in data analysis greatly supports analytical thinking. Considering they share a root word in common, it makes sense that these skills rely on each other.

Data analysis could mean very different things for varying occupations.

If you work for a retail company, it could mean:

Examining quarterly clothing sales

Considering why the numbers are what they are, and if that’s satisfactory

Researching possibilities for how to increase revenue

Make decisions about whether to stay on the current trajectory or make changes to increase sales

Following-up

If you own a blog , it could mean:

Reading your website’s Google Analytics for each post

Determining increases or decreases in traffic and why that may be

Including traffic data points in a spreadsheet to consider trends

Coming up with strategies to boost website traffic based on success trends

Continually updating analytic data

Research . Conducting worthwhile research is very important in building viable solutions. Once you’ve noticed an issue or a way things could be done better, you must look for solutions towards improvement.

That depends on research. Luckily, we live in the age of the internet. Quite literally, we have a world of information available at our fingertips. You’re living proof of this — just look at what you’re doing right now by reading this article.

Carrying out research on important analytical skills, in order to improve your resume and employee profile. Using detailed research in your work style enhances your analytical problem-solving process.

Research involves:

Utilizing reliable resources

Fact-checking

Having an informational goal in mind

Attention to detail

Staying focused

Organizing data

Effectively presenting results

Critical thinking . Critical thinking is the boat that keeps the rest of your analytical skills afloat. It’s largely about having logic and reason at work.

It also involves always being open to learning more. Critical thinkers draw practical connections to further a company’s success. This is an extremely valuable skill for employers because critical thinkers can:

Determine why issues arise

Assess the strengths and weaknesses of a particular strategy

Deciphering complex issues into smaller steps

Develop logical plans

Efficiently solve problems

Articulate their thinking to others

Communication . You may have the ability to deep-dive into research and think critically about the results. However, this isn’t very helpful without being able to accurately translate these findings to others.

Communication is key to developing workplace relations and completing projects productively. Throughout the analytical problem-solving process, be sure to keep your co-workers and supervisors in the loop about everything you’re doing and the conclusions you’re drawing. They could have input that affects your course of action or expands on your ideas.

Communication skills involve:

Friendliness

Emotion control

Listening to others

Asking questions

Accepting and returning feedback

Paying attention to non-verbal communication

Coordination

Presentation

Following-up on past interactions

Problem-solving. Problem-solving skills may sound synonymous with analytical, but really, it’s just another skill involved in the analytical process. Employers seek to hire applicants who are adept at problem-solving to handle any unexpected circumstances or issues.

After identifying an issue and conducting proper research, brainstorming potential solutions is next. You use problem-solving abilities to organize all the information you’ve uncovered to produce a logical plan for action.

Problem-solving skills involve:

Active listening

Data analysis

Consulting multiple sources

Strong communication

Formulating strategy

Time management

Interpersonal skills

Decision-making

Visualization. One of the traits that make for a strong analytical thinker is a visualization for an end goal. Having a clear vision in mind is necessary for creating a plan that works well. After all, you have to know what outcome you’re looking for to analyze whether it was successful later.

Without an objective, your research and strategy can become disorganized. Throughout the analytical process, keeping your original goal in mind can make your analytical work more productive.

Goal visualization involves:

Taking data into account

Acknowledging your team’s strengths and weaknesses

Deciding what your team’s overall goal is

Discussing the best routes for achieving this objective

Creativity . Creative thinkers have the ability to formulate new ideas and ways of doing things. This can be extremely productive when using analytical reasoning skills.

A large component to coming up with effective solutions to problems that involve innovation. Creative employees make groundbreaking improvements from problems.

Creativity involves:

Imagination

Keeping goals in mind

Problem-solving

Experimentation

Transforming ideas into action

Other useful analytical skills include:

Time-Management

Recognizing achievements

Providing feedback

Computer skills

Clarification

Organization

There are four main ways to showcase your analytical skills as part of your job search :

On your resume

In your cover letter

In a job interview

47 Martin Ln. Orlando, FL , 44587 (771)-409-3376 [email protected] Shelby Malcolm Passionate and creative graphic designer with 4 years of experience and a B.A. in Design. Strong communication and problem-solving skills. SKILLS Adobe Photoshop Adobe Illustrator Proficient in Inkscape Creative Dependable Fast learner Problem-solving EXPERIENCE Ecosphere Design Lab, Orlando, FL — Graphic Designer March 2018 – PRESENT Outlining design concepts Coordinating with a team of 6 Direct client requests Illustration Considering industry trends Creating a range of ideas Promoted from Junior graphic designer after the first six months Innovation Graphics, Orlando, FL — Junior Graphic Designer January 2015 – January 2018 Communicating with clients Providing customer service Brainstorming idea for advertisements and logos Utilizing revision when needed Awarded a salary increase of 2% after the first year EDUCATION The University of Tampa, Tampa, FL — B.A. in Design August 2011 – May 2015

Jacob Jones 912 W Evans St. Sedona, AZ , 98211 (398)-197-1126 [email protected] LinkIn.com/in/JacobJones Organized and meticulous social media manager with 5+ years of experience. B.A. in Human Studies from the University of Arizona. Strengths in interpersonal skills and branding. Professional Experience Liberty Public Relations , Sedona, AZ Social Media Manager September 2017-Present Scheduled and coordinated meetings Interacted directly with clients Coordinated with marketing teams Manager profiles for several prominent clients Created detailed plans for success with milestones of completion Handled arising PR issues Awarded $2,500 bonus after the first year Gold Star Media Management , Sedona, AZ Social Media Marketing Intern, June 2016– August 2017 Memo creation and direction Email management Organizing social media post schedules Analyzing post success Collaborated on a team to design branding Aided in brand creation for up-and-coming companies Skills Social media Marketing Branding Google analytics HTML Attention to detail Critical thinking skills Adaptable Education University of Arizona, Tucson, AZ BA in Human Studies, May 2016 GPA: 3.5 out of 4.0

Nicholas Phillips Flexible and outgoing investigative journalist . Possess a Bachelor’s in English and a Masters in Journalism. Strong skills in creative thinking and problem-solving. 22 Main St. Houston, TX , 23014 (129)-828-1192 [email protected] NicholasPhillips.com EXPERIENCE XYZ News Channel, Houston, TX — Investigative Journalist April 2016 – PRESENT Search out newsworthy stories Conduct relevant research Communicating with co-workers and sources Fact-checking Interviewing subjects Developing story outlines Adhering to journalistic integrity Promoting the success and viewership of XYZ Awarded with two raises totaling $16,000 Houston Local News, Houston, TX — Journalist January 2014-April 2016 Thinking creatively to discover eye-catching stories and events Gathering information and subjects via extensive research Assessing lead quality Meeting set deadlines Coordinating with team of 10 Networking to establish working relationships Around Town Quarterly, Houston, TX — Journalist Intern June 2013- January 2014 Assisting in administrative work Conducting assigned research for topics Contributing to weekly brainstorms Editing and proofreading Assisting in interviews EDUCATION The University of Texas, Austin, TX — Master’s in Journalism September 2011 – June 2013 The University of Tennessee, Knoxville, TN– Bachelor’s in English August 2007-May2011. SKILLS Research Writing Bilingual Presentation Integrity Flexible Sociable LANGUAGES Fluency in English and Spanish

During my time as a Marketing Manager for XYZ Inc., I made it my mission to cut the budget while still growing our digital marketing presence. By recognizing that 80% of our traffic was coming from 20% of our content creators, I made the decision to cut our writing staff down significantly. What we saw was a 70% drop in spending on content creation, while traffic grew by an average of 24% monthly. Other accomplishments from this role include: Performed competitor keyword research to increase our organic reach by 29% YoY Developed a website design in tandem with product team and based on user feedback to increase engagement by 76% Identified and implemented best practices for email marketing and affiliate campaigns to increase conversion rates by 15% and revenue by 11%

In a job interview, you’ll hear a lot of questions designed to test your analytical skills. Let’s go over a couple of common interview questions , along with example answers that clearly highlight your supreme analytical powers:

For me, it’s all about maximizing both efficiency and effectiveness. I independently track how much time each of my tasks takes, and what the return on that time investment is. For example, when my team had to code a whole new content cluster using a wildly different style than our home page , I started by assessing which features were most sought after by users. I then implemented those changes and used A/B testing to determine the effectiveness. I found that adding trailing social engagement buttons along the left-hand side of the page upped engagement by over 20%, and it was a relatively simple thing to do. When you see that a huge chunk of your results come from small changes, it becomes easier to prioritize and identify the successful things you’re doing.

When I’m facing a problem I haven’t seen before, my first step is research. Whether that means looking online for tutorials covering the topic or speaking to an expert in the company, fact-finding is critical. Then, I like to implement imperfect changes — I say “imperfect” because I find many people suffer from “analysis paralysis.” Instead, I’m happier to put out the minimal viable product and iterate from there. A lot of the time, the issues you expect from a problem never arise, and ones you never consider crop up unannounced. That’s why I feel more comfortable having an actual product to tweak and perfect, rather than trying to find the perfect solution the first time.

Whether you’re hoping to earn a promotion or leverage your analytical skills into a new job, one of the best ways to showcase your analytical skills is to let others do it for you. By that we mean you should make it so clear that you’re an analytical juggernaut at work that your supervisors recognize it as your stand-out trait.

