logical problem solving and analytical abilities

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

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The Most Important Logical Thinking Skills (With Examples)

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Find a Job You Really Want In

Logical thinking skills like critical-thinking, research, and creative thinking are valuable assets in the workplace. These skills are sought after by many employers, who want employees that take into account facts and data before deciding on an important course of action. This is because such solutions will ensure the organization’s processes can continue to operate efficiently.

So, if you’re a job seeker or employee looking to explore and brush up on your logical thinking skills, you’re in luck. This article will cover examples of logical thinking skills in the workplace, as well as what you can do to showcase those skills on your resume and in interviews.

Key Takeaways:

Logical thinking is problem solving based on reasoning that follows a strictly structured progression of analysis.

Critical thinking, research, creativity, mathematics, reading, active listening, and organization are all important logical thinking skills in the workplace.

Logical thinking provides objectivity for decision making that multiple people can accept.

Deduction follows valid premises to reach a logical conclusion.

It can be very helpful to demonstrate logical thinking skills at a job interview.

What is logical thinking?

10 examples of logical thinking skills, examples of logical thinking in the workplace, what is deductive reasoning, logical thinking in a job interview, logical thinking skills faq, final thoughts.

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Logical thinking is the ability to reason out an issue after observing and analyzing it from all angles . You can then form a conclusion that makes the most sense. It also includes the ability to take note of reactions and feedback to aid in the formation of the conclusion.

Logical thinking skills enable you to present your justification for the actions you take, the strategies you use, and the decisions you make. You can easily stand in front of your clients, peers, and supervisors and defend your product, service, and course of action if the necessity arises.

Logical thinking is an excellent way of solving complex problems. You can break the problem into smaller parts; solve them individually in a sequence, then present the complete solution. However, it is not infallible.

So, when a problem in the workplace feels overwhelming, you may want to think about it logically first.

Logical thinking skills are a skill set that enables you to reason logically when solving problems. They enable you to provide well-reasoned answers to any issues that arise. They also empower you to make decisions that most people will consider rational.

Critical-thinking skills. If you are a critical thinker, then you can analyze and evaluate a problem before making judgments. You need to improve your critical thinking process to become a logical thinker.

Your critical thinking skills will improve your ability to solve problems. You will be the go-to employee concerning crises. People can rely on you to be reasonable whenever an issue arises instead of letting biases rule you.

Research skills. If you are a good researcher , then you can search and locate data that can be useful when presenting information on your preferred subject.

The more relevant information you have about a particular subject, the more accurate your conclusions are likely to be. The sources you use must be reputable and relevant.

For this reason, your ability to ferret out information will affect how well you can reason logically.

Creative thinking skills. If you are a creative thinker , then you can find innovative solutions to problems.

You are the kind of person that can think outside the box when brainstorming ideas and potential solutions. Your thinking is not rigid. Instead, you tend to look at issues in ways other people have not thought of before.

While logical thinking is based on data and facts, that doesn’t mean it is rigid. You can creatively find ways of sourcing that data or experimenting so that you can form logical conclusions. Your strategic thinking skills will also help enable you to analyze reactions or collect feedback .

Mathematical skills. If you are skilled in mathematics , then you can work well with numbers and represent mathematical ideas using visual symbols. Your brain must be able to compute information.

Business is a numbers game. That means you must have some knowledge of mathematics. You must be able to perform basic mathematical tasks involving addition, subtractions, divisions, multiplications, etc.

So, to become a logical thinker, you must be comfortable working with numbers. You will encounter them in many business-related complex problems. And your ability to understand them will determine whether you can reach an accurate logical conclusion that helps your organization.

Reading skills. If you are a good reader , then you can make sense of the letters and symbols that you see. Your ability to read will determine your competency concerning your logical thinking and reasoning skills.

And that skill set will come in handy when you are presented with different sets of work-related statements from which you are meant to conclude. Such statements may be part of your company policy, technical manual, etc.

Active listening skills. Active listening is an important communication skill to have. If you are an active listener, then you can hear, understand what is being said, remember it, and respond to it if necessary.

Not all instructions are written. You may need to listen to someone to get the information you need to solve problems before you write it down. In that case, your active listening skills will determine how well you can remember the information so that you can use it to reason things out logically.

Information ordering skills. If you have information ordering skills, then you can arrange things based on a specified order following the set rules or conditions. These things may include mathematical operations, words, pictures, etc.

Different organizations have different business processes. The workflow in one organization will be not similar to that of another organization even if both belong to the same industry.

Your ability to order information will depend on an organization’s culture . And it will have a major impact on how you can think and reason concerning solutions to your company problems.

If you follow the wrong order, then no matter how good your problem-solving techniques are your conclusions may be wrong for your organization.

Persuasion skills. Logical thinking can be useful when persuading others, especially in the workplace.

For example, lets say one of your co-workers wants to take a project in an impulsive direction, which will increase the budget. However, after you do your research, you realize a budget increase would be impossible.

You can then use your logical thinking skills to explain the situation to your co-worker , including details facts and numbers, which will help dissuade them from making an uninformed decision.

Decision making skills. Decision making skills go hand and hand with logical thinking, as being able to think logically about solutions and research topics will make it far easier to make informed decisions.

After all, no one likes making a decision that feels like a shot in the dark, so knowing crucial information about the options aviable to you, and thinking about them logically, can improve your confidence around decision making.

Confidence skills. Confidence that stems from an emotional and irrational place will always be fragile, but when you have more knowledge available to you through logical thinking, you can be more confident in your confidence skills.

For instance, if an employee asked you to answer an important question, you will have a lot more confidence in your answer if you can think logically about it, as opposed to having an air of uncertainty.

To improve your logic skills, it would be wise to practice how to solve problems based on facts and data. Below are examples of logical thinking in the workplace that will help you understand this kind of reasoning so that you can improve your thinking:

The human resource department in your organization has determined that leadership skills are important for anyone looking to go into a senior management position. So, it decides that it needs proof of leadership before hiring anyone internally. To find the right person for the senior management position , every candidate must undertake a project that involves a team of five. Whoever leads the winning team will get the senior managerial position.

This example shows a logical conclusion that is reached by your organization’s human resource department. In this case, your HR department has utilized logical thinking to determine the best internal candidate for the senior manager position.

It could be summarized as follows:

Statement 1: People with excellent leadership skills that produce winning teams make great senior managers. Statement 2: Candidate A is an excellent leader that has produced a winning team. Conclusion: Candidate A will make an excellent senior manager .

A marketing company researches working women on behalf of one of their clients – a robotics company. They find out that these women feel overwhelmed with responsibilities at home and in the workplace. As a result, they do not have enough time to clean, take care of their children, and stay productive in the workplace. A robotics company uses this research to create a robot cleaner that can be operated remotely . Then they advertise this cleaner specifically to working women with the tag line, “Working women can do it all with a little bit of help.” As a result of this marketing campaign, their revenues double within a year.

This example shows a logical conclusion reached by a robotics company after receiving the results of marketing research on working women. In this case, logical thinking has enabled the company to come up with a new marketing strategy for their cleaning product.

Statement 1: Working women struggle to keep their homes clean. Statement 2: Robot cleaners can take over cleaning duties for women who struggle to keep their homes clean. Conclusion: Robot cleaner can help working women keep their homes clean.

CalcX. Inc. has created a customer survey concerning its new finance software. The goal of the survey is to determine what customers like best about the software. After reading through over 100 customer reviews and ratings, it emerges that 60% of customers love the new user interface because it’s easy to navigate. CalcX. Inc. then decides to improve its marketing strategy. It decides to train every salesperson to talk about the easy navigation feature and how superior it is to the competition. So, every time a client objects to the price, the sales rep could admit that it is expensive, but the excellent user interface makes up for the price. At the end of the year, it emerges that this strategy has improved sales revenues by 10%.

The above example shows how logical thinking has helped CalcX. Sell more software and improve its bottom line.

Statement 1: If the majority of customers like a particular software feature, then sales reps should use it to overcome objections and increase revenues. Statement 2: 60% of the surveyed customers like the user interface of the new software, and; they think it makes navigation easier. Conclusion: The sales reps should market the new software’s user interface and the fact that it is easy to navigate to improve the company’s bottom line.

A political candidate hires a focus group to discuss hot-button issues they feel strongly about. It emerges that the group is torn on sexual reproductive health issues, but most support the issue of internal security . However, nearly everyone is opposed to the lower wages being paid due to the current economic crisis. Based on the results of this research, the candidate decides to focus on improving the economy and security mechanisms in the country. He also decides to let go of the sexual productive health issues because it would potentially cause him to lose some support.

In this case, the political candidate has made logical conclusions on what topics he should use to campaign for his seat with minimal controversies so that he doesn’t lose many votes.

This situation could be summarized as follows:

Statement 1: Most people find sexual reproductive health issues controversial and cannot agree. Statement 2: Most people feel that the internal security of the country is in jeopardy and something should be done about it. Statement 3: Most people want higher wages and an improved economy. Statement 4: Political candidates who want to win must avoid controversy and speak up on things that matter to people. Conclusion: To win, political candidates must focus on higher wages, an improved economy, and the internal security of the country while avoiding sexual reproductive health matters.

Deductive reasoning is an aspect of logical reasoning. It is a top-down reasoning approach that enables you to form a specific logical conclusion based on generalities. Therefore, you can use one or more statements, usually referred to as premises, to conclude something.

For example:

Statement 1: All mothers are women Statement 2: Daisy is a mother. Conclusion: Daisy is a woman.

Based on the above examples, all mothers are classified as women, and since Daisy is a mother, then it’s logical to deduce that she is a woman too.

It’s worth noting though, that deductive reasoning does not always produce an accurate conclusion based on reality.

Statement 1: All caregivers in this room are nurses. Statement 2: This dog, Tom, is a caregiver . Conclusion: This dog, Tom, is a nurse .

From the above example, we have deduced that Tom, the dog, is a nurse simply because the first statement stated that all caregivers are nurses. And yet, in reality, we know that dogs cannot be nurses. They do not have the mental capacity to become engaged in the profession.

For this reason, you must bear in mind that an argument can be validly based on the conditions but it can also be unsound if some statements are based on a fallacy.

Since logical thinking is so important in the workplace, most job interviewers will want to see you demonstrate this skill at the job interview. It is very important to keep in mind your logical thinking skills when you talk about yourself at the interview.

There are many ways in which an interviewer may ask you to demonstrate your logical thinking skills. For example:

You may have to solve an example problem. If the interviewer provides you a problem similar to one you might find at your job, make sure to critically analyze the problem to deduce a solution.

You may be asked about a previous problem or conflict you had to solve. This classic question provides you the opportunity to show your skills in action, so make sure to highlight the objectivity and logic of your problem solving.

Show your logic when talking about yourself. When given the opportunity to talk about yourself, highlight how logic comes into play in your decision making. This could be in how you picked the job position, why you choose your career or education, or what it is about yourself that makes you a great candidate.