In practice, that can take a few different forms. Here are some examples of how you can show off your analytical skills in your work:

Take on leadership roles.

Volunteer for assignments that give you a chance to hone and show off your capacity for analysis.

Go out of your way to improve an inefficient or ineffective process.

There’s not a job out there that doesn’t utilize and benefit from analytical skills. Go out there and identify problems, offer solutions, and be critical with your evaluations. That’s how you wind up with a letter of recommendation that touts your ability to analyze situations effectively.

An employee with keen analytical skills has a bright future ahead of them. No matter what field or industry you work in, developing your analytical skills can help you achieve your career goals.

To improve your analytical skills:

Take tests. There are tons of free resources online for testing your analytical skills and ability to think critically. These are often math- or logic-based, and they can help train your brain to approach problems strategically.

Step into leadership roles. Leaders need a whole host of attributes to succeed , but analytical skills are a critical part of the job. Look for opportunities to lead projects to put your analytical skills to the test.

Play games. Not just any games, though. Think logic games like Rubik’s Cubes, Sudoku puzzles, and Chess. These games will strengthen your analytical skills while having fun. Plus, studies have shown that engaging in cognitively stimulating activities like these reduces your risk of cognitive decline and dementia.

Enroll in classes. It doesn’t even really matter what subject you choose to study, although if your goal is career growth, it should pertain to your job in some way. The important part is that when you’re learning new things, you’re forcing your brain out of its cognitive comfort zone.

Find a mentor . This is good advice regardless of what skills you’re trying to develop. A mentor in your field who has successfully weathered the challenges of your role is like a cheat code for strengthening your analytical skills.

Become a close reader. If you remember close reading from your high school English class, you’re probably groaning right now. But it turns out that was one of the truly valuable strategies you were taught in school.

You don’t need to be reading a text to be a close reader . When you watch movies and shows, see an advertisement, or listen to a politician’s speech, do your best to read between the lines. Look for plot holes, assess why an ad is effective (or not), and pay attention to what the politician isn’t saying.

What are examples of analytical skills?

Some examples of analytical skills include:

Critical thinking

Communication

Visualization

What type of skills are analytical skills?

Analytical skills are soft skills that allow you to collect and analyze information in a way that allows you to solve problems and make decisions well.

You use analytical skills in your daily work tasks, when you’re making schedules, and when you’re making important management decisions, to give just a few examples.

How do you say you have good analytical skills?

You say you have good analytical skills by providing examples of times you used your analytical skills. You can do this in your resume, in your cover letter, and during your interview. You can also showcase your analytical skills while you work.

What jobs use analytical skills?

Some jobs that use analytical skills include software engineer, cybersecurity analyst, and accountant. Many people in the finance, technological, and scientific industries use analytical skills in their day-to-day roles.

Analytical skills are useful in a variety of roles and positions, across a variety of industries. You can showcase your experience with them on your resume by listing specific examples of times that you have solved problems or addressed situations using analytical skills.

Harvard Business School Online – 4 Ways to Improve Your Analytical Skills

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Sky Ariella is a professional freelance writer, originally from New York. She has been featured on websites and online magazines covering topics in career, travel, and lifestyle. She received her BA in psychology from Hunter College.

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How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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Analytical Problem-Solving

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This chapter deals with the concept of “problem” in Analytical Chemistry, and is concerned with the impact and consequences, both internal and external, of solving analytical problems. The analytical problem as a target has invigorated Classical Analytical Chemistry with new challenges and goals beyond its chemical metrological role; also, it has led to analytical chemical knowledge crossing further traditional boundaries and reaching society at large to respond to the increasing needs for socio-economically useful answers. The ubiquity of the analytical problem in the analytical chemical and socio-economic realms has turned it into their interface and main link. So much so that solving analytical problems has become a priority goal in fulfilling the practical requirements of Analytical Chemistry; one that has required expanding the scope of representativeness to accommodate the results to the client’s requirements. This chapter describes the steps involved in the analytical problem-solving process, and the potential coincidence or divergence between the information required by the client and that actually delivered by the analytical chemist. Also, it relates “quality”, a general concept discussed at length in Chap.  8 , to “analytical quality”, which constitutes the central core of the topic: solving analytical problems.

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Valcárcel Cases, M., López-Lorente, Á.I., López-Jiménez, M.Á. (2018). Analytical Problem-Solving. In: Foundations of Analytical Chemistry. Springer, Cham. https://doi.org/10.1007/978-3-319-62872-1_7

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Problem Solving, Critical Thinking, and Analytical Reasoning Skills Sought by Employers

In this section:

Problem Solving

• Critical Thinking

Analytical Reasoning

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Critical thinking, analytical reasoning, and problem-solving skills are required to perform well on tasks expected by employers. 1 Having good problem-solving and critical thinking skills can make a major difference in a person’s career. 2

Every day, from an entry-level employee to the Chairman of the Board, problems need to be resolved. Whether solving a problem for a client (internal or external), supporting those who are solving problems, or discovering new problems to solve, the challenges faced may be simple/complex or easy/difficult.

A fundamental component of every manager's role is solving problems. So, helping students become a confident problem solver is critical to their success; and confidence comes from possessing an efficient and practiced problem-solving process.

Employers want employees with well-founded skills in these areas, so they ask four questions when assessing a job candidate 3 :

• Evaluation of information: How well does the applicant assess the quality and relevance of information?
• Analysis and Synthesis of information: How well does the applicant analyze and synthesize data and information?
• Drawing conclusions: How well does the applicant form a conclusion from their analysis?
• Acknowledging alternative explanations/viewpoints: How well does the applicant consider other options and acknowledge that their answer is not the only perspective?

When an employer says they want employees who are good at solving complex problems, they are saying they want employees possessing the following skills:

• Analytical Thinking — A person who can use logic and critical thinking to analyze a situation.
• Critical Thinking – A person who makes reasoned judgments that are logical and well thought out.
• Initiative — A person who will step up and take action without being asked. A person who looks for opportunities to make a difference.
• Creativity — A person who is an original thinker and have the ability to go beyond traditional approaches.
• Resourcefulness — A person who will adapt to new/difficult situations and devise ways to overcome obstacles.
• Determination — A person who is persistent and does not give up easily.
• Results-Oriented — A person whose focus is on getting the problem solved.

Two of the major components of problem-solving skills are critical thinking and analytical reasoning.  These two skills are at the top of skills required of applicants by employers.

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Critical Thinking 4

“Mentions of critical thinking in job postings have doubled since 2009, according to an analysis by career-search site Indeed.com.” 5 Making logical and reasoned judgments that are well thought out is at the core of critical thinking. Using critical thinking an individual will not automatically accept information or conclusions drawn from to be factual, valid, true, applicable or correct. “When students are taught how to use critical thinking to tap into their creativity to solve problems, they are more successful than other students when they enter management-training programs in large corporations.” 6

A strong applicant should question and want to make evidence-based decisions. Employers want employees who say things such as: “Is that a fact or just an opinion? Is this conclusion based on data or gut feel?” and “If you had additional data could there be alternative possibilities?” Employers seek employees who possess the skills and abilities to conceptualize, apply, analyze, synthesize, and evaluate information to reach an answer or conclusion.

Employers require critical thinking in employees because it increases the probability of a positive business outcome. Employers want employees whose thinking is intentional, purposeful, reasoned, and goal directed.

Recruiters say they want applicants with problem-solving and critical thinking skills. They “encourage applicants to prepare stories to illustrate their critical-thinking prowess, detailing, for example, the steps a club president took to improve attendance at weekly meetings.” 7

Employers want students to possess analytical reasoning/thinking skills — meaning they want to hire someone who is good at breaking down problems into smaller parts to find solutions. “The adjective, analytical, and the related verb analyze can both be traced back to the Greek verb, analyein — ‘to break up, to loosen.’ If a student is analytical, you are good at taking a problem or task and breaking it down into smaller elements in order to solve the problem or complete the task.” 9

Analytical reasoning connotes a person's general aptitude to arrive at a logical conclusion or solution to given problems. Just as with critical thinking, analytical thinking critically examines the different parts or details of something to fully understand or explain it. Analytical thinking often requires the person to use “cause and effect, similarities and differences, trends, associations between things, inter-relationships between the parts, the sequence of events, ways to solve complex problems, steps within a process, diagraming what is happening.” 10

Analytical reasoning is the ability to look at information and discern patterns within it. “The pattern could be the structure the author of the information uses to structure an argument, or trends in a large data set. By learning methods of recognizing these patterns, individuals can pull more information out of a text or data set than someone who is not using analytical reasoning to identify deeper patterns.” 11

Employers want employees to have the aptitude to apply analytical reasoning to problems faced by the business. For instance, “a quantitative analyst can break down data into patterns to discern information, such as if a decrease in sales is part of a seasonal pattern of ups and downs or part of a greater downward trend that a business should be worried about. By learning to recognize these patterns in both numbers and written arguments, an individual gains insights into the information that someone who simply takes the information at face value will miss.” 12

Managers with excellent analytical reasoning abilities are considered good at, “evaluating problems, analyzing them from more than one angle and finding a solution that works best in the given circumstances”. 13 Businesses want managers who can apply analytical reasoning skills to meet challenges and keep a business functioning smoothly

A person with good analytical reasoning and pattern recognition skills can see trends in a problem much easier than anyone else.

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Real World Problem-Solving

Real world problem-solving (RWPS) is what we do every day. It requires flexibility, resilience, resourcefulness, and a certain degree of creativity. A crucial feature of RWPS is that it involves continuous interaction with the environment during the problem-solving process. In this process, the environment can be seen as not only a source of inspiration for new ideas but also as a tool to facilitate creative thinking. The cognitive neuroscience literature in creativity and problem-solving is extensive, but it has largely focused on neural networks that are active when subjects are not focused on the outside world, i.e., not using their environment. In this paper, I attempt to combine the relevant literature on creativity and problem-solving with the scattered and nascent work in perceptually-driven learning from the environment. I present my synthesis as a potential new theory for real world problem-solving and map out its hypothesized neural basis. I outline some testable predictions made by the model and provide some considerations and ideas for experimental paradigms that could be used to evaluate the model more thoroughly.

1. Introduction

In the Apollo 13 space mission, astronauts together with ground control had to overcome several challenges to bring the team safely back to Earth (Lovell and Kluger, 2006 ). One of these challenges was controlling carbon dioxide levels onboard the space craft: “For 2 days straight [they] had worked on how to jury-rig the Odysseys canisters to the Aquarius's life support system. Now, using materials known to be available onboard the spacecraft—a sock, a plastic bag, the cover of a flight manual, lots of duct tape, and so on—the crew assembled a strange contraption and taped it into place. Carbon dioxide levels immediately began to fall into the safe range” (Team, 1970 ; Cass, 2005 ).

The success of Apollo 13's recovery from failure is often cited as a glowing example of human resourcefulness and inventiveness alongside more well-known inventions and innovations over the course of human history. However, this sort of inventive capability is not restricted to a few creative geniuses, but an ability present in all of us, and exemplified in the following mundane example. Consider a situation when your only suit is covered in lint and you do not own a lint remover. You see a roll of duct tape, and being resourceful you reason that it might be a good substitute. You then solve the problem of lint removal by peeling a full turn's worth of tape and re-attaching it backwards onto the roll to expose the sticky side all around the roll. By rolling it over your suit, you can now pick up all the lint.

In both these examples (historic as well as everyday), we see evidence for our innate ability to problem-solve in the real world. Solving real world problems in real time given constraints posed by one's environment are crucial for survival. At the core of this skill is our mental capability to get out of “sticky situations” or impasses, i.e., difficulties that appear unexpectedly as impassable roadblocks to solving the problem at hand. But, what are the cognitive processes that enable a problem solver to overcome such impasses and arrive at a solution, or at least a set of promising next steps?

A central aspect of this type of real world problem solving, is the role played by the solver's surrounding environment during the problem-solving process. Is it possible that interaction with one's environment can facilitate creative thinking? The answer to this question seems somewhat obvious when one considers the most famous anecdotal account of creative problem solving, namely that of Archimedes of Syracuse. During a bath, he found a novel way to check if the King's crown contained non-gold impurities. The story has traditionally been associated with the so-called “Eureka moment,” the sudden affective experience when a solution to a particularly thorny problem emerges. In this paper, I want to temporarily turn our attention away from the specific “aha!” experience itself and take particular note that Archimedes made this discovery, not with his eyes closed at a desk, but in a real-world context of a bath 1 . The bath was not only a passive, relaxing environment for Archimedes, but also a specific source of inspiration. Indeed it was his noticing the displacement of water that gave him a specific methodology for measuring the purity of the crown; by comparing how much water a solid gold bar of the same weight would displace as compared with the crown. This sort of continuous environmental interaction was present when the Apollo 13 engineers discovered their life-saving solution, and when you solved the suit-lint-removal problem with duct tape.

The neural mechanisms underlying problem-solving have been extensively studied in the literature, and there is general agreement about the key functional networks and nodes involved in various stages of problem-solving. In addition, there has been a great deal of work in studying the neural basis for creativity and insight problem solving, which is associated with the sudden emergence of solutions. However, in the context of problem-solving, creativity, and insight have been researched as largely an internal process without much interaction with and influence from the external environment (Wegbreit et al., 2012 ; Abraham, 2013 ; Kounios and Beeman, 2014 ) 2 . Thus, there are open questions of what role the environment plays during real world problem-solving (RWPS) and how the brain enables the assimilation of novel items during these external interactions.

In this paper, I synthesize the literature on problem-solving, creativity and insight, and particularly focus on how the environment can inform RWPS. I explore three environmentally-informed mechanisms that could play a critical role: (1) partial-cue driven context-shifting, (2) heuristic prototyping and learning novel associations, and (3) learning novel physical inferences. I begin first with some intuitions about real world problem solving, that might help ground this discussion and providing some key distinctions from more traditional problem solving research. Then, I turn to a review of the relevant literature on problem-solving, creativity, and insight first, before discussing the three above-mentioned environmentally-driven mechanisms. I conclude with a potential new model and map out its hypothesized neural basis.

2. Problem solving, creativity, and insight

2.1. what is real world problem-solving.

Archimedes was embodied in the real world when he found his solution. In fact, the real world helped him solve the problem. Whether or not these sorts of historic accounts of creative inspiration are accurate 3 , they do correlate with some of our own key intuitions about how problem solving occurs “in the wild.” Real world problem solving (RWPS) is different from those that occur in a classroom or in a laboratory during an experiment. They are often dynamic and discontinuous, accompanied by many starts and stops. Solvers are never working on just one problem. Instead, they are simultaneously juggling several problems of varying difficulties and alternating their attention between them. Real world problems are typically ill-defined, and even when they are well-defined, often have open-ended solutions. Coupled with that is the added aspect of uncertainty associated with the solver's problem solving strategies. As introduced earlier, an important dimension of RWPS is the continuous interaction between the solver and their environment. During these interactions, the solver might be inspired or arrive at an “aha!” moment. However, more often than not, the solver experiences dozens of minor discovery events— “hmmm, interesting…” or “wait, what?…” moments. Like discovery events, there's typically never one singular impasse or distraction event. The solver must iterate through the problem solving process experiencing and managing these sorts of intervening events (including impasses and discoveries). In summary, RWPS is quite messy and involves a tight interplay between problem solving, creativity, and insight. Next, I explore each of these processes in more detail and explicate a possible role of memory, attention, conflict management and perception.

2.2. Analytical problem-solving

In psychology and neuroscience, problem-solving broadly refers to the inferential steps taken by an agent 4 that leads from a given state of affairs to a desired goal state (Barbey and Barsalou, 2009 ). The agent does not immediately know how this goal can be reached and must perform some mental operations (i.e., thinking) to determine a solution (Duncker, 1945 ).

The problem solving literature divides problems based on clarity (well-defined vs. ill-defined) or on the underlying cognitive processes (analytical, memory retrieval, and insight) (Sprugnoli et al., 2017 ). While memory retrieval is an important process, I consider it as a sub-process to problem solving more generally. I first focus on analytical problem-solving process, which typically involves problem-representation and encoding, and the process of forming and executing a solution plan (Robertson, 2016 ).

2.2.1. Problem definition and representation

An important initial phase of problem-solving involves defining the problem and forming a representation in the working memory. During this phase, components of the prefrontal cortex (PFC), default mode network (DMN), and the dorsal anterior cingulate cortex (dACC) have been found to be activated. If the problem is familiar and well-structured, top-down executive control mechanisms are engaged and the left prefrontal cortex including the frontopolar, dorso-lateral (dlPFC), and ventro-lateral (vlPFC) are activated (Barbey and Barsalou, 2009 ). The DMN along with the various structures in the medial temporal lobe (MTL) including the hippocampus (HF), parahippocampal cortex, perirhinal and entorhinal cortices are also believed to have limited involvement, especially in episodic memory retrieval activities during this phase (Beaty et al., 2016 ). The problem representation requires encoding problem information for which certain visual and parietal areas are also involved, although the extent of their involvement is less clear (Anderson and Fincham, 2014 ; Anderson et al., 2014 ).

2.2.1.1. Working memory

An important aspect of problem representation is the engagement and use of working memory (WM). The WM allows for the maintenance of relevant problem information and description in the mind (Gazzaley and Nobre, 2012 ). Research has shown that WM tasks consistently recruit the dlPFC and left inferior frontal cortex (IC) for encoding an manipulating information; dACC for error detection and performance adjustment; and vlPFC and the anterior insula (AI) for retrieving, selecting information and inhibitory control (Chung and Weyandt, 2014 ; Fang et al., 2016 ).

2.2.1.2. Representation

While we generally have a sense for the brain regions that are functionally influential in problem definition, less is known about how exactly events are represented within these regions. One theory for how events are represented in the PFC is the structured event complex theory (SEC), in which components of the event knowledge are represented by increasingly higher-order convergence zones localized within the PFC, akin to the convergence zones (from posterior to anterior) that integrate sensory information in the brain (Barbey et al., 2009 ). Under this theory, different zones in the PFC (left vs. right, anterior vs. posterior, lateral vs. medial, and dorsal vs. ventral) represent different aspects of the information contained in the events (e.g., number of events to be integrated together, the complexity of the event, whether planning, and action is needed). Other studies have also suggested the CEN's role in tasks requiring cognitive flexibility, and functions to switch thinking modes, levels of abstraction of thought and consider multiple concepts simultaneously (Miyake et al., 2000 ).