Why is it important to think logically?

It’s important to think logically because it allows you to analyze a situation and come up with a logical solution. It allows for you to reason through the important decisions and solve problems with a better understanding of what needs to be done. This is necessary for developing a strong career.

Why is logic important?

Logic is important because it helps develop critical thinking skills. Critical thinking skills are important because they help you analyze and evaluate a problem before you make a decision. It also helps you improve your problem-solving skills to allow you to make better decisions.

How do you improve your logical thinking skills?

When improving your logical thinking skills make sure you spend time on a creative hobby and practice questioning. Creative hobbies can help reduce stress levels, and lower stress leads to having an easier time focusing on tasks and making logical thinking. Creative hobbies can include things like drawing, painting, and writing.

Another way to improve your logical thinking is to start asking questions about things. Asking questions allows for you to discover new things and learn about new topics you may not have thought about before.

What are logical thinking skills you need to succeed at work?

There are many logical thinking skills you need to succeed in the workplace. Our top four picks include:

Observation

Active Listening

Problem-solving

Logical thinking skills are valuable skills to have. You need to develop them so that you can become an asset to any organization that hires you. Be sure to include them in your resume and cover letter .

And if you make it to the interview, also ensure that you highlight these skills. You can do all this by highlighting the career accomplishments that required you to use logical thinking in the workplace.

It’s Your Yale – Consider Critical Thinking Skills to Articulate Your Work Quality

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Roger Raber has been a content writer at Zippia for over a year and has authored several hundred articles. Having retired after 28 years of teaching writing and research at both the high school and college levels, Roger enjoys providing career details that help inform people who are curious about a new job or career. Roger holds a BA in English from Cleveland State University and a MA from Marygrove college.

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• What Is Analytical...

What Is Analytical Intelligence and How Is It Used? (With Examples)

10 min read · Updated on September 18, 2023

Witness the transformative power of analytical intelligence and make more informed choices

The facets of human cognition – how you gain knowledge and understanding – are as diverse as the situations we find ourselves in. Analytical intelligence represents one of those facets. It's sometimes referred to as critical thinking and is, basically, how you dissect information to figure out what's going on and come up with solutions. 

Has anyone ever told you that you think strategically or are good at coming up with innovative ideas? If so, you're probably an analytical thinker; someone who's really good at examining information, finding patterns, and drawing logical conclusions. You may even hold some type of analytical job – possibly involving research, data analysis , or management consulting.

Perhaps you want to be an analytical thinker but don't think you're quite there yet. Well, then, welcome to “What is analytical intelligence and how is it used?”. Here, you'll learn how to refine your skills by not only learning what analytical intelligence is, but also by understanding its relevance in different contexts and looking at practical applications of its use. 

What is analytical intelligence?

At its core, analytical intelligence is your ability to solve problems and employ logical reasoning to analyze a situation, break down the data, and draw conclusions based on evidence. A great example of someone who was known for analytical intelligence is Sherlock Holmes. He had what could be called a mental toolkit for solving puzzles and problems by looking at a scene and using logic to deduce what had happened. He even said as much when he uttered the phrase, “It's elementary, my dear Watson.” 

The psychology behind analytical intelligence

That mental toolkit contains things like systematic, logical, and objective reasoning, to allow your working memory to temporarily hold information while you question assumptions and draw conclusions based on deductive or inductive reasoning. During the course of solving a problem, you may also use what's called metacognition, where you think about your own thinking to evaluate the effectiveness of your conclusions and adjust your approach .

There are 5 basic steps in leveraging analytical intelligence to solve problems:

1. Observation

This involves paying close attention to everything surrounding an issue or problem that needs to be solved. It means that you have to be fully present and attentive at the moment, and take in as much information as possible to see things that others miss, understanding that even the tiniest detail can make the biggest difference. On top of that, observation can also mean that you have to get information from disparate sources and combine what you've learned in an objective way. The main goal here is to make sure you don't let your own opinions and biases cloud what you see. 

2. Detect patterns

After you have the information you need, it's critical to find similarities and connections between pieces of information to figure out how everything fits together. It could be similarities in data, behaviors, and occurrences that are related to the problem at hand. For example, a Sales Analyst may find that sales increase during certain months of the year, causing a trend that needs to be capitalized on to increase profits. Identifying patterns helps the bigger picture to come into focus, so that you can reasonably predict outcomes or anticipate what might happen next. 

3. Put the puzzle together

This is where logical thinking reigns supreme. You have to take all the information you've gathered and the patterns you've detected to piece things together in a coherent and meaningful way. That means you have to use reasoning to figure out how the pieces of information and the patterns relate to each other. Often, you'll find there is a cause-and-effect relationship. If you go back to our sales example, you'll probably find that the months with the pattern of increased sales are due to increased customer demand – probably around a holiday. At this point, you should start to build a story based on what you've learned and come to a point where you can start to explain the basis of the situation.

4. Get proof

However, you still need evidence to support your conclusions. If you were to walk up to a manager right now and tell them to put more money into marketing because customers are buying more products during certain months, that manager would tell you to prove it. You'd have to be able to present things such as sales data and competitor analysis to confirm any hypothesis you've drawn about increased sales during particular months. But that's not enough. You also have to test the hypothesis, to ensure that your conclusions are based on solid facts. This helps you to eliminate assumptions, emotions, and biases to support your claims and add credibility to your process.

5. Draw conclusions

This is where everything comes together to allow you to communicate your findings – either in a report or a presentation – to the people who make decisions. Once you've convinced people that your conclusions are solid and things begin to get implemented, you have to gauge the outcomes to be sure that the desired effect is being achieved. Analytical thinkers know that sometimes, course corrections have to be made for continuous improvement. 

The relevance of analytical intelligence

The beauty of analytical intelligence is that it's a super useful tool that you can use in all aspects of life - not just at work. Using it doesn't make you a know-it-all; it just means that you're good at breaking down problems to make smart choices. 

Here are some examples of where analytical intelligence can serve you well:

Science and research

Scientists use analytical thinking to break down complex problems, gather data, and uncover the mysteries of the universe. For instance, when scientists study climate change they use analytical thinking to analyze temperature patterns, carbon dioxide levels, and other data to understand what's happening to our planet.

Business and marketing

Businesses rely on analytical thinkers to use analytical skills like analyzing stocks, predicting market trends, and managing investments. In marketing, it's used to understand customer behavior and improve advertising strategies. Business owners are always trying to figure out how to increase profitability - the goal is, after all, to keep the doors open. Analytical intelligence helps you to analyze sales data, customer feedback, and market trends to make informed choices.

Everyday life

Even in your daily life, analytical thinking is quite handy. Let's say you're planning a road trip. You use analytical thinking to figure out the best route, estimate fuel costs, and decide where to stop along the way. It also helps you to make choices like which smartphone to buy, by comparing features and prices.

Are analytical people smart?

Yes, analytical people are smart, but again, that doesn't mean they are know-it-alls. It's a different kind of smart. People's brains work in different ways, and having analytical intelligence just means that you're great at problem-solving , thinking critically, and making sense of complex issues. In fact, because of how logical your brain is, you may find that you're really good at science but need a little help with art or music. Everyone has their strengths!

Being an analytical thinker also has little to do with having a high IQ. Don't be confused; IQ and analytical intelligence do go together, but it's not a causal relationship. IQ tests measure a lot of different types of intelligence , including analytical skills, spatial reasoning, and memory.

Some examples of analytical intelligence

We've already given a glimpse into how analytical intelligence works in roles like science, business, and marketing, but it's really useful in other areas as well. If you're in a profession that requires clear thinking, number-crunching, or problem-solving, analytical intelligence would be a great tool to have at your disposal. 

Here are some analytical intelligence examples:

Improving patient care at a health clinic

Increasing stock at a retail store to meet customer demand

Fixing a broken engine block on an automobile

Discovering a new drug that cures a disease

Designing a bridge that will support hundreds of cars traveling over a river every day

Writing a compelling news story based on a current event

Evaluating world finance markets to recommend investment opportunities

Adjusting conservation strategies to preserve ecosystems

Debugging software to improve uptime

Creating a new curriculum based on student performance data to increase test scores

As you can see, it doesn't matter what field you're in, analytical intelligence is very useful. 

Do you possess analytical intelligence?

At this point, you may be asking yourself, “How do I know if I'm analytical?” You can perform some self-assessments and take some quizzes to find out:

Self-assessment: Take a moment to reflect on your problem-solving style. Do you often break down complex issues into smaller parts to understand them better? Do you rely on data and evidence to make decisions rather than going with your gut feeling? If you answered "yes," you likely have analytical tendencies.

Analytical thinker quiz: Many quizzes and assessments are available online to help you to identify your thinking style; use your preferred online search platform and look up the term "analytical thinker quiz," and you'll be presented with quite a few. These quizzes often ask questions related to your problem-solving approach, decision-making, and how you handle information, and can provide valuable insights into your analytical intelligence.

Tips for developing analytical skills

However, even if you discover that you're not very good at analytical thinking, you can enhance your skills. Improving analytical intelligence is an ongoing process that requires regular practice. It's a good idea to work on analytical intelligence skills even if you're more of a creative thinker, because everyone runs into issues at some point in life or at work that require logical thinking.

A great way to increase analytical intelligence is by questioning assumptions and seeking evidence to support your beliefs and decisions. You can also engage in activities that challenge your analytical abilities, such as puzzles, brain teasers, and logic games. If you read a lot of books, articles, and research papers on topics that require analytical thinking, you can expand your knowledge and stimulate your mind. Additionally, analyze real-world situations and problems in your daily life and break them down into smaller components. Identify patterns, and consider multiple perspectives before making decisions.

Don't allow challenges to overwhelm you. Instead, embrace them and view them as opportunities to enhance your problem-solving skills. Collaborate with others on projects that involve analytical thinking, because different perspectives can lead to more comprehensive solutions. It's also a good idea to seek feedback from peers or mentors to refine your analytical thinking and decision-making processes.

Your new superpower

Analytical intelligence plays a major role in everyone's life and, because of that, it's less a skill and more a superpower – especially considering that we all live in a world of information overload and rapid change. In some instances, analytical intelligence could be the very thing that opens doors to new opportunities, propelling you toward innovation and excellence at work and in life. 

The bottom line is that, because the world at large needs people who can give insight and clarity into what's going on, analytical intelligence becomes a huge asset that you should grab onto - even if that means you need to practice to improve your skills. 

Some of those doors to new opportunities will need the help of a powerful resume to open. Is yours ready to tell the story of your analytical intelligence abilities? Upload it for a free review and find out.

Recommended reading: 

Practical Intelligence: What it is and How To Develop It

Cultural Intelligence: What is it and Why is it Important?

Why the Qualities of a Person Matter at Work and in Life

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Analytical thinking skills: definition, examples & ways to improve

Analytical skills are required in every industry. They help employees investigate a problem and find an efficient solution for companies’ success. In this article, we’ll explore why analytical skills matter, how to highlight them in various scenarios, and improve.