Thus, when the problem is well-structured, problem representation is largely an executive control activity coordinated by the PFC in which problem information from memory populates WM in a potentially structured representation. Once the problem is defined and encoded, planning and execution of a solution can begin.

2.2.2. Planning

The central executive network (CEN), particularly the PFC, is largely involved in plan formation and in plan execution. Planning is the process of generating a strategy to advance from the current state to a goal state. This in turn involves retrieving a suitable solution strategy from memory and then coordinating its execution.

2.2.2.1. Plan formation

The dlPFC supports sequential planning and plan formation, which includes the generation of hypothesis and construction of plan steps (Barbey and Barsalou, 2009 ). Interestingly, the vlPFC and the angular gyrus (AG), implicated in a variety of functions including memory retrieval, are also involved in plan formation (Anderson et al., 2014 ). Indeed, the AG together with the regions in the MTL (including the HF) and several other regions form a what is known as the “core” network. The core network is believed to be activated when recalling past experiences, imagining fictitious, and future events and navigating large-scale spaces (Summerfield et al., 2010 ), all key functions for generating plan hypotheses. A recent study suggests that the AG is critical to both episodic simulation, representation, and episodic memory (Thakral et al., 2017 ). One possibility for how plans are formulated could involve a dynamic process of retrieving an optimal strategy from memory. Research has shown significant interaction between striatal and frontal regions (Scimeca and Badre, 2012 ; Horner et al., 2015 ). The striatum is believed to play a key role in declarative memory retrieval, and specifically helping retrieve optimal (or previously rewarded) memories (Scimeca and Badre, 2012 ). Relevant to planning and plan formation, Scimeca & Badre have suggested that the striatum plays two important roles: (1) in mapping acquired value/utility to action selection, and thereby helping plan formation, and (2) modulation and re-encoding of actions and other plan parameters. Different types of problems require different sets of specialized knowledge. For example, the knowledge needed to solve mathematical problems might be quite different (albeit overlapping) from the knowledge needed to select appropriate tools in the environment.

Thus far, I have discussed planning and problem representation as being domain-independent, which has allowed me to outline key areas of the PFC, MTL, and other regions relevant to all problem-solving. However, some types of problems require domain-specific knowledge for which other regions might need to be recruited. For example, when planning for tool-use, the superior parietal lobe (SPL), supramarginal gyrus (SMG), anterior inferior parietal lobe (AIPL), and certain portions of the temporal and occipital lobe involved in visual and spatial integration have been found to be recruited (Brandi et al., 2014 ). It is believed that domain-specific information stored in these regions is recovered and used for planning.

2.2.2.2. Plan execution

Once a solution plan has been recruited from memory and suitably tuned for the problem on hand, the left-rostral PFC, caudate nucleus (CN), and bilateral posterior parietal cortices (PPC) are responsible for translating the plan into executable form (Stocco et al., 2012 ). The PPC stores and maintains “mental template” of the executable form. Hemispherical division of labor is particularly relevant in planning where it was shown that when planning to solve a Tower of Hanoi (block moving) problem, the right PFC is involved in plan construction whereas the left PFC is involved in controlling processes necessary to supervise the execution of the plan (Newman and Green, 2015 ). On a separate note and not the focus of this paper, plan execution and problem-solving can require the recruitment of affective and motivational processing in order to supply the agent with the resolve to solve problems, and the vmPFC has been found to be involved in coordinating this process (Barbey and Barsalou, 2009 ).

2.3. Creativity

During the gestalt movement in the 1930s, Maier noted that “most instances of “real” problem solving involves creative thinking” (Maier, 1930 ). Maier performed several experiments to study mental fixation and insight problem solving. This close tie between insight and creativity continues to be a recurring theme, one that will be central to the current discussion. If creativity and insight are linked to RWPS as noted by Maier, then it is reasonable to turn to the creativity and insight literature for understanding the role played by the environment. A large portion of the creativity literature has focused on viewing creativity as an internal process, one in which the solvers attention is directed inwards, and toward internal stimuli, to facilitate the generation of novel ideas and associations in memory (Beaty et al., 2016 ). Focusing on imagination, a number of researchers have looked at blinking, eye fixation, closing eyes, and looking nowhere behavior and suggested that there is a shift of attention from external to internal stimuli during creative problem solving (Salvi and Bowden, 2016 ). The idea is that shutting down external stimuli reduces cognitive load and focuses attention internally. Other experiments studying sleep behavior have also noted the beneficial role of internal stimuli in problem solving. The notion of ideas popping into ones consciousness, suddenly, during a shower is highly intuitive for many and researchers have attempted to study this phenomena through the lens of incubation, and unconscious thought that is internally-driven. There have been several theories and counter-theories proposed to account specifically for the cognitive processes underlying incubation (Ritter and Dijksterhuis, 2014 ; Gilhooly, 2016 ), but none of these theories specifically address the role of the external environment.

The neuroscience of creativity has also been extensively studied and I do not focus on an exhaustive literature review in this paper (a nice review can be found in Sawyer, 2011 ). From a problem-solving perspective, it has been found that unlike well-structured problems, ill-structured problems activate the right dlPFC. Most of the past work on creativity and creative problem-solving has focused on exploring memory structures and performing internally-directed searches. Creative idea generation has primarily been viewed as internally directed attention (Jauk et al., 2012 ; Benedek et al., 2016 ) and a primary mechanism involved is divergent thinking , which is the ability to produce a variety of responses in a given situation (Guilford, 1962 ). Divergent thinking is generally thought to involve interactions between the DMN, CEN, and the salience network (Yoruk and Runco, 2014 ; Heinonen et al., 2016 ). One psychological model of creative cognition is the Geneplore model that considers two major phases of generation (memory retrieval and mental synthesis) and exploration (conceptual interpretation and functional inference) (Finke et al., 1992 ; Boccia et al., 2015 ). It has been suggested that the associative mode of processing to generate new creative association is supported by the DMN, which includes the medial PFC, posterior cingulate cortex (PCC), tempororparietal juntion (TPJ), MTL, and IPC (Beaty et al., 2014 , 2016 ).

That said, the creativity literature is not completely devoid of acknowledging the role of the environment. In fact, it is quite the opposite. Researchers have looked closely at the role played by externally provided hints from the time of the early gestalt psychologists and through to present day studies (Öllinger et al., 2017 ). In addition to studying how hints can help problem solving, researchers have also looked at how directed action can influence subsequent problem solving—e.g., swinging arms prior to solving the two-string puzzle, which requires swinging the string (Thomas and Lleras, 2009 ). There have also been numerous studies looking at how certain external perceptual cues are correlated with creativity measures. Vohs et al. suggested that untidiness in the environment and the increased number of potential distractions helps with creativity (Vohs et al., 2013 ). Certain colors such as blue have been shown to help with creativity and attention to detail (Mehta and Zhu, 2009 ). Even environmental illumination, or lack thereof, have been shown to promote creativity (Steidle and Werth, 2013 ). However, it is important to note that while these and the substantial body of similar literature show the relationship of the environment to creative problem solving, they do not specifically account for the cognitive processes underlying the RWPS when external stimuli are received.

2.4. Insight problem solving

Analytical problem solving is believed to involve deliberate and conscious processing that advances step by step, allowing solvers to be able to explain exactly how they solved it. Inability to solve these problems is often associated with lack of required prior knowledge, which if provided, immediately makes the solution tractable. Insight, on the other hand, is believed to involve a sudden and unexpected emergence of an obvious solution or strategy sometimes accompanied by an affective aha! experience. Solvers find it difficult to consciously explain how they generated a solution in a sequential manner. That said, research has shown that having an aha! moment is neither necessary nor sufficient to insight and vice versa (Danek et al., 2016 ). Generally, it is believed that insight solvers acquire a full and deep understanding of the problem when they have solved it (Chu and Macgregor, 2011 ). There has been an active debate in the problem solving community about whether insight is something special. Some have argued that it is not, and that there are no special or spontaneous processes, but simply a good old-fashioned search of a large problem space (Kaplan and Simon, 1990 ; MacGregor et al., 2001 ; Ash and Wiley, 2006 ; Fleck, 2008 ). Others have argued that insight is special and suggested that it is likely a different process (Duncker, 1945 ; Metcalfe, 1986 ; Kounios and Beeman, 2014 ). This debate lead to two theories for insight problem solving. MacGregor et al. proposed the Criterion for Satisfactory Progress Theory (CSPT), which is based on Newell and Simons original notion of problem solving as being a heuristic search through the problem space (MacGregor et al., 2001 ). The key aspect of CSPT is that the solver is continually monitoring their progress with some set of criteria. Impasses arise when there is a criterion failure, at which point the solver tries non-maximal but promising states. The representational change theory (RCT) proposed by Ohlsson et al., on the other hand, suggests that impasses occur when the goal state is not reachable from an initial problem representation (which may have been generated through unconscious spreading activation) (Ohlsson, 1992 ). In order to overcome an impasse, the solver needs to restructure the problem representation, which they can do by (1) elaboration (noticing new features of a problem), (2) re-encoding fixing mistaken or incomplete representations of the problem, and by (3) changing constraints. Changing constraints is believed to involve two sub-processes of constraint relaxation and chunk-decomposition.

The current position is that these two theories do not compete with each other, but instead complement each other by addressing different stages of problem solving: pre- and post-impasse. Along these lines, Ollinger et al. proposed an extended RCT (eRCT) in which revising the search space and using heuristics was suggested as being a dynamic and iterative and recursive process that involves repeated instances of search, impasse and representational change (Öllinger et al., 2014 , 2017 ). Under this theory, a solver first forms a problem representation and begins searching for solutions, presumably using analytical problem solving processes as described earlier. When a solution cannot be found, the solver encounters an impasse, at which point the solver must restructure or change the problem representation and once again search for a solution. The model combines both analytical problem solving (through heuristic searches, hill climbing and progress monitoring), and creative mechanisms of constraint relaxation and chunk decomposition to enable restructuring.

Ollingers model appears to comprehensively account for both analytical and insight problem solving and, therefore, could be a strong candidate to model RWPS. However, while compelling, it is nevertheless an insufficient model of RWPS for many reasons, of which two are particularly significant for the current paper. First, the model does explicitly address mechanisms by which external stimuli might be assimilated. Second, the model is not sufficiently flexible to account for other events (beyond impasse) occurring during problem solving, such as distraction, mind-wandering and the like.

So, where does this leave us? I have shown the interplay between problem solving, creativity and insight. In particular, using Ollinger's proposal, I have suggested (maybe not quite explicitly up until now) that RWPS involves some degree of analytical problem solving as well as the post-impasse more creative modes of problem restructuring. I have also suggested that this model might need to be extended for RWPS along two dimensions. First, events such as impasses might just be an instance of a larger class of events that intervene during problem solving. Thus, there needs to be an accounting of the cognitive mechanisms that are potentially influenced by impasses and these other intervening events. It is possible that these sorts of events are crucial and trigger a switch in attentional focus, which in turn facilitates switching between different problem solving modes. Second, we need to consider when and how externally-triggered stimuli from the solver's environment can influence the problem solving process. I detail three different mechanisms by which external knowledge might influence problem solving. I address each of these ideas in more detail in the next two sections.

3. Event-triggered mode switching during problem-solving

3.1. impasse.

When solving certain types of problems, the agent might encounter an impasse, i.e., some block in its ability to solve the problem (Sprugnoli et al., 2017 ). The impasse may arise because the problem may have been ill-defined to begin with causing incomplete and unduly constrained representations to have been formed. Alternatively, impasses can occur when suitable solution strategies cannot be retrieved from memory or fail on execution. In certain instances, the solution strategies may not exist and may need to be generated from scratch. Regardless of the reason, an impasse is an interruption in the problem solving process; one that was running conflict-free up until the point when a seemingly unresolvable issue or an error in the predicted solution path was encountered. Seen as a conflict encountered in the problem-solving process it activates the anterior cingulate cortex (ACC). It is believed that the ACC not only helps detect the conflict, but also switch modes from one of “exploitation” (planning) to “exploration” (search) (Quilodran et al., 2008 ; Tang et al., 2012 ), and monitors progress during resolution (Chu and Macgregor, 2011 ). Some mode switching duties are also found to be shared with the AI (the ACC's partner in the salience network), however, it is unclear exactly the extent of this function-sharing.

Even though it is debatable if impasses are a necessary component of insight, they are still important as they provide a starting point for the creativity (Sprugnoli et al., 2017 ). Indeed, it is possible that around the moment of impasse, the AI and ACC together, as part of the salience network play a crucial role in switching thought modes from analytical planning mode to creative search and discovery mode. In the latter mode, various creative mechanisms might be activated allowing for a solution plan to emerge. Sowden et al. and many others have suggested that the salience network is potentially a candidate neurobiological mechanism for shifting between thinking processes, more generally (Sowden et al., 2015 ). When discussing various dual-process models as they relate to creative cognition, Sowden et al. have even noted that the ACC activation could be useful marker to identify shifting as participants work creative problems.

3.2. Defocused attention

As noted earlier, in the presence of an impasse there is a shift from an exploitative (analytical) thinking mode to an exploratory (creative) thinking mode. This shift impacts several networks including, for example, the attention network. It is believed attention can switch between a focused mode and a defocused mode. Focused attention facilitates analytic thought by constraining activation such that items are considered in a compact form that is amenable to complex mental operations. In the defocused mode, agents expand their attention allowing new associations to be considered. Sowden et al. ( 2015 ) note that the mechanism responsible for adjustments in cognitive control may be linked to the mechanisms responsible for attentional focus. The generally agreed position is that during generative thinking, unconscious cognitive processes activated through defocused attention are more prevalent, whereas during exploratory thinking, controlled cognition activated by focused attention becomes more prevalent (Kaufman, 2011 ; Sowden et al., 2015 ).

Defocused attention allows agents to not only process different aspects of a situation, but to also activate additional neural structures in long term memory and find new associations (Mendelsohn, 1976 ; Yoruk and Runco, 2014 ). It is believed that cognitive material attended to and cued by positive affective state results in defocused attention, allowing for more complex cognitive contexts and therefore a greater range of interpretation and integration of information (Isen et al., 1987 ). High attentional levels are commonly considered a typical feature of highly creative subjects (Sprugnoli et al., 2017 ).

4. Role of the environment

In much of the past work the focus has been on treating creativity as largely an internal process engaging the DMN to assist in making novel connections in memory. The suggestion has been that “individual needs to suppress external stimuli and concentrate on the inner creative process during idea generation” (Heinonen et al., 2016 ). These ideas can then function as seeds for testing and problem-solving. While true of many creative acts, this characterization does not capture how creative ideas arise in many real-world creative problems. In these types of problems, the agent is functioning and interacting with its environment before, during and after problem-solving. It is natural then to expect that stimuli from the environment might play a role in problem-solving. More specifically, it can be expected that through passive and active involvement with the environment, the agent is (1) able to trigger an unrelated, but potentially useful memory relevant for problem-solving, (2) make novel connections between two events in memory with the environmental cue serving as the missing link, and (3) incorporate a completely novel information from events occuring in the environment directly into the problem-solving process. I explore potential neural mechanisms for these three types of environmentally informed creative cognition, which I hypothesize are enabled by defocused attention.

4.1. Partial cues trigger relevant memories through context-shifting

I have previously discussed the interaction between the MTL and PFC in helping select task-relevant and critical memories for problem-solving. It is well-known that pattern completion is an important function of the MTL and one that enables memory retrieval. Complementary Learning Theory (CLS) and its recently updated version suggest that the MTL and related structures support initial storage as well as retrieval of item and context-specific information (Kumaran et al., 2016 ). According to CLS theory, the dentate gyrus (DG) and the CA3 regions of the HF are critical to selecting neural activity patterns that correspond to particular experiences (Kumaran et al., 2016 ). These patterns might be distinct even if experiences are similar and are stabilized through increases in connection strengths between the DG and CA3. Crucially, because of the connection strengths, reactivation of part of the pattern can activate the rest of it (i.e., pattern completion). Kumaran et al. have further noted that if consistent with existing knowledge, these new experiences can be quickly replayed and interleaved into structured representations that form part of the semantic memory.

Cues in the environment provided by these experiences hold partial information about past stimuli or events and this partial information converges in the MTL. CLS accounts for how these cues might serve to reactivate partial patterns, thereby triggering pattern completion. When attention is defocused I hypothesize that (1) previously unnoticed partial cues are considered, and (2) previously noticed partial cues are decomposed to produce previously unnoticed sub-cues, which in turn are considered. Zabelina et al. ( 2016 ) have shown that real-world creativity and creative achievement is associated with “leaky attention,” i.e., attention that allows for irrelevant information to be noticed. In two experiments they systematically explored the relationship between two notions of creativity— divergent thinking and real-world creative achievement—and the use of attention. They found that attentional use is associated in different ways for each of the two notions of creativity. While divergent thinking was associated with flexible attention, it does not appear to be leaky. Instead, selective focus and inhibition components of attention were likely facilitating successful performance on divergent thinking tasks. On the other hand, real-world creative achievement was linked to leaky attention. RWPS involves elements of both divergent thinking and of real-world creative achievement, thus I would expect some amount of attentional leaks to be part of the problem solving process.

Thus, it might be the case that a new set of cues or sub-cues “leak” in and activate memories that may not have been previously considered. These cues serve to reactivate a diverse set of patterns that then enable accessing a wide range of memories. Some of these memories are extra-contextual, in that they consider the newly noticed cues in several contexts. For example, when unable to find a screwdriver, we might consider using a coin. It is possible that defocused attention allows us to consider the coin's edge as being a potentially relevant cue that triggers uses for the thin edge outside of its current context in a coin. The new cues (or contexts) may allow new associations to emerge with cues stored in memory, which can occur during incubation. Objects and contexts are integrated into memory automatically into a blended representation and changing contexts disrupts this recognition (Hayes et al., 2007 ; Gabora, 2016 ). Cue-triggered context shifting allows an agent to break-apart a memory representation, which can then facilitate problem-solving in new ways.

4.2. Heuristic prototyping facilitates novel associations

It has long been the case that many scientific innovations have been inspired by events in nature and the surrounding environment. As noted earlier, Archimedes realized the relationship between the volume of an irregularly shaped object and the volume of water it displaced. This is an example of heuristic prototyping where the problem-solver notices an event in the environment, which then triggers the automatic activation of a heuristic prototype and the formation of novel associations (between the function of the prototype and the problem) which they can then use to solve the problem (Luo et al., 2013 ). Although still in its relative infancy, there has been some recent research into the neural basis for heuristic prototyping. Heuristic prototype has generally been defined as an enlightening prototype event with a similar element to the current problem and is often composed of a feature and a function (Hao et al., 2013 ). For example, in designing a faster and more efficient submarine hull, a heuristic prototype might be a shark's skin, while an unrelated prototype might be a fisheye camera (Dandan et al., 2013 ).