What’s analytical thinking?

Analytical thinking involves the research and analysis of complex issues for developing new ideas or finding solutions. Analytical skills are critical for work and listed as required in many job descriptions.

When do we use our analytical skills at work?

We need analytical skills for working with data and brainstorming ideas, solutions, and making decisions based on factors and options.

When we use critical thinking at work, we follow several steps before we create an idea or find a solution. The result of analytical thinking is usually followed by gathering and analyzing information.

Why are analytical thinking skills important?

Analytical skills are crucial because they allow you to solve problems and make decisions. These abilities are in demand by many employers in various industries.

Nowadays job applicants are measured both by hard and soft skills. Analytical skills are soft skills you can use in any industry. They show the level of professionalism, so you can highlight them if you want to get a job.

Companies value employees’ analytical skills because they help them achieve corporate goals and stay competitive on the market. Understanding problems and analyzing the situation are vital for every business.

Many jobs require using analytical thinking, including programming, customer service, teaching, marketing, and others. Some positions may require industry-specific hard skills, too. Still, analytical skills can be transferred to every industry. If you have strong analytical skills, you can apply for many vacancies.

5 must-have analytical skills

Many valuable analytical skills are worth including on your resume. Here are five must-have skills.

Creative thinking

Creative thinking relates to problem-solving and is a key skill for many jobs. To analyze information you need to be creative to notice hidden spots or trends not everyone can see. Creative thinkers can find a non-trivial solution that is more valuable than the obvious one. Creative people think outside the box to work out an effective solution or brainstorm ideas.

If you are a creative thinker, you will be able to:

• Optimize processes and operations.
• Collaborate for brainstorming with others.
• Solve complex problems in a non-trivial way.
• Think strategically.
• Integrate massive volumes of information into existing solutions.

Conducting an in-depth research is an integral part of analytical thinking. To solve a problem, you need to learn more about it. In simple words, you need to gather information before analyzing it.

This part of the analytical thinking process can involve various types of research and depends on the source of data. You can do online research, gathering information by comparing competitives, reviewing official documents, or interviewing experts, etc. It’s also valuable to know what kind of data is required for problem-solving.

To conduct a research, you need to be able to:

• Investigate the topic based on different data sources.
• Work with metrics.
• Prioritize data sources.
• Pay attention to the accuracy of the collected data.

Data analysis

Data analysis is one of the most crucial parts of analytical thinking. To solve a problem, you need to be able to analyze the information for identifying trends in a large volume of raw data. It is not enough to just read the information; you need to understand which information is worth highlighting for decision-making.

Using analytical thinking, you may need to be able to conduct some of the types of data analysis below:

• Quantitative/qualitative analysis
• Business analysis
• Industry or competitor analysis
• ROI analysis
• Process/Operational analysis
• Financial analysis

Problem-solving

After you collect and analyze the information, you need to identify the problem. Once it’s identified, you can find a reasonable solution. How? With your problem-solving skills, you need to be able to sort the data to find a rational and effective solution.

Sometimes you may need to identify small problems that cause a more significant way. Problem-solving skills will help you detect them and prevent a bigger one.

Communication

It’s useful to be able to research, analyze, and solve problems, but it means nothing if you lack compelling communication skills. Working with a team, you need to express your idea as clearly as you can. An effective communicator will not only solve the problem but will also save time.

How to show analytical skills?

Now you understand which of the analytical skills you possess, you need to know how to highlight them to do your best at getting a job or growing your career.

Mention on your resume

Including analytical skills on your resume, you will make it more attractive for employers. You can include them in the following sections:

• Professional history

Tell in the job interview

When telling about your working experience, be as specific as you can. Give detailed responses and show how analytical skills improved or solved your former employer’s issues. You may also be offered to do a pre-employment test to show your analytical skills.

Use at the workplace

Once you get a job, don’t stop using analytical skills. Be proactive in solving problems. Don’t be afraid of being a volunteer to participate in problem-solving and decision-making. It will be a great opportunity to highlight the analytical skills you possess.

7 ways to improve analytical skills

Like other skills, analytical thinking skills are natural but not inborn. To land a job you want or succeed in professional growth, you need to improve analytical skills. Use these tips we’ve worked out for students and employees who are interested in developing analytical skills.

1. Play brain games

If you want to improve analytical skills, you play brain games like chess, Sudoku, puzzles, and others. They can help you train thinking critically. Playing 15-20 minutes a day can stimulate your brain function and strengthen analytical skills.

Brain games are fun and make your pastime more productive. Instead of watching TV all evening, play a brain game alone or with your family. The best part is that you can play them online wherever you are.

LogicLike is an excellent brain training app with access to 3500 tasks in your smartphone for free. This is a unique platform with a systematized complex that makes up the best collection of brain games up to date. At any point, you can run a memory test or IQ quiz to check the progress and focus on improving your thinking skills.

LogicLike’s games include:

• Logic games
• 3D-thinking: spatial games
• True or false
• Smart counting
• Scaling and transfusion
• Chess problems for rookies
• Games in tables: honeycombs, Sudoku, kakuro

• Flexible mind and confidence Training on LogicLike, you develop logical reasoning, savvy and self-confidence!
• Good foundation for career growth We teach to deal with information efficiently and develop logic!
• Great for any age LogicLike is fun and helpful activity for kids and adults!

2. Take an online course on a new topic

After graduating from university, we may become passive about learning new things. Once we get a job and know what we are good at, we stop learning and may relax for some time.

Indeed, education plays an important part in professional growth. You should try to expand your knowledge to stay competitive in the job market.

You can take up an online course on the topic you are not good at. For example, not many employers are advanced users of MS Word. If you have time for education, it’s time to challenge yourself with a new topic. You will not only get new knowledge but also improve your analytical skills, including data research and analysis.

3. Solve math problems

Mathematics involves logic and solving a problem step-by-step. Since all math problems are based on logic, solving them will sharpen your analytical skills.

Practice various forms of math problems that will build your problem-solving abilities. You can visit additional math classes at college or university. Reasoning with others will also develop your communication skills. If you prefer doing it online, you can download an app with math games on your smartphone.

More than 150,000 users all over the world keep their brain toned thanks to Logiclike.

4. Participate in debates

Debates are one of the best activities that improve analytical skills, ranging from research to communication. If you are unfamiliar with this activity, you should try it. You can join your local debate club or organize a debate evening with your friends.

Why is it useful for analytical skills?

Taking part in a debate, you become more sociable because you meet new people and discuss various topics. To be well-prepared for debates, you need to research the topic, ask questions, and be ready with substantial arguments.

Debates are an efficient way to challenge yourself and improve your analytical skills.

5. Join online communities

Online communities are a good place to find like-minded people to discuss any issue you are interested in. Researching and reasoning together with other community members will encourage your analytical skills.

Don’t be shy when you need to ask or express your point of view. Anyway, you are there for getting new knowledge or sharing your ideas with others.

6. Develop curiosity by asking questions

Asking questions is the inborn talent we use from childhood. Indeed, questions are a good tool for developing curiosity. Curious people are more motivated and creative.

When you are interested in any topic, don’t be afraid of asking questions. Ask anyone who is an expert in the field of knowledge are you are interested in. Finally, the more questions you ask, the more answers and information you get.

After all, curiosity encourages us to ask questions. Don’t leave them unanswered!

7. Never make quick and crash decisions

To be an efficient problem-solver, you need to take time to think about the problem. Thinking about things and considering multiple factors and options are good habits if you want to develop analytical things.

Useful tips to have at hand:

• Analyze different scenarios of the solution you find to solve the problem. Think of their pros and cons.
• Consider the solution from multiple sides before you choose the best option.
• Don’t choose the easiest solution that lays on the surface. If you think more, you may find another solution that is more efficient.

Key takeaways:

• Analytical skills are soft skills required in many industry fields.
• Among the must-have analytical skills are creative thinking, research, data analysis, problem-solving, and communication.
• You can highlight your analytical skills on your resume, on the job, and at the workplace.
• You need to improve your analytical skills. You can play brain games, take an online course on a new topic, solve math problems, join a debate club, or online communities.

More than 550,000 parents from all over the world are already improving thinking skills with their kids.

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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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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.

About the Author

Analytical Skills: Why They Matter and How to Develop Them

Analytical skills involve collecting, analyzing, and interpreting information to solve problems. They are crucial in work and daily life, and can be developed through practice. This article explores their importance and ways to improve them.

Have you ever wondered what analytical skills are and why they are important? Analytical skills are the ability to collect, analyze and interpret information to solve problems and make decisions. These skills are highly valued in the workplace and also in our daily lives.

In today's fast-paced world, we are constantly bombarded with information. Whether it's in the form of news, social media, or data, we need to be able to analyze and interpret this information to make informed decisions. Analytical skills are essential for success in many fields, including business, finance, science, and technology.

While some people may possess natural analytical skills, they can also be developed and improved with practice. In this article, we will explore what analytical skills are, why they are important, and how you can improve them. Whether you're looking to advance in your career or simply want to make better decisions in your personal life, enhancing your analytical skills can have a significant impact.

What are Analytical skills?

Analytical skills are vital for any successful professional seeking to provide quality solutions to problems. These skills involve the sharpness to detect patterns, formulate theories, and observe data for the detection of discrepancies or similarities. It requires organizing of information systematically gathered from facts and opinions leading to a logical conclusion or solution.

Analytical skills require the ability to identify the problem and its cause and correlate it with available data to discover an appropriate course of action or an optimal result.

Employers typically wish to see individuals with these increasingly important analytical skills when searching for job candidates. The individuals must demonstrate the capability of having good problem-solving abilities and applying them in creative ways that bring about a successful outcome.

This combination allows companies and organizations alike greater flexibility when faced with various problems and unique situations requiring quick solutions.

How Does Analytical Thinking Work?

Analytical skills are an essential component of many job roles today. They enable you to evaluate different scenarios to solve problems that may not have obvious answers and identify the most beneficial solution for your organization.

An example of such a problem can be seen in our restaurant manager, who has been going over budget on food for the past two weeks. After reviewing the menus, customer orders, and food costs from suppliers, they identified that seafood prices had risen due to supply chain disruption caused by bad weather.

Using their analytical skills, they could connect the dots between these variables. This enabled them to come up with a new strategy for dealing with this issue which involved talking to their seafood supplier and working out a new deal with them to bring costs back down.

This is just one example of how analytical skills can help people extensively in their day-to-day job roles, allowing them to make better decisions and produce more successful outcomes for their organization.

Why are Analytical Skills Important?

Analytical skills are vital in most professional environments and help ensure good decision-making. Analytical skills involve breaking down, analyzing, and debugging intricate puzzles or situations to find the best resolution for any problem. These skills are transferrable to different positions as they indicate a mindset that prioritizes the situation's unique factors.