Research has shown that activating the feature function of the right heuristic prototype and linking it by way of semantic similarity to the required function of the problem was the key mechanism people used to solve several scienitific insight problems (Yang et al., 2016 ). A key region activated during heuristic prototyping is the dlPFC and it is believed to be generally responsible for encoding the events into memory and may play an important role in selecting and retrieving the matched unsolved technical problem from memory (Dandan et al., 2013 ). It is also believed that the precuneus plays a role in automatic retrieval of heuristic information allowing the heuristic prototype and the problem to combine (Luo et al., 2013 ). In addition to semantic processing, certain aspects of visual imagery have also been implicated in heuristic prototyping leading to the suggestion of the involvement of Broadman's area BA 19 in the occipital cortex.

There is some degree of overlap between the notions of heuristic prototyping and analogical transfer (the mapping of relations from one domain to another). Analogical transfer is believed to activate regions in the left medial fronto-parietal system (dlPFC and the PPC) (Barbey and Barsalou, 2009 ). I suggest here that analogical reasoning is largely an internally-guided process that is aided by heuristic prototyping which is an externally-guided process. One possible way this could work is if heuristic prototyping mechanisms help locate the relevant memory with which to then subsequently analogize.

4.3. Making physical inferences to acquire novel information

The agent might also be able to learn novel facts about their environment through passive observation as well as active experimentation. There has been some research into the neural basis for causal reasoning (Barbey and Barsalou, 2009 ; Operskalski and Barbey, 2016 ), but beyond its generally distributed nature, we do not know too much more. Beyond abstract causal reasoning, some studies looked into the cortical regions that are activated when people watch and predict physical events unfolding in real-time and in the real-world (Fischer et al., 2016 ). It was found that certain regions were associated with representing types of physical concepts, with the left intraparietal sulcus (IPS) and left middle frontal gyrus (MFG) shown to play a role in attributing causality when viewing colliding objects (Mason and Just, 2013 ). The parahippocampus (PHC) was associated with linking causal theory to observed data and the TPJ was involved in visualizing movement of objects and actions in space (Mason and Just, 2013 ).

5. Proposed theory

I noted earlier that Ollinger's model for insight problem solving, while serving as a good candidate for RWPS, requires extension. In this section, I propose a candidate model that includes some necessary extensions to Ollinger's framework. I begin by laying out some preliminary notions that underlie the proposed model.

5.1. Dual attentional modes

I propose that the attention-switching mechanism described earlier is at the heart of RWPS and enables two modes of operation: focused and defocused mode. In the focused mode, the problem representation is more or less fixed, and problem solving proceeds in a focused and goal directed manner through search, planning, and execution mechanisms. In the defocused mode, problem solving is not necessarily goal directed, but attempts to generate ideas, driven by both internal and external items.

At first glance, these modes might seem similar to convergent and divergent thinking modes postulated by numerous others to account for creative problem solving. Divergent thinking allows for the generation of new ideas and convergent thinking allows for verification and selection of generated ideas. So, it might seem that focused mode and convergent thinking are similar and likewise divergent and defocused mode. They are, however, quite different. The modes relate less to idea generation and verification, and more to the specific mechanisms that are operating with regard to a particular problem at a particular moment in time. Convergent and divergent processes may be occurring during both defocused and focused modes. Some degree of divergent processes may be used to search and identify specific solution strategies in focused mode. Also, there might be some degree of convergent idea verification occuring in defocused mode as candidate items are evaluated for their fit with the problem and goal. Thus, convergent and divergent thinking are one amongst many mechanisms that are utilized in focused and defocused mode. Each of these two modes has to do with degree of attention placed on a particular problem.

There have been numerous dual-process and dual-systems models of cognition proposed over the years. To address criticisms raised against these models and to unify some of the terminology, Evans & Stanovich proposed a dual-process model comprising Type 1 and Type 2 thought (Evans and Stanovich, 2013 ; Sowden et al., 2015 ). Type 1 processes are those that are believed to be autonomous and do not require working memory. Type 2 processes, on the other hand, are believed to require working memory and are cognitively decoupled to prevent real-world representations from becoming confused with mental simulations (Sowden et al., 2015 ). While acknowledging various other attributes that are often used to describe dual process models (e.g., fast/slow, associative/rule-based, automatic/controlled), Evans & Stanovich note that these attributes are merely frequent correlates and not defining characteristics of Type 1 or Type 2 processes. The proposed dual attentional modes share some similarities with the Evans & Stanovich Type 1 and 2 models. Specifically, Type 2 processes might occur in focused attentional mode in the proposed model as they typically involve the working memory and certain amount of analytical thought and planning. Similarly, Type 1 processes are likely engaged in defocused attentional mode as there are notions of associative and generative thinking that might be facilitated when attention has been defocused. The crucial difference between the proposed model and other dual-process models is that the dividing line between focused and defocused attentional modes is the degree of openness to internal and external stimuli (by various networks and functional units in the brain) when problem solving. Many dual process models were designed to classify the “type” of thinking process or a form of cognitive processing. In some sense, the “processes” in dual process theories are characterized by the type of mechanism of operation or the type of output they produced. Here, I instead characterize and differentiate the modes of thinking by the receptivity of different functional units in the brain to input during problem solving.

This, however, raises a different question of the relationship between these attentional modes and conscious vs. unconscious thinking. It is clear that both the conscious and unconscious are involved in problem solving, as well as in RWPS. Here, I claim that a problem being handled is, at any given point in time, in either a focused mode or in a defocused mode. When in the focused mode, problem solving primarily proceeds in a manner that is available for conscious deliberation. More specifically, problem space elements and representations are tightly managed and plans and strategies are available in the working memory and consciously accessible. There are, however, secondary unconscious operations in the focused modes that includes targeted memory retrieval and heuristic-based searches. In the defocused mode, the problem is primarily managed in an unconscious way. The problem space elements are broken apart and loosely managed by various mechanisms that do not allow for conscious deliberation. That said, it is possible that some problem parameters remain accessible. For example, it is possible that certain goal information is still maintained consciously. It is also possible that indexes to all the problems being considered by the solver are maintained and available to conscious awareness.

5.2. RWPS model

Returning to Ollinger's model for insight problem solving, it now becomes readily apparent how this model can be modified to incorporate environmental effects as well as generalizing the notion of intervening events beyond that of impasses. I propose a theory for RWPS that begins with standard analytical problem-solving process (See Figures ​ Figures1, 1 , ​ ,2 2 ).

Summary of neural activations during focused problem-solving (Left) and defocused problem-solving (Right) . During defocused problem-solving, the salience network (insula and ACC) coordinates the switching of several networks into a defocused attention mode that permits the reception of a more varied set of stimuli and interpretations via both the internally-guided networks (default mode network DMN) and externally guided networks (Attention). PFC, prefrontal cortex; ACC, anterior cingulate cortex; PCC, posterior cingulate cortex; IPC, inferior parietal cortex; PPC, posterior parietal cortex; IPS, intra-parietal sulcus; TPJ, temporoparietal junction; MTL, medial temporal lobe; FEF, frontal eye field.

Proposed Model for Real World Problem Solving (RWPS). The corresponding neural correlates are shown in italics. During problem-solving, an initial problem representation is formed based on prior knowledge and available perceptual information. The problem-solving then proceeds in a focused, goal-directed mode until the goal is achieved or a defocusing event (e.g., impasse or distraction) occurs. During focused mode operation, the solver interacts with the environment in directed manner, executing focused plans, and allowing for predicted items to be activated by the environment. When a defocusing event occurs, the problem-solving then switches into a defocused mode until a focusing event (e.g., discovery) occurs. In defocused mode, the solver performs actions unrelated to the problem (or is inactive) and is receptive to a set of environmental triggers that activate novel aspects using the three mechanisms discussed in this paper. When a focusing event occurs, the diffused problem elements cohere into a restructured representation and problem-solving returns into a focused mode.

5.2.1. Focused problem solving mode

Initially, both prior knowledge and perceptual entities help guide the creation of problem representations in working memory. Prior optimal or rewarding solution strategies are obtained from LTM and encoded in the working memory as well. This process is largely analytical and the solver interacts with their environment through focused plan or idea execution, targeted observation of prescribed entities, and estimating prediction error of these known entities. More specifically, when a problem is presented, the problem representations are activated and populated into working memory in the PFC, possibly in structured representations along convergence zones. The PFC along with the Striatum and the MTL together attempt at retrieving an optimal or previously rewarded solution strategy from long term memory. If successfully retrieved, the solution strategy is encoded into the PPC as a mental template, which then guides relevant motor control regions to execute the plan.

5.2.2. Defocusing event-triggered mode switching

The search and solve strategy then proceeds analytically until a “defocusing event” is encountered. The salience network (AI and ACC) monitor for conflicts and attempt to detect any such events in the problem-solving process. As long as no conflicts are detected, the salience network focuses on recruiting networks to achieve goals and suppresses the DMN (Beaty et al., 2016 ). If the plan execution or retrieval of the solution strategy fails, then a defocusing event is detected and the salience network performs mode switching. The salience network dynamically switches from the focused problem-solving mode to a defocused problem-solving mode (Menon, 2015 ). Ollinger's current model does not account for other defocusing events beyond an impasse, but it is not inconceivable that there could be other such events triggered by external stimuli (e.g., distraction or an affective event) or by internal stimuli (e.g., mind wandering).

5.2.3. Defocused problem solving mode

In defocused mode, the problem is operated on by mechanisms that allow for the generation and testing of novel ideas. Several large-scale brain networks are recruited to explore and generate new ideas. The search for novel ideas is facilitated by generally defocused attention, which in turn allows for creative idea generation from both internal as well as external sources. The salience network switches operations from defocused event detection to focused event or discovery detection, whereby for example, environmental events or ideas that are deemed interesting can be detected. During this idea exploration phase, internally, the DMN is no longer suppressed and attempts to generate new ideas for problem-solving. It is known that the IPC is involved in the generation of new ideas (Benedek et al., 2014 ) and together with the PPC in coupling different information together (Simone Sandkühler, 2008 ; Stocco et al., 2012 ). Beaty et al. ( 2016 ) have proposed that even this internal idea-generation process can be goal directed, thereby allowing for a closer working relationship between the CEN and the DMN. They point to neuroimaging evidence that support the possibility that the executive control network (comprising the lateral prefrontal and inferior parietal regions) can constrain and direct the DMN in its process of generating ideas to meet task-specific goals via top down monitoring and executive control (Beaty et al., 2016 ). The control network is believed to maintain an “internal train of thought” by keeping the task goal activated, thereby allowing for strategic and goal-congruent searches for ideas. Moreover, they suggest that the extent of CEN involvement in the DMN idea-generation may depend on the extent to which the creative task is constrained. In the RWPS setting, I would suspect that the internal search for creative solutions is not entirely unconstrained, even in the defocused mode. Instead, the solver is working on a specified problem and thus, must maintain the problem-thread while searching for solutions. Moreover, self-generated ideas must be evaluated against the problem parameters and thereby might need some top-down processing. This would suggest that in such circumstances, we would expect to see an increased involvement of the CEN in constraining the DMN.

On the external front, several mechanisms are operating in this defocused mode. Of particular note are the dorsal attention network, composed of the visual cortex (V), IPS and the frontal eye field (FEF) along with the precuneus and the caudate nucleus allow for partial cues to be considered. The MTL receives synthesized cue and contextual information and populates the WM in the PFC with a potentially expanded set of information that might be relevant for problem-solving. The precuneus, dlPFC and PPC together trigger the activation and use of a heuristic prototype based on an event in the environment. The caudate nucleus facilitates information routing between the PFC and PPC and is involved in learning and skill acquisition.

5.2.4. Focusing event-triggered mode switching

The problem's life in this defocused mode continues until a focusing event occurs, which could be triggered by either external (e.g., notification of impending deadline, discovery of a novel property in the environment) or internal items (e.g., goal completion, discovery of novel association or updated relevancy of a previously irrelevant item). As noted earlier, an internal train of thought may be maintained that facilitates top-down evaluation of ideas and tracking of these triggers (Beaty et al., 2016 ). The salience network switches various networks back to the focused problem-solving mode, but not without the potential for problem restructuring. As noted earlier, problem space elements are maintained somewhat loosely in the defocused mode. Thus, upon a focusing event, a set or subset of these elements cohere into a tight (restructured) representation suitable for focused mode problem solving. The process then repeats itself until the goal has been achieved.

5.3. Model predictions

5.3.1. single-mode operation.

The proposed RWPS model provides several interesting hypotheses, which I discuss next. First, the model assumes that any given problem being worked on is in one mode or another, but not both. Thus, the model predicts that there cannot be focused plan execution on a problem that is in defocused mode. The corollary prediction is that novel perceptual cues (as those discussed in section 4) cannot help the solver when in focused mode. The corollary prediction, presumably has some support from the inattentional blindness literature. Inattentional blindness is when perceptual cues are not noticed during a task (e.g., counting the number of basketball passes between several people, but not noticing a gorilla in the scene) (Simons and Chabris, 1999 ). It is possible that during focused problem solving, that external and internally generated novel ideas are simply not considered for problem solving. I am not claiming that these perceptual cues are always ignored, but that they are not considered within the problem. Sometimes external cues (like distracting occurrences) can serve as defocusing events, but the model predicts that the actual content of these cues are not themselves useful for solving the specific problem at hand.

When comparing dual-process models Sowden et al. ( 2015 ) discuss shifting from one type of thinking to another and explore how this shift relates to creativity. In this regard, they weigh the pros and cons of serial vs. parallel shifts. In dual-process models that suggest serial shifts, it is necessary to disengage one type of thought prior to engaging the other or to shift along a continuum. Whereas, in models that suggest parallel shifts, each of the thinking types can operate in parallel. Per this construction, the proposed RWPS model is serial, however, not quite in the same sense. As noted earlier, the RWPS model is not a dual-process model in the same sense as other dual process model. Instead, here, the thrust is on when the brain is receptive or not receptive to certain kinds of internal and external stimuli that can influence problem solving. Thus, while the modes may be serial with respect to a certain problem, it does not preclude the possibility of serial and parallel thinking processes that might be involved within these modes.

5.3.2. Event-driven transitions

The model requires an event (defocusing or focusing) to transition from one mode to another. After all why else would a problem that is successfully being resolved in the focused mode (toward completion) need to necessarily be transferred to defocused mode? These events are interpreted as conflicts in the brain and therefore the mode-switching is enabled by the saliency network and the ACC. Thus, the model predicts that there can be no transition from one mode to another without an event. This is a bit circular, as an event is really what triggers the transition in the first place. But, here I am suggesting that an external or internal cue triggered event is what drives the transition, and that transitions cannot happen organically without such an event. In some sense, the argument is that the transition is discontinuous, rather than a smooth one. Mind-wandering is good example of when we might drift into defocused mode, which I suggest is an example of an internally driven event caused by an alternative thought that takes attention away from the problem.

A model assumption underlying RWPS is that events such as impasses have a similar effect to other events such as distraction or mind wandering. Thus, it is crucial to be able to establish that there exists of class of such events and they have a shared effect on RWPS, which is to switch attentional modes.

5.3.3. Focused mode completion

The model also predicts that problems cannot be solved (i.e., completed) within the defocused mode. A problem can be considered solved when a goal is reached. However, if a goal is reached and a problem is completed in the defocused mode, then there must have not been any converging event or coherence of problem elements. While it is possible that the solver arbitrarily arrived at the goal in a diffused problem space and without conscious awareness of completing the task or even any converging event or problem recompiling, it appears somewhat unlikely. It is true that there are many tasks that we complete without actively thinking about it. We do not think about what foot to place in front of another while walking, but this is not an instance of problem solving. Instead, this is an instance of unconscious task completion.

5.3.4. Restructuring required

The model predicts that a problem cannot return to a focused mode without some amount of restructuring. That is, once defocused, the problem is essentially never the same again. The problem elements begin interacting with other internally and externally-generated items, which in turn become absorbed into the problem representation. This prediction can potentially be tested by establishing some preliminary knowledge, and then showing one group of subjects the same knowledge as before, while showing the another group of subjects different stimuli. If the model's predictions hold, the problem representation will be restructured in some way for both groups.

There are numerous other such predictions, which are beyond the scope of this paper. One of the biggest challenges then becomes evaluating the model to set up suitable experiments aimed at testing the predictions and falsifying the theory, which I address next.

6. Experimental challenges and paradigms

One of challenges in evaluating the RWPS is that real world factors cannot realistically be accounted for and sufficiently controlled within a laboratory environment. So, how can one controllably test the various predictions and model assumptions of “real world” problem solving, especially given that by definition RWPS involves the external environment and unconscious processing? At the expense of ecological validity, much of insight problem solving research has employed an experimental paradigm that involves providing participants single instances of suitably difficult problems as stimuli and observing various physiological, neurological and behavioral measures. In addition, through verbal protocols, experimenters have been able to capture subjective accounts and problem solving processes that are available to the participants' conscious. These experiments have been made more sophisticated through the use of timed-hints and/or distractions. One challenge with this paradigm has been the selection of a suitable set of appropriately difficult problems. The classic insight problems (e.g., Nine-dot, eight-coin) can be quite difficult, requiring complicated problem solving processes, and also might not generalize to other problems or real world problems. Some in the insight research community have moved in the direction of verbal tasks (e.g., riddles, anagrams, matchstick rebus, remote associates tasks, and compound remote associates tasks). Unfortunately, these puzzles, while providing a great degree of controllability and repeatability, are even less realistic. These problems are not entirely congruent with the kinds of problems that humans are solving every day.

The other challenge with insight experiments is the selection of appropriate performance and process tracking measures. Most commonly, insight researchers use measures such as time to solution, probability of finding solution, and the like for performance measures. For process tracking, verbal protocols, coded solution attempts, and eye tracking are increasingly common. In neuroscientific studies of insight various neurological measures using functional magnetic resonance imaging (fMRI), electroencephalography (EEGs), transcranial direct current stimulation (tDCS), and transcranial magnetic stimulation (tMS) are popular and allow for spatially and temporally localizing an insight event.