This means they can be used across multiple sectors as employers look for those who can use their analytical thinking within the organization's specific context, such as marketing research analysts, management executives, budget planners, or financial managers.

Good analytical skills not only give an individual a competitive edge when it comes to career prospects but also aid in navigating interpersonal relationships revolving around one's job. Working with data is important for understanding how a team works together, how negotiations should be conducted, or simply brainstorming potential strategies for training employees or solutions for problems posed by outside contractors.

As a result, having highly developed analytical skills can give someone an advantage over their peers in career growth prospects and allow them to identify new opportunities owing to their experience.

Key Analytical Skills

Here are some key analytical skills that employers look for when assessing job candidates:

Problem-Solving

Problem-solving skills are essential for effectively tackling any situation. These skills involve the ability to navigate complex systems and identify possible solutions. After an issue has been identified, research needs to be conducted to understand the problem better and find potential solutions. The next step is using creative problem-solving skills to design a solution that could potentially work for all parties involved. It's important to consider other people’s input as well, so asking for feedback can also provide valuable insights into how effective a proposed solution is.

For example, if the manager of a recreation center wanted to introduce new exercise classes for members, they would need to determine which classes are popular among members and when the classes should take place. In this case, surveys could be used to collect data from the members and gain insight into everyone’s preferences. With the relevant data collected, problem-solving skills can then be utilized to create a workout schedule that meets the needs of both members and staff. To make sure the schedule works, it's also important to collect feedback from members on how effectively their needs were met with the new class schedule.

Critical Thinking

Critical thinking is an essential skill for any business, no matter the size or scope. By utilizing critical thinking techniques, individuals and organizations can think outside the box to come up with innovative solutions to common problems. This is particularly true in terms of process-based systems, such as inventory management.

A great example of this would be a logistics company that has been using the same system for decades but could benefit from an updated approach. With critical thinking, an operations manager might identify areas where the existing system needs to be improved or replaced completely with something more efficient and cost-effective.

These are just some of the ways critical thinking can help businesses evolve beyond traditional practices and explore new approaches that will result in increased efficiencies. Through questioning preconceived notions and exploring new ideas, companies can hone their processes, innovate products and services, and ensure they remain viable in their respective markets.

Also, effective critical thinkers can potentially steer businesses away from costly blunders when making decisions that will affect people or resources. It is easy to see why strengthening an understanding of critical thinking is beneficial to highly successful businesses worldwide.

Analytical skills are key for many professional roles, but sometimes they alone aren’t enough. This is where creativity comes in. Creative thinking involves looking beyond traditional approaches and finding innovative solutions to problems. It gives analytical people the edge when it comes to big-picture thinking and problem-solving.

For instance, in the workplace, creativity could be used to devise a new product feature based on customer feedback or propose a data-driven presentation. Creativity is an important skill for many industries including data science, finance, marketing and more. With creative thinking, analytical minds can work smarter, not harder - combining their expertise with imagination to develop out-of-the-box solutions.

Examples of analytical creativity skills include ideation (generating creative ideas), innovation (turning those ideas into tangible solutions) and collaboration (working with others to bring a concept to life).

By improving analytical skills through creative thinking, professionals can bring unique value and perspective to their work and stand out in a crowded field.

Communication

Communication skills are an important asset to have when it comes to analytical thinking. Without the ability to communicate your ideas effectively, they wouldn't have any impact on a team. Breaking down complex analytical questions and data into more digestible pieces is a vital communication skill for teams to take away actionable insights.

For example, presenting data visualizations clearly and concisely can give team members an understanding of company performance or project progress. Similarly, verbal communication is important for taking the high-level findings from a statistical analysis and making them easily understandable for everyone.

When it comes to communicating analytical information to teams, storytelling is also key. By narrating the story behind data and its interpretation, you can make abstract concepts easier to comprehend as you bring it all together.

Research is often a vital part of finding solutions to problems and ensuring that the best way forward is chosen. It entails connecting with knowledgeable individuals, gathering facts from various internal and external sources, and understanding what data plays in solving the problem at hand.

Additionally, research in certain fields may involve running experiments or testing products or strategies as part of the greater research process. Overall, research skills involve being aware of which information sources are valuable or integral to finding a solution to a specific issue; this could mean vetting potential experts in an area of knowledge for consultation or seeking user insights through surveys and polls outside of an organization.

Along with giving one access to useful resources, strong research skills also involves understanding how all the pieces of data fit together so that a logical conclusion can be formed.

How to Improve Your Analytical Skills

Improving your analytical skills offers a wide range of benefits for your career. As one of the most sought-after qualities in the job market today, demonstrating your ability to think critically and objectively is key for setting yourself apart in an increasingly competitive hiring process. To maximize the impact of these skills, here are a few tips on cultivating your analytical capabilities and reinforcing their importance for future job opportunities.

First, seek out leadership roles that involve making tough decisions requiring a high level of thinking. Examples include positions such as project managers or administrators. In these roles, you’ll be encouraged to ask probing questions, brainstorm solutions, evaluate risks, and develop strategies accordingly.

Even if you don’t manage a team yet, there are plenty of ways to practice analytical thinking at all levels; consider tweaking tasks assigned by your team leader as an opportunity to apply creative approaches or suggest alternative solutions that might improve efficiency. Enrolling in data-driven decision-making classes can also help reinforce these concepts further by focusing on practical tools such as Excel spreadsheets or statistical methods used in business scenarios.

Keeping up-to-date with industry trends would ultimately allow you to stay informed about innovative approaches while consolidating fundamental concepts along the way.

Finally, stay on top of the latest methodologies and practices related to analytical thinking. Reading industry-specific articles or attending seminars can provide a great opportunity to learn about new ideas and trends in the field.

Additionally, consider reaching out to mentors or colleagues who are well-versed in this area for advice or guidance; having an experienced set of eyes review your work and provide feedback is invaluable in helping you make the best decisions and grasp the fundamentals of analytical thinking.

How to Highlight Your Analytical Skills

Analytical skills on your resume.

Analytical skills are an important asset for any job seeker to have on their resume. They can reflect a candidate’s problem-solving and critical thinking abilities, qualities that many employers value in a potential hire.

The most obvious way of adding analytical skills to your resume is to include them in your skills section. However, to show off your analytical expertise, make sure to utilize it in both your summary and professional history sections.

The summary section is a great place to showcase how you can employ analytical skills successfully. Describing an instance or success story showing off your problem-solving abilities can be invaluable when sought after by employers. This allows readers to get a snapshot of the types of challenges you faced previously and how you solved them using quantitative and qualitative data gathered from various sources.

Additionally, within the work experience section, providing details about particular projects you worked on as applicable can allow readers a better understanding of your ability with analytics.

Adding more detail here can further demonstrate your capacity for complex analysis and implementation of solutions based on analytics-driven sources of data.

Analytical Skills in an Interview

Interviewers often gauge applicants' analytical skills by how well they demonstrate them during the job interview. While this is particularly important for positions requiring a high degree of analysis, such as data analysts or software developers, it still applies to almost any job.

Employers want to know that applicants can think critically and make sound decisions.

To demonstrate analytical skills in an interview, utilize the STAR method when answering questions where you can highlight your abilities. The STAR method consists of identifying a Situation or Task, detailing Actions taken by yourself (or your team), and highlighting the Results that stem from those actions.

Explaining this all in detail shows employers how you were able to assess various factors and apply solutions resulting in positive outcomes. Furthermore, simple things like writing down notes during interviews to demonstrate the ability to gather relevant information and analyze it can also prove helpful.

Analytical skills are essential to many professional and personal tasks. They enable people to make sound decisions and think critically, which is important for many jobs and roles. Developing and showcasing these skills is important to increase the chances of success in any field. While it is important to demonstrate these skills on your resume, it is equally important to showcase them during the interview process as well.

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How to develop and demonstrate your problem-solving skills

Analytical and critical thinking skills, why employers want these skills, examples of how analytical or problem solving skills can be developed or evidenced, final thought....

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We all solve problems on a daily basis, in academic situations, at work and in our day-to-day lives.  Some of the problems that are typically faced by students include: 

• Putting together an argument for an essay
• Dealing with an awkward customer when working part-time in a shop or restaurant
• Thinking about how you are going to manage your budget to keep you going until the end of term
• Working out why your printer won’t respond
• Developing a strategy to reach the next level of a computer game.

Any job will also bring problems to be faced. It is important to show to a recruiter that you have the right skills to resolve these problems, and the personal resilience to handle the challenges and pressure they may bring. You need to be able to: 

• Evaluate information or situations
• Break them down into their key components
• Consider various ways of approaching and resolving them
• Decide on the most appropriate of these ways

Solving these problems involves both analytical and creative skills . Which particular skills are needed will vary, depending on the problem and your role in the organisation, but the following skills are key to problem-solving:

• Lateral Thinking
• Logical Reasoning
• Persistence 

Analytical and critical thinking skills help you to evaluate the problem and to make decisions. A l ogical and methodical approach is best in some circumstances: for example, you will need to be able to draw on your academic or subject knowledge to identify solutions of a practical or technical nature.  In other situations, using creativity or l ateral thinking will be necessary to come up with ideas for resolving the problem and find fresh approaches  Not everyone has these two types of skills in equal measure: for this reason, team working is often a key component in problem-solving. Further skills, such as communication, persuasion and negotiation , are important in finding solutions to problems involving people.

Whatever issue you are faced with, some steps are fundamental: 

• I dentify the problem
• D efine the problem
• E xamine the options
• A ct on a plan
• L ook at the consequences

This is the IDEAL model of problem-solving.  The final stage is to put the solution you have decided on into practice and check the results. 

Any workplace, project or task will have challenges or obstacles which need to be overcome. If an organisation employs people who are adept at solving problems at all levels, it reduces the need for complex chains of command or lessens demand on managers' time. In short, it will help save time and therefore money.  Analytical skills are perhaps becoming increasingly important; we are all bombarded with huge amounts of information every day. Being able to quickly yet comprehensively identify and evaluate the most important or relevant information for the organisation or your specific job role will be an increasingly useful skill. 

• Leisure activities (e.g. chess, logic games, computing).
• Overcoming obstacles to achieve an ambition or goal.
• Working in a customer environment and resolving complaints, particularly in situations where there is no protocol.
• Research (e.g. for essays or projects, or within the workplace).
• Particular achievements in the workplace (e.g. devising new working practices to improve efficiency, information systems development, diagnosing and rectifying faults or issues).
• Creative solutions to coursework problems.
• Identifying appropriate source material for assignments. 

A large cosmetics company had a problem in that some of the soap boxes coming off the production lines were empty. The problem was quickly isolated to the assembly line, which transported the packaged boxes of soap to the delivery department: some soap boxes went through the assembly line empty. The management asked its engineers to solve the problem. They spent much time and money in designing a machine with high-resolution monitors manned by staff; to scan all the boxes on the line to make sure they weren't empty.  A workman hearing about this, came up with another solution. He got a powerful industrial fan and pointed it at the assembly line. As each soap box passed the fan, the empty boxes were blown off the line. Moral: the simplest solution is usually the best!

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Problem-solving and analytical skills

• Putting together an argument for an essay
• Dealing with an awkward customer when working part-time in a shop or restaurant
• Debugging a computer program
• Managing your budget to keep you going until the end of term
• Working out why your printer won’t respond
• Developing a strategy to reach the next level of a computer game

All jobs involve problems that need to be solved. It’s important to show that you have the right skills to resolve these problems, and the personal resilience to handle the challenges and pressure they may bring.

Solving these problems involves both analytical and creative skills. The skills required can vary, depending on the problem and your role in the organisation, but the following skills are key to problem-solving: analytical ability, lateral thinking, initiative, logical reasoning and persistence.

Analytical and critical thinking skills help you to evaluate the problem and to make decisions. A logical and methodical approach is best in some circumstances: for example, you will need to be able to draw on your academic or subject knowledge to identify solutions of a practical or technical nature. In other situations, using creativity or lateral thinking will be necessary to come up with ideas for resolving the problem and find fresh approaches. Whatever issue you are faced with, some steps are fundamental:

• I dentify the problem
• Clarifying the nature of a problem
• Formulating questions
• Gathering information systematically
• Collating and organising data
• Condensing and summarising information
• D efine the problem
• Managing the problem
• Using the information gathered effectively
• Using techniques such as brainstorming and lateral thinking to consider options
• Analysing these options in greater depth
• Identifying steps that can be taken to achieve the objective
• E xamine the options
• Deciding between the possible options for what action to take
• Deciding on further information to be gathered before taking action
• Deciding on resources (time, funding, staff etc.) to be allocated to this problem
• A ct on a plan
• Implementing action
• Providing information to other stakeholders; delegating tasks
• Reviewing progress
• L ook at the consequences
• Monitoring the outcome of the action taken
• Reviewing the problem and problem-solving process to avoid similar situations in future

At any stage of this process, it may be necessary to return to an earlier stage – for example, if further problems arise or if a solution does not appear to be working as desired.

Developing your analytical and problem-solving skills

Most problem-solving skills are developed through everyday life and experience. However, the following interests and activities may be useful in demonstrating a high level of these skills - this may be particularly important when applying to employers in areas such as engineering, IT, operational research and some areas of finance:

• ‘Mind games’ such as cryptic crosswords, Sudoku, chess, bridge
• Computer games – the best of these can involve strategic planning, critical and statistical analysis and assessing the pros and cons of different courses of action
• Practical interests such as programming, computer repairs, car maintenance, or DIY
• Working with sound or lighting equipment for a band, event or show
• Academic study: evaluating different sources of information for essays, designing and constructing a shelter for an architecture project; setting up a lab experiment

Problem-solving skills and graduate jobs: what do recruiters want?

Analytical ability, problem-solving skills and using initiative are among the top ten skills recruiters want graduates to demonstrate. They want people who will take the personal responsibility to make sure targets are met, who can see that there might be a better way of doing something, and who are prepared to research and implement change - people who don’t panic or give up when things go wrong but who will seek a way around the problem. These problems may be similar to academic problems or may be more practical problems such as those involved in people management.

These skills can be asked for in a variety of ways.  Many job ads will simply ask for candidates who can take the initiative or have the ability to resolve problems. Others, however, may not make it so clear.  You have to learn to interpret phrases like:

• “Someone keen to take responsibility and with the confidence to challenge established practices and come up with new ways of working…”
• “An enquiring mind and the ability to understand and solve complex challenges are necessary…”
• “We are looking for innovative minds and creative spirits ...”
• “The ability to use your own initiative, to think for yourself, to be creative and pro-active...”
• “The ability to resolve problems, to think logically and/or laterally, to use ingenuity to overcome difficulties and to research and implement solutions...”

How will they assess these skills?

On application forms

• Describe a situation in which you analysed data and solved a complex problem
• Describe a complex problem you have faced and the steps that you took to solve it
• Describe a setback in your life and say what you did to overcome it. What lessons did you learn from this?
• Describe a time when you demonstrated creativity in solving a difficult problem
• Give me a specific example of a time when you used good judgment and logic in solving a problem

When answering these questions, cover the process you used to solve the problem rather than just outlining the problem itself. Give examples of how you used initiative/creativity, or made effective use of resources, in solving the problem. It is also useful to say what you learned from this process, especially if the problem was not resolved to your complete satisfaction.

Evidence you could give to an employer to convince them that you have problem-solving skills:

• Analysing data from a project or experiment
• Working on a computer helpdesk
• Advising a client at the Kent Law Clinic
• Implementing a new filing system in an office job
• Acting as a student rep
• Dealing with staff problems or unexpected staff shortages in a part-time job
• Coping with living on a limited student budget

Example from an application form

“Give an example of a time when you have successfully resolved a complex problem .”

In the sixth form, I took part with two friends in a “Robot Challenge” competition. The brief was to design and build a robot that could perform a dance routine synchronised with a music soundtrack. My responsibility was to control the movement of the robot through the sensors and actuators. This was a complex task because of the number of movements that the robot was required to execute and the different stimuli to which it had to respond. In addition, the robot proved particularly sensitive to changes in light levels and I needed to experiment with a number of adaptations to discover the optimum balance between responsiveness and reliability.

Our team achieved second place in the local competition and progressed to the regional final, where we came fifth out of 25 teams.

Through psychometric tests

The most common of these tests involve verbal and numerical reasoning: you may also encounter diagrammatic reasoning and critical thinking tests. They may be administered online at an early stage of the selection process, or at first interview or assessment centres. (link to Psychometric testing pages)

At interview

If your application form has included competency-based questions such as the ones above, you can expect the employer to ask for more detail at interview, about the problem or the situation and the way that you went about finding a solution. Be prepared to be asked about alternative ways in which you might have gone about tackling this problem and what you would have done if things hadn’t worked out.

Hypothetical questions

Hypothetical questions ask you about the course of action you might take in the event of some fictional situation, often work-related. There is usually no right or wrong answer to these questions: the interviewers are seeking to assess your logical thinking and common sense. You may need to ask questions to clarify the situation and gather more information. You can expect your answers to be challenged, the interviewers asking questions such as  “Yes, but what if …?”, or “Have you thought about ….?”, or “Why would you do that …?” This doesn’t mean that there is anything wrong with the answer you have given – just that the interviewers are trying to find out how you have arrived at your solution to the problem. They may also be testing you out to see how you cope with pressure and how well you can argue a point. Although the situation is hypothetical, if you have been faced with any similar situation in real life you can use this, and the way that you handled it then, to support your answer.

• "You are working on the till in a retail store when a customer’s credit card is refused. The cardholder is a regular customer who is trying to buy a present for their mother’s birthday the following day. How would you deal with this situation?"
• "Your manager regularly leaves you in charge of a small office in his absence. The other staff regularly complain to you about the way he runs things, and how irritated they are by his interference in their day-to-day work - what do you do?"
• "You work in a company that manufactures meat pies and pasties. Sales have been falling for several years and you are asked to come up with ideas to revive the company”

Technical questions

These are most commonly asked at interviews for science, engineering and IT posts. They may relate to your previous relevant work experience or to a student project, or may relate to hypothetical situations:

• “The scenario was that we were in charge of lighting a theatre. We were given different examples of what type of problem could be caused by various faults in the lighting plan and who this problem would affect. It got harder as different conditions were added to the original ones and you had to take more and more information into consideration, such as: certain lights need to always be turned on first; some lights need to be warmed up in the breaks; different lights create different effects.”
•  “If I were organising a national cancer screening campaign, what standards/precautions/feasibility/practicality checks would I do before implementing the scheme?” 

Ethical questions

These are particularly common in interviews for medicine and law. Again, there is often no right or wrong answer, although you should be aware of the legal and regulatory framework behind these questions. You will be expected to put both sides of the argument before giving your opinion and can expect to be challenged and asked to justify your opinion.

• Should doctors be authorised to remove organs from a dead person without obtaining consent from their relatives?
• A patient urgently requires a bone marrow transplant but the only suitable donor is her brother, who has severe physical and mental disabilities. Can this brother donate?
• Should conjoined twins be separated even if it is almost certain that one of them will die in the process?
• Since the victims in rape cases have anonymity, should the same anonymity be granted to the accused?

Case study interviews

This type of interview is often used for graduate positions in management consultancy and investment banking. Case questions are business problems designed not only to test your logical and analytical thinking skills, ability to solve problems but also to make you think on your feet. Often there are no right answers to these types of questions, but they give the selector an idea of how you think, your reasoning skills, how you react under pressure and your common sense. The problems may be brief (sometimes seemingly bizarre) “estimation” or “brain teaser” questions such as “ How many cars are there in the EU?”,  or “ How many laptops will be purchased in the UK in 2020?”,  or “ Why are manhole covers round?”

Alternatively, you may be asked questions related to the issues facing real-life clients:

• A manufacturer of umbrellas, based in the west of Ireland, wants to expand into mainland Europe.  What issues should they consider? What risks might they face?
• A parcel delivery company plans to offer a new service where customers can hand a package directly to one of the company's drivers instead of taking it to a depot. What issues need to be thought about?

Through group tasks and discussions at assessment centres

Almost all assessment centres will involve a strong element of group work. These tasks may involve the group sitting around a table discussing a problem or may be more active and practical. The decision reached by the group is likely to be less important than the way in which the group works together to reach its decision – these tasks aim to test your team-working and negotiation, as well as your problem-solving, skills.

• “We were asked to come up with a business proposal for building a computer network between an imaginary group of islands, to be presented to the island’s government.”
• “We were provided with information on four sites that were possible locations for the construction of a nuclear power station. This included information on the environment, the local economy, transport links and the estimated costs of construction. We had to select one and recommend it to the Secretary of State for Energy, giving the reasons for our decision.”
• “We were given a task involving Lego bricks - we had to work out how many bricks we wanted to use to build the tallest tower possible at the lowest cost.”
• “A large part of the Army Officer selection process takes place outdoors – the teams of candidates have to negotiate an obstacle course using ladders, ropes, poles and planks.”

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Analytical Thinking vs Problem Solving: A Comprehensive Comparison

Analytical thinking and problem solving are crucial skills in various aspects of life, including personal and professional situations. While they may seem interchangeable, there are distinct differences between the two. Analytical thinking focuses on breaking down complex information into smaller, manageable components to understand a situation and evaluate alternatives effectively. On the other hand, problem solving involves devising practical solutions to overcome challenges or resolve issues that arise in daily life or the workplace.

Both analytical thinking and problem-solving skills contribute to making well-informed decisions, managing risks, and achieving success in various areas of life. By understanding these skills’ distinctions and applying them effectively, individuals can enhance their performance in the workplace, handle complex situations with ease, and make better choices in their personal lives.

Key Takeaways

• Analytical thinking is about understanding complex situations, while problem-solving focuses on finding practical solutions.
• Mastery of both skills leads to informed decision-making and improved risk management.
• These abilities are essential for workplace success and overall personal growth.

Understanding Analytical Thinking

Nature of Analytical Thinking

Analytical thinking refers to a mental process in which a person systematically breaks down complex problems or situations into smaller, manageable components. This enables the identification of essential elements and their relationships, leading to an effective solution. Analytical thinkers excel in identifying patterns, interpreting data, and drawing conclusions based on factual information. Unlike reactive problem-solving, which focuses on finding immediate remedies, analytical thinking is strategic in nature, seeking long-term solutions by addressing the root causes of a problem.

Key components of analytical thinking include reasoning, fact-checking, and questioning assumptions. This skill set allows individuals to approach problems with an open mind, meticulously gather and analyze data, and make well-informed decisions. Ultimately, analytical thinking leads to more informed and strategic decision-making, increasing the likelihood of success in professional and personal endeavors.

How Analytical Thinking Works

The process of analytical thinking unfolds in several stages:

• Identify the problem or situation : Determine the issue that needs addressing and clearly define its scope.
• Gather relevant data : Collect information related to the problem from various sources, ensuring its accuracy and reliability.
• Break down the problem : Dissect the problem into smaller, manageable parts to gain a better understanding of its intricacies.
• Analyze and interpret data : Examine the data to identify patterns, trends, and relationships, and derive insights using logical reasoning.
• Question assumptions : Challenge any preconceived notions or biases that may skew the analysis and arrive at the most objective conclusions possible.
• Generate solutions : Propose potential solutions based on the analysis, weighing their pros and cons.

It is important to note that analytical thinking is not solely reserved for mathematicians or scientists but is a valuable skill applicable to a wide range of disciplines and professions. From business analysts, who require analytical thinking and problem-solving skills to identify and implement changes, to daily decision-making in personal lives, analytical reasoning plays a vital role in successfully navigating through various complexities.

Significance of Problem Solving

Features of problem solving.

Problem solving is an essential skill that helps individuals and organizations tackle challenges effectively. Problem-solving skills enable individuals to identify problems or obstacles, analyze the situation, and find appropriate solutions. These skills include critical thinking, analytical reasoning, decision-making, and learning from the process. People with strong problem-solving abilities can better cope with stress, handle risk, and adapt to change in a fast-paced environment.

In the context of decision-making, problem solving requires individuals to evaluate multiple options and select the one with the highest probability of success. A well-developed thinking process is crucial to identifying and analyzing creative solutions, as it helps individuals see beyond the apparent issues and delve deeper into the underlying causes.

Process of Problem Solving

The process of problem-solving typically involves several stages:

• Identify the problem : Recognizing the issue at hand and understanding its impact on the situation.
• Gather information : Collecting relevant data and facts that will help in understanding the problem.
• Analyze the problem : Examining the situation, breaking it into smaller parts, and identifying the root causes.
• Generate solutions : Brainstorming various possible solutions and evaluating their feasibility.
• Choose the best solution : Using decision-making skills to select the most suitable solution based on available information.
• Implement the solution : Putting the chosen solution into action and monitoring its effectiveness.
• Evaluate and learn : Reflecting on the outcomes and learning from the experience for future problem-solving situations.

By sharpening problem-solving skills and employing an organized thinking process, individuals can enhance their abilities to overcome challenges and make informed decisions, leading to personal and professional growth.

Comparing Analytical Thinking and Problem Solving

Similarities.

Both analytical thinking and problem solving involve the process of breaking down complex situations into smaller, manageable components. In both approaches, individuals need to evaluate the information at hand, identify patterns, and derive conclusions based on the evidence. This often involves receiving feedback, adapting to new information, and adjusting one’s approach.

Moreover, practicing both analytical thinking and problem-solving techniques can lead to improved decision-making abilities. This development, in turn, translates into greater efficiency and effectiveness in personal and professional contexts.

Differences

While analytical thinking and problem solving share some similarities, they also have notable differences. Analytical thinking typically follows a linear and sequential process, whereas problem solving might involve iterative processes and creative solutions.

Analytical thinking often focuses on dissecting a situation or a problem, looking for underlying patterns, and finding ways to logically deduce solutions. On the other hand, problem solving might require a combination of analytical and creative thinking, especially when faced with novel or ambiguous challenges. Problem solvers often need to develop unique strategies and evaluate alternative solutions before settling on the most effective approach.

In conclusion, analytical thinking and problem-solving, while both essential skills, have distinct applications and methods, and their effective use can be instrumental in achieving success in various aspects of life.

Ways to Improve Both Techniques

Developing analytical thinking.

Developing analytical thinking is vital for individuals seeking to improve their problem-solving abilities. One effective strategy is to practice creative activities, such as brainstorming or solving puzzles, to challenge the brain and foster development. Engaging in these tasks allows for the creation of new connections and enhances cognitive flexibility.

Another useful approach is to focus on communication and the art of listening. Active listening enables a better understanding of various perspectives and leads to well-informed decisions. Moreover, discussing complex topics can strengthen one’s ability to analyze and evaluate information effectively.

Collaborating with others can also help individuals enhance their analytical thinking skills. By working together, people can build on each other’s strengths and overcome challenges. Additionally, they can exchange ideas and learn from different viewpoints, which may lead to innovative solutions.

Enhancing Problem Solving Skills

To enhance problem-solving skills, one must be willing to take action and embrace challenges. Tackling problems head-on allows for growth and the development of practical strategies. Regular practice is essential for refining these skills and building confidence in decision-making.

Integrating soft skills, such as empathy and adaptability, play an essential role in problem-solving. Employing these abilities can improve interpersonal communication and contribute to the formation of more effective solutions.

Utilizing a methodical approach to problem-solving can also yield positive results. Techniques like breaking down complex issues into manageable steps or generating multiple possible solutions can enable a more comprehensive analysis, increasing the likelihood of success in overcoming challenges.

Finally, don’t shy away from seeking feedback from peers and mentors. Constructive criticism can highlight areas for improvement and further facilitate the development of both analytical thinking and problem-solving skills. Remember, the key to growth lies in continuous learning and adapting to new situations with confidence and clarity.

Importance in Workplace and Career Success

Relevance in the workplace.

Analytical thinking and problem solving play crucial roles in the workplace. These skills enable employees to efficiently tackle a variety of tasks and challenges. Analytical thinking refers to gathering, organizing, and evaluating information to detect patterns and identify problems. Effective problem solving involves devising creative solutions based on these findings 1 . In the modern workplace, individuals with strong analytical thinking skills can identify issues and make well thought-out decisions that contribute to overall company success 2 .

Effective communication is an important aspect of analytical thinking and problem solving. In a professional setting, employees must often convey their findings and ideas to stakeholders, ensuring that solutions are implemented appropriately and any concerns are addressed. This communication can lead to improved collaboration, clearer goals, and faster resolution of issues 3 .

Implication for Career Success

In addition to benefitting the workplace as a whole, strong analytical thinking and problem-solving skills are critical for individual career success. These skills can help professionals stand out among their peers and demonstrate their value to their organization. Professionals who can apply analytical thinking and problem-solving techniques are viewed as being able to think critically, make decisions, and take initiative, which are all highly valued by employers 4 .

Individuals who possess these skills are often able to make more informed judgments and sound decisions. This can lead to career advancement and job stability, as they are viewed as capable and dependable. Developing analytical thinking and problem-solving abilities can also open doors to new opportunities and industries, making individuals more versatile and efficient in their careers 5 .

Role in Decision Making and Risk Management

Influence on decision making.

Analytical thinking plays a crucial role in decision making, as it involves breaking things down into their component parts and using deductive reasoning to draw conclusions from given evidence and assumptions source . This allows individuals and organizations to carefully consider the pros and cons of each option, determine the feasibility of implementing potential solutions, and weigh the costs and benefits associated with each decision.

Problem-solving, on the other hand, is an analytical method that focuses on identifying potential solutions to specific situations source , sometimes requiring personal decision-making that may involve judgments or decisions on the way to find the best outcome. Both analytical thinking and problem-solving contribute to effective decision-making processes, as they provide tools and techniques for examining different courses of action and limiting uncertainties.

Contribution to Risk Management

Risk management is a critical aspect of decision-making, as it helps organizations and individuals identify, assess, and mitigate potential risks associated with various decisions. Analytical thinking contributes to risk management by enabling decision-makers to collect and analyze data, evaluate risks and their potential consequences, and make informed decisions based on the results source .

Similarly, problem-solving assists in risk management by addressing potential challenges that may arise during the implementation of solutions, such as examining potential obstacles, resource constraints, and other factors that may impact the success of an initiative source . By combining the strengths of both analytical thinking and problem-solving, decision-makers can enhance their risk management strategies and ensure a higher probability of success in their respective decisions.

In summary, analytical thinking and problem-solving are essential tools in decision-making and risk management, as they provide the necessary framework for evaluating options, weighing potential outcomes, and identifying potential challenges. By utilizing these methods, decision-makers can make more informed choices and mitigate potential risks associated with their decisions.

Utilization in Business Analysis

Application in business analysis.

Analytical thinking and problem solving are essential skills for business analysts in their day-to-day work. They are responsible for identifying, researching, and understanding complex business problems, as well as finding effective solutions to address them. By using their analytical thinking skills, business analysts can gather, assess, and interpret data from various sources to develop a comprehensive understanding of the situation at hand [1] .

When approaching a problem, business analysts consider several key factors, such as people, processes, and technology. They employ systems thinking to understand the enterprise holistically and how all these elements interact. This mindset helps them to not only identify the root cause of a problem, but also to develop solutions that address the underlying issues effectively [2] .

Understanding Financial Data

One key area where business analysts apply their analytical and problem-solving skills is in the realm of financial data. Here, they are tasked with interpreting complex financial information to derive valuable insights and make informed decisions for the organization.

In this context, their analytical thinking skills enable business analysts to:

• Gather relevant financial data from multiple sources
• Identify patterns, trends, and potential issues
• Assess the quality and accuracy of the data
• Develop conclusions and recommendations based on the analyzed data

By employing problem-solving skills, business analysts can:

• Understand the impact of financial data on business processes and performance
• Identify potential areas for improvement or optimization
• Propose and evaluate relevant solutions for financial issues [3]

Overall, business analysis relies heavily on the combination of analytical thinking and problem-solving skills to address various challenges faced by organizations. The ability to understand and interpret financial data significantly contributes to the success and growth of any enterprise.

Real Life Examples

Analytical thinking and problem solving are essential skills in both personal and professional life. They allow individuals to tackle complex issues, identify the root causes, and develop effective solutions. Let’s examine some real-life examples that emphasize the differences between these two thought processes.

In the workplace, an employee might face a challenge in increasing sales. Applying analytical thinking , the individual would gather data, identify patterns, and evaluate market trends to understand the factors impacting sales performance. With this information, they can determine which areas need improvement and develop targeted strategies to address the issue. For example, they may discover that customers are dissatisfied with the available products in a particular category, prompting changes in the company’s product offering.

On the other hand, problem-solving involves addressing specific situations, such as dealing with a dissatisfied customer. In this instance, the employee would need to rely on their experience and emotional intelligence to find a solution. They would listen to the customer’s concerns, empathize with their feelings, and proactively offer options to resolve the problem. This process may include correcting mistakes made during a transaction or offering compensation for a negative experience.

Another example can be found in the realm of personal finance. Analytical thinking would be employed to evaluate one’s financial situation and understand patterns in spending habits. This analysis could reveal areas where money may be saved or better utilized. For instance, it may uncover excessive spending on dining out or ineffective monthly budgeting practices.

Conversely, problem-solving can come into play when an unexpected financial emergency occurs. In such cases, one would need to quickly evaluate the situation and devise creative solutions to address the crisis. This might involve temporarily reducing non-essential expenses, seeking additional sources of income, or negotiating payment plans with creditors.

In both of these real-life scenarios, analytical thinking and problem-solving work in tandem, complementing each other to achieve effective outcomes. While individuals may favor one approach over the other, it is crucial to recognize and develop both skillsets to navigate the complexities of modern life successfully.

• https://www.glassdoor.com/blog/guide/analytical-thinking/ ↩
• https://www.indeed.com/career-advice/career-development/problem-solving-and-decision-making ↩
• https://www.radford.edu/content/cobe/innovation-analytics/analytics/career-prep/report-e.html ↩
• https://www.indeed.com/career-advice/career-development/critical-thinking-vs-problem-solving ↩
• https://www.amanet.org/analytical-thinking-problem-solving-and-decision-making/ ↩

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How to assess reasoning skills

Identifying individuals with excellent reasoning skills is a common goal when making new hires. The ability of your employees to analyze information, think critically, and draw logical conclusions is crucial in today’s dynamic professional landscape. 

Pre-employment assessments offer great value by effectively assessing these essential capabilities. 

TestGorilla’s assessments objectively gauge a candidate’s ability to solve problems, evaluate arguments, and draw logical inferences. By leveraging these assessments, you can secure candidates with the cognitive skills necessary for analytical thinking and decision-making.

Table of contents

What is a reasoning skills assessment, why are reasoning skills important, what skills and traits do employees with good reasoning have, tests for evaluating reasoning skills, how testgorilla can help you find candidates with reasoning skills.

A reasoning skills assessment is a valuable tool that can provide insights into a candidate’s ability to analyze information, think critically, and make logical deductions. 

This assessment aims to evaluate an individual’s cognitive skills related to problem-solving, decision-making, and analytical thinking.

There are several types of cognitive ability tests that can aid in assessing reasoning. During a reasoning skills assessment, candidates are presented with various scenarios, questions, or problems that require them to apply logical thinking and problem-solving techniques. 

It can involve evaluating arguments, identifying patterns, making inferences, or solving puzzles. 

Assessments often use standardized tests or exercises that measure different aspects of reasoning. They’re designed to objectively evaluate a candidate’s cognitive abilities rather than simply relying on qualifications or experience. 

Using a reasoning skills assessment, you can make more informed decisions about a candidate’s aptitude for sound reasoning, problem-solving, and decision-making.

Effective problem-solving

Employees with solid reasoning skills can tackle complex problems with clarity and efficiency. They can analyze information, identify patterns, and make logical connections, enabling them to devise smart ways to meet challenges. 

Their problem-solving ability enhances productivity, streamlines work processes, and drives continuous organizational improvement. This is why you need analytic skills testing in your hiring process if you want to find the best candidates.

Quality decision-making

Reasoning skills contribute to effective decision-making. Employees who think critically and can logically evaluate information are more likely to make informed decisions based on evidence and careful analysis. 

Their ability to weigh options, consider potential outcomes, and anticipate risks helps mitigate errors.

Adaptability and flexibility

Individuals who can think critically and analyze situations from different angles are better equipped to embrace new challenges, adjust their approach, and find new strategies. 

Their adaptability fosters resilience, enabling them to thrive in fast-paced industries and contribute to organizational growth and success.

Enhanced innovation

Reasoning skills are at the core of innovative thinking. Employees who excel in reasoning can identify gaps, find opportunities, and connect seemingly unrelated ideas or concepts. 

Their ability to analyze data, draw logical conclusions, and come up with creative new tactics drives innovation. Hiring individuals with superb reasoning skills encourage the development of new groundbreaking ideas.

Effective risk management

Employees with exemplary reasoning abilities can evaluate potential risks, weigh their impact, and consider mitigation strategies. 

Their ability to anticipate challenges and make calculated decisions reduces the likelihood of costly errors or setbacks, contributing to effective risk management within your organization.

Continued learning and growth

People with great reasoning skills tend to be lifelong learners. They have a natural curiosity and a desire to expand their knowledge and skills. 

Their ability to think critically and adapt enables them to embrace new information, learn from experiences, and grow professionally. 

Effective communication and collaboration

Employees with reasoning skills can think critically and express their ideas clearly. They can engage in meaningful discussions, contribute valuable insights, and articulate their viewpoints. 

They can also understand and respect diverse perspectives, leading to enhanced teamwork, collaboration, and the generation of new, exciting courses of action through collective intelligence.

Critical thinking

Individuals with good reasoning skills demonstrate strong critical thinking abilities. They can analyze information objectively, evaluate arguments, and identify logical inconsistencies. 

Their critical thinking skills enable them to approach problems and challenges with a logical and rational mindset, enabling them to make sound decisions and solve complex issues effectively.

Problem-solving aptitude

Excellent reasoning skills often go hand in hand with exceptional problem-solving aptitude. Candidates who excel in reasoning can break down complex problems into manageable components, identify patterns, and come up with innovative new strategies. 

They exhibit a natural curiosity, a willingness to explore different approaches, and the ability to think outside the box, enabling them to overcome obstacles and find creative resolutions.

Analytical thinking

A key trait of individuals with good reasoning skills is their ability to think analytically. They can dissect complex information, identify key components, and draw connections between various data points. 

With their analytical thinking skills, they can examine data objectively, discern trends or patterns, and make informed decisions based on evidence and logical deductions.

Logical reasoning

Strong reasoning skills are often indicative of individuals who possess logical reasoning abilities. They can follow sequences, identify cause-and-effect relationships, and draw conclusions based on deductive or inductive reasoning. 

Their logical reasoning skills enable them to evaluate options, anticipate potential outcomes, and choose the most appropriate course of action.

Flexible thinking

Employees with good reasoning skills often exhibit cognitive flexibility. They can adapt their thinking and approach to different situations, incorporating new information and adjusting their perspectives as needed. 

Their cognitive flexibility lets them consider multiple viewpoints, explore alternative options, and navigate complex challenges with an open mind. They re-evaluate assumptions and revise their thinking based on new insights or evidence.

Communication skills

For reasoning skills to be effective in the workplace, communication is key. It’s important that employees can articulate their thoughts clearly, present logical arguments, and express complex ideas in a concise manner. 

The ability to communicate effectively helps to convey the reasoning process, engage in meaningful discussions, and collaborate with others, fostering better teamwork and understanding within the organization. 

Workplace communication tests can evaluate candidates’ ability to communicate at work.

Individuals with good reasoning skills demonstrate a natural curiosity and a thirst for continuous learning. 

They have a genuine interest in expanding their knowledge, exploring new ideas, and seeking out information to enhance their understanding. 

Their curiosity drives them to stay updated on industry trends, engage in self-improvement, and continuously develop their reasoning abilities.

When it comes to assessing a candidate’s reasoning skills, it’s important to delve deeper beyond surface-level observations. Understanding their critical thinking, problem-solving, and decision-making abilities is crucial. That’s where TestGorilla can lend a hand. 

Our extensive test library is a treasure trove of options to suit your needs. You can mix and match tests to create an assessment that aligns perfectly with your company’s requirements. 

Whether you’re searching for top-notch analysts or logical thinkers who thrive in challenging situations, our tests can help you discover exceptional candidates with the cognitive skills to excel.

Here are some of our most popular tests for assessing reasoning skills:

Critical Thinking test

At TestGorilla, we understand the significance of this test in evaluating a candidate’s ability to analyze information, make logical connections, and approach problems from multiple perspectives.

By incorporating the Critical Thinking test into your reasoning skills assessment, you gain valuable insights into an individual’s cognitive abilities and capacity to think critically in real-world scenarios. 

This test goes beyond simple memorization or rote learning; it assesses how candidates can apply their knowledge, reason through complex situations, and arrive at sound conclusions.

Verbal Reasoning test

Our Verbal Reasoning test is essential because it assesses language comprehension, critical thinking, and problem-solving abilities. It evaluates an individual’s capacity to understand written information and draw logical conclusions. 

This test also indirectly measures language proficiency and communication skills. Verbal reasoning tests are widely used because they predict academic and occupational success, and they provide a fair and accessible assessment tool for individuals from diverse backgrounds.

Spatial Reasoning test

TestGorilla’s Spatial Reasoning test assesses a candidate’s capacity to perceive and understand spatial relationships, shapes, and patterns. 

This skill is particularly relevant in fields such as engineering, architecture, design, and logistics, where professionals often encounter complex spatial problems. 

The Spatial Reasoning test also assesses a candidate’s capacity to mentally visualize and manipulate objects in space. These abilities are essential for tasks that involve spatial planning, such as interpreting maps, organizing physical spaces, or understanding 3D models. 

Candidates who perform well in spatial reasoning tests demonstrate a heightened ability to think ahead, anticipate outcomes, and develop effective strategies based on spatial information. 

Numerical Reasoning test

The Numerical Reasoning test provides valuable insights into a job candidate’s reasoning skills, particularly in terms of quantitative analysis, problem-solving, and logical thinking. 

By assessing a candidate’s proficiency in interpreting numerical data and making accurate deductions, this test assists you in identifying those who possess the numerical acumen necessary for roles involving financial analysis, data-driven decision-making, and problem-solving using quantitative methods.

Mechanical Reasoning test

While not all job roles require mechanical reasoning, this test is pertinent for positions that involve machinery, engineering, or technical operations by providing crucial insights into a candidate’s reasoning abilities in these areas.

The Mechanical Reasoning test evaluates a candidate’s understanding of mechanical principles and ability to apply that knowledge to solve problems. 

This test presents candidates with scenarios and questions that require them to analyze mechanical systems, interpret diagrams, and make logical deductions.

Problem Solving test

Problem-solving tests evaluate a candidate’s aptitude for analyzing issues from different perspectives, breaking them down into manageable components, and applying logical reasoning to reach effective resolutions. 

The Problem Solving test measures a candidate’s ability to think critically, make sound judgments, and adapt their problem-solving approach as necessary. 

Strong problem-solving skills are not limited to specific industries or job roles; they are highly transferable and valuable across various fields, including business, technology, healthcare, and customer service.

Attention to Detail (Textual) test

TestGorilla’s Attention to Detail (Textual) test offers valuable insights into a job candidate’s reasoning skills, particularly in assessing their ability to analyze and comprehend written information with precision and accuracy.

In most professional settings, the ability to pay close attention to detail is paramount. The Attention to Detail (Textual) test assesses a candidate’s proficiency in reading, comprehending, and scrutinizing written information, ensuring accuracy and completeness.

Big 5 (OCEAN) test

Reasoning skills are not solely dependent on cognitive abilities but are also influenced by an individual’s personality traits. 

The Big 5 (OCEAN) test assesses a candidate’s personality dimensions, providing a deeper understanding of their approach to challenges, level of openness to new ideas, organizational skills, propensity for collaboration, and emotional stability. 

For example, candidates with a high score in Conscientiousness demonstrate meticulous attention to detail and a structured approach to problem-solving, while those who get a high score in Openness exhibit creativity and a willingness to explore new ways of moving forward. 

By considering these traits alongside reasoning skills, you can gain a comprehensive understanding of a candidate’s potential to excel in tasks requiring critical thinking and reasoning.

Understanding Instructions test

The Understanding Instructions test plays a useful role in evaluating a job candidate’s reasoning skills, specifically their ability to understand and execute tasks based on given instructions accurately. 

This test focuses on assessing an individual’s attention to detail, critical thinking, and capacity to analyze and interpret instructions. 

It offers valuable insights into a candidate’s logical reasoning, problem-solving skills, and potential for success in roles that require close adherence to guidelines.

If you’re looking to identify candidates with exceptional reasoning skills, TestGorilla is here to support your hiring journey. With our extensive range of scientifically designed tests, we provide you with a powerful tool to assess and evaluate critical thinking and problem-solving abilities. 

By incorporating TestGorilla’s assessments into your hiring process, you’ll gain valuable insights into each candidate’s capacity to analyze, strategize, and make informed decisions, setting the stage for building a team of exceptional talent.

At TestGorilla, we understand that finding individuals who can think critically and adapt to complex challenges is crucial for your company’s success. Our tests are carefully crafted to gauge candidates’ logical reasoning, analytical skills, and cognitive abilities, giving you a comprehensive understanding of their reasoning prowess. 

By relying on TestGorilla’s innovative assessment platform, you can confidently identify top-tier candidates who will contribute fresh perspectives, creativity, and ingenuity to your organization.

Let us help you identify candidates with the critical thinking, problem-solving, and decision-making abilities your company needs to thrive.

Sign up for TestGorilla’s free plan today and experience the power of our reasoning skills assessments firsthand.

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Open Access

Peer-reviewed

Research Article

Does mathematics training lead to better logical thinking and reasoning? A cross-sectional assessment from students to professors

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Writing – original draft, Writing – review & editing

Affiliation School of Mathematics and Statistics, The University of Sydney, Sydney, Australia

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliation School of Arts and Humanities, Edith Cowan University, Joondalup, Australia

• Clio Cresswell, 
• Craig P. Speelman

• Published: July 29, 2020
• https://doi.org/10.1371/journal.pone.0236153
• Peer Review
• Reader Comments

Mathematics is often promoted as endowing those who study it with transferable skills such as an ability to think logically and critically or to have improved investigative skills, resourcefulness and creativity in problem solving. However, there is scant evidence to back up such claims. This project tested participants with increasing levels of mathematics training on 11 well-studied rational and logical reasoning tasks aggregated from various psychological studies. These tasks, that included the Cognitive Reflection Test and the Wason Selection Task, are of particular interest as they have typically and reliably eluded participants in all studies, and results have been uncorrelated with general intelligence, education levels and other demographic information. The results in this study revealed that in general the greater the mathematics training of the participant, the more tasks were completed correctly, and that performance on some tasks was also associated with performance on others not traditionally associated. A ceiling effect also emerged. The work is deconstructed from the viewpoint of adding to the platform from which to approach the greater, and more scientifically elusive, question: are any skills associated with mathematics training innate or do they arise from skills transfer?

Citation: Cresswell C, Speelman CP (2020) Does mathematics training lead to better logical thinking and reasoning? A cross-sectional assessment from students to professors. PLoS ONE 15(7): e0236153. https://doi.org/10.1371/journal.pone.0236153

Editor: Jérôme Prado, French National Center for Scientific Research (CNRS) & University of Lyon, FRANCE

Received: January 13, 2020; Accepted: June 30, 2020; Published: July 29, 2020

Copyright: © 2020 Cresswell, Speelman. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper and its Supporting Information files.

Funding: The authors received no specific funding for this work.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Mathematics is often promoted as endowing those who study it with a number of broad thinking skills such as: an ability to think logically, analytically, critically and abstractly; having capacity to weigh evidence with impartiality. This is a view of mathematics as providing transferable skills which can be found across educational institutions, governments and corporations worldwide. A view material to the place of mathematics in curricula.

Consider the UK government’s commissioned inquiry into mathematics education “Making Mathematics Count” ascertaining the justification that “mathematical training disciplines the mind, develops logical and critical reasoning, and develops analytical and problem-solving skills to a high degree” [ 1 p11]. The Australian Mathematical Sciences Institute very broadly states in its policy document “Vision for a Maths Nation” that “Not only is mathematics the enabling discipline, it has a vital productive role planning and protecting our well-being” (emphasis in original) [ 2 ]. In Canada, British Columbia’s New 2016 curriculum K-9 expressly mentions as part of its “Goals and Rationale”: “The Mathematics program of study is designed to develop deep mathematical understanding and fluency, logical reasoning, analytical thought, and creative thinking.” [ 3 ]. Universities, too, often make such specific claims with respect to their teaching programs. “Mathematics and statistics will help you to think logically and clearly, and apply a range of problem-solving strategies” is claimed by The School of Mathematical Sciences at Monash University, Australia [ 4 ]. The School of Mathematics and Statistics at The University of Sydney, Australia, directly attributes as part of particular course objectives and outcomes skills that include “enhance your problem-solving skills” as part of studies in first year [ 5 ], “develop logical thinking” as part of studies in second year, which was a statement drafted by the lead author in fact [ 6 ], and “be fluent in analysing and constructing logical arguments” as part of studies in third year [ 7 ]. The University of Cambridge’s Faculty of Mathematics, UK, provides a dedicated document “Transferable Skills in the Mathematical Tripos” as part of its undergraduate mathematics course information, which again lists “analytic ability; creativity; initiative; logical and methodical reasoning; persistence” [ 8 ].

In contrast, psychological research, which has been empirically investigating the concept of transferability of skills since the early 1900s, points quite oppositely to reasoning skills as being highly domain specific [ 9 ]. Therefore, support for claims that studying mathematics engenders more than specific mathematics knowledge is highly pertinent. And yet it is largely absent. The 2014 Centre for Curriculum Redesign (CCR) four part paper “Mathematics for the 21st Century: What Should Students Learn?” concludes in its fourth paper titled “Does mathematics education enhance higher-order thinking skills?” with a call to action “… there is not sufficient evidence to conclude that mathematics enhances higher order cognitive functions. The CCR calls for a much stronger cognitive psychology and neuroscience research base to be developed on the effects of studying mathematics” [ 10 ].

Inglis and Simpson [ 11 ], bringing up this very issue, examined the ability of first-year undergraduate students from a high-ranking UK university mathematics department, on the “Four Cards Problem” thinking task, also known as the Wason Selection Task. It is stated as follows.

Each of the following cards have a letter on one side and a number on the other.

Here is a rule: “if a card has a D on one side, then it has a 3 on the other”. Your task is to select all those cards, but only those cards, which you would have to turn over in order to find out whether the rule is true or false. Which cards would you select?

This task involves understanding conditional inference, namely understanding the rule “If P then Q” and with this, deducing the answer as “P and not Q” or “D and 7”. Such logical deduction indeed presents as a good candidate to test for a potential ability of the mathematically trained. This task has also been substantially investigated in the domain of the psychology of reasoning [ 12 p8] revealing across a wide range of publications that only around 10% of the general population reach the correct result. The predominant mistake being to pick “D and 3”; where in the original study by Wason [ 13 ] it is suggested that this was picked by 65% of people. This poor success rate along with a standard mistake has fuelled interest in the task as well as attempts to understand why it occurs. A prevailing theory being the so named matching bias effect; the effect of disproportionately concentrating on items specifically mentioned in the situation, as opposed to reasoning according to logical rules.

Inglis and Simpson’s results isolated mathematically trained individuals with respect to this task. The participants were under time constraint and 13% of the first-year undergraduate mathematics students sampled reached the correct response, compared to 4% of the non-mathematics (arts) students that was included. Of note also was the 24% of mathematics students as opposed to 45% of the non-mathematics students who chose the standard mistake. The study indeed unveiled that mathematically trained individuals were significantly less affected by the matching bias effect with this problem than the individuals without mathematics training. However, the achievement of the mathematically trained group was still far from masterful and the preponderance for a non-standard mistake compared with non-mathematically trained people is suggestive. Mathematical training appears to engender a different thinking style, but it remains unclear what the difference is.

Inglis, Simpson and colleagues proceeded to follow up their results with a number of studies concentrated on conditional inference in general [ 14 , 15 ]. A justification for this single investigatory pathway being that if transfer of knowledge is present, something subtle to test for in the first place, a key consideration should be the generalisation of learning rather than the application of skills learned in one context to another (where experimenter bias in the choice of contexts is more likely to be an issue). For this they typically used sixteen “if P then Q” comprehension tasks, where their samples across a number of studies have included 16-year-old pre-university mathematics students (from England and Cyprus), mathematics honours students in their first year of undergraduate university study, third year university mathematics students, and associated control groups. The studies have encompassed controls for general intelligence and thinking disposition prior to training, as well as follows ups of up to two years to address the issue of causation. The conclusive thinking pattern that has emerged is a tendency of the mathematical groups towards a greater likelihood of rejecting the invalid denial of the antecedent and affirmation of the consequent inferences. But with this, and this was validated by a second separate study, the English mathematics group actually became less likely to endorse the valid modus tollens inference. So again, mathematical training appears to engender a different thinking style, but there are subtleties and it remains unclear what the exact difference is.

This project was designed to broaden the search on the notion that mathematics training leads to increased reasoning skills. We focused on a range of reasoning problems considered in psychological research to be particularly insightful into decision making, critical thinking and logical deduction, with their distinction in that the general population generally struggles with answering them correctly. An Australian sample adds diversity to the current enquiries that have been European focussed. Furthermore, in an effort to identify the impact of mathematics training through a possible gradation effect, different levels of mathematically trained individuals were tested for performance.

Well-studied thinking tasks from a variety of psychological studies were chosen. Their descriptions, associated success rates and other pertinent