Thus, the challenge for RWPS is two-fold: (1) selection of stimuli (real world problems) that are generalizable, and (2) selection of measures (or a set of measures) that can capture key aspects of the problem solving process. Unfortunately, these two challenges are somewhat at odds with each other. While fMRI and various neuroscientific measures can capture the problem solving process in real time, it is practically difficult to provide participants a realistic scenario while they are laying flat on their back in an fMRI machine and allowed to move nothing more than a finger. To begin addressing this conundrum, I suggest returning to object manipulation problems (not all that different from those originally introduced by Maier and Duncker nearly a century ago), but using modern computing and user-interface technologies.

One pseudo-realistic approach is to generate challenging object manipulation problems in Virtual Reality (VR). VR has been used to describe 3-D environment displays that allows participants to interact with artificially projected, but experientially realistic scenarios. It has been suggested that virtual environments (VE) invoke the same cognitive modules as real equivalent environmental experience (Foreman, 2010 ). Crucially, since VE's can be scaled and designed as desired, they provide a unique opportunity to study pseudo-RWPS. However, a VR-based research approach has its limitations, one of which is that it is nearly impossible to track participant progress through a virtual problem using popular neuroscientific measures such as fMRI because of the limited mobility of connected participants.

Most of the studies cited in this paper utilized an fMRI-based approach in conjunction with a verbal or visual task involving problem-solving or creative thinking. Very few, if any, studies involved the use physical manipulation, and those physical manipulations were restricted to limited finger movements. Thus, another pseudo-realistic approach is allowing subjects to teleoperate robotic arms and legs from inside the fMRI machine. This paradigm has seen limited usage in psychology and robotics, in studies focused on Human-Robot interaction (Loth et al., 2015 ). It could be an invaluable tool in studying real-time dynamic problem-solving through the control of a robotic arm. In this paradigm a problem solving task involving physical manipulation is presented to the subject via the cameras of a robot. The subject (in an fMRI) can push buttons to operate the robot and interact with its environment. While the subjects are not themselves moving, they can still manipulate objects in the real world. What makes this paradigm all the more interesting is that the subject's manipulation-capabilities can be systematically controlled. Thus, for a particular problem, different robotic perceptual and manipulation capabilities can be exposed, allowing researchers to study solver-problem dynamics in a new way. For example, even simple manipulation problems (e.g., re-arranging and stacking blocks on a table) can be turned into challenging problems when the robotic movements are restricted. Here, the problem space restrictions are imposed not necessarily on the underlying problem, but on the solver's own capabilities. Problems of this nature, given their simple structure, may enable studying everyday practical creativity without the burden of devising complex creative puzzles. Crucial to note, both these pseudo-realistic paradigms proposed demonstrate a tight interplay between the solver's own capabilities and their environment.

7. Conclusion

While the neural basis for problem-solving, creativity and insight have been studied extensively in the past, there is still a lack of understanding of the role of the environment in informing the problem-solving process. Current research has primarily focused on internally-guided mental processes for idea generation and evaluation. However, the type of real world problem-solving (RWPS) that is often considered a hallmark of human intelligence has involved both a dynamic interaction with the environment and the ability to handle intervening and interrupting events. In this paper, I have attempted to synthesize the literature into a unified theory of RWPS, with a specific focus on ways in which the environment can help problem-solve and the key neural networks involved in processing and utilizing relevant and useful environmental information. Understanding the neural basis for RWPS will allow us to be better situated to solve difficult problems. Moreover, for researchers in computer science and artificial intelligence, clues into the neural underpinnings of the computations taking place during creative RWPS, can inform the design the next generation of helper and exploration robots which need these capabilities in order to be resourceful and resilient in the open-world.

Author contributions

The author confirms being the sole contributor of this work and approved it for publication.

Conflict of interest statement

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

Acknowledgments

I am indebted to Professor Matthias Scheutz, Professor Elizabeth Race, Professor Ayanna Thomas, and Professor. Shaun Patel for providing guidance with the research and the manuscript. I am also grateful for the facilities provided by Tufts University, Medford, MA, USA.

1 My intention is not to ignore the benefits of a concentrated internal thought process which likely occurred as well, but merely to acknowledge the possibility that the environment might have also helped.

2 The research in insight does extensively use “hints” which are, arguably, a form of external influence. But these hints are highly targeted and might not be available in this explicit form when solving problems in the real world.

3 The accuracy of these accounts has been placed in doubt. They often are recounted years later, with inaccuracies, and embellished for dramatic effect.

4 I use the term “agent” to refer to the problem-solver. The term agent is more general than “creature” or “person” or “you" and is intentionally selected to broadly reference humans, animals as well as artificial agents. I also selectively use the term “solver.”

Funding. The research for this Hypothesis/Theory Article was funded by the authors private means. Publication costs will be covered by my institution: Tufts University, Medford, MA, USA.

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What Are Analytical Skills?

Definition & Examples of Analytical Skills

How Analytical Skills Work

Types of analytical skills, highlighting analytical skills.

Analytical skills refer to the ability to collect and analyze information,  problem-solve , and make decisions. Employees who possess these skills can help solve a company’s problems and improve its overall productivity and success.

Learn more about analytical skills and how they work.

Employers look for employees with the ability to investigate a problem and find the ideal solution in a timely, efficient manner. The skills required to solve problems are known as analytical skills.

You use analytical skills when detecting patterns, brainstorming, observing, interpreting data, integrating new information, theorizing, and making decisions based on the multiple factors and options available. 

Solutions can be reached by clear-cut, methodical approaches, or through more creative techniques. Both ways of solving a problem require analytical skills.

Most types of work require analytical skills. You use them to solve problems that may not have obvious solutions or that have several variables.

Let's say you're the manager of a restaurant and have been going over budget on food for the past two weeks. You review the menus and what customers have ordered along with food costs from your suppliers.

You see that the cost of seafood has increased over the past two weeks. When you talk to the supplier, they explain that there's been a disruption in the supply chain due to weather. They've increased costs to compensate. You decide to reduce your seafood order to lower costs and work with your chef to develop new specials that take advantage of other protein options.

In this example, you used analytical skills to review data from different sources, integrated new information, and made a decision based on your observations.

Catherine Song / The Balance

The best analytical skills to highlight on a resume depend on the position you're applying for. Here are five skills to consider.

Communication

Analysis only goes so far if you can't share and implement your findings. You need to be an effective communicator to discuss the patterns you see and your conclusions and recommendations.

Analytical communication skills include:

• Problem sensitivity
• Active listening
• Oral communication
• Written communication
• Conducting presentations 

Analyzing information often requires a creative eye to spot trends in the data that others may not find. Creativity is also important when it comes to problem-solving. The obvious solution is not always the best option. Employees with strong analytical skills will think outside the box to come up with effective solutions to big problems.

Creative skill sets include:

• Brainstorming
• Collaboration
• Optimization
• Predictive modeling
• Restructuring 
• Strategic planning
• Integration

Critical Thinking

Critical thinking refers to evaluating information and then making a decision based on your findings. Critical thinking is what helps an employee make decisions that help solve problems for a company. It may include:

• Process management
• Benchmarking
• Big data analytics
• Business intelligence
• Case analysis
• Causal relationships
• Classifying
• Comparative analysis
• Correlation
• Decision-making
• Deductive reasoning
• Inductive reasoning
• Diagnostics
• Data interpretation
• Prioritization
• Troubleshooting

Data Analysis

No matter what your career field, being good at analysis means being able to examine a large volume of data and identify trends in that data. You have to go beyond just reading and understanding information to make sense of it by highlighting patterns for top decision-makers.

There are many different types of data analysis, but some of the most common ones in today's workplace include:

• Business analysis
• Strengths, weaknesses, opportunities, and threats (SWOT) analysis
• Cost analysis
• Credit analysis
• Critical analysis
• Descriptive analysis
• Financial analysis
• Industry research
• Policy analysis
• Predictive analytics 
• Prescriptive analytics
• Process analysis
• Qualitative analysis
• Quantitative analysis
• Return on investment (ROI) analysis

You must learn more about a problem before you can solve it, so an essential analytical skill is being able to collect data and research a topic. This can involve reviewing spreadsheets, researching online, collecting data, and looking at competitor information. 

Analytical research skills include:

• Investigation
• Data collection
• Checking for accuracy

Analytical thinking is a soft skill , but field-specific, technical types of analysis are hard skills. Both should be highlighted on your resume and in interviews.

Analytical skills are sought after employers, so it's best to highlight these skills when you're applying and interviewing for jobs. Consider:

• Adding relevant skills to your resume : Keywords  are an essential component of a resume, as hiring managers use the words and phrases of a resume and cover letter to screen job applicants, often through recruitment management software.
• Highlighting skills in your cover letter : Mention your analytical skills and give a specific example of a time when you demonstrated those skills.
• Provide examples in your job interview : They can be from past work, volunteer, or school experiences.

Key Takeaways

• Analytical skills refer to the ability to collect and analyze information, problem-solve, and make decisions.
• You use analytical skills when detecting patterns, brainstorming, observing, interpreting data, and making decisions based on the multiple factors and options available to you. 
• Most types of work require analytical skills. You use them to solve problems that may not have obvious solutions or have several variables.
• There are many types of analytical skills, including communication, creativity, critical thinking, data analysis, and research. 
• Highlight and provide examples of your skills in your resume, cover letter, and interviews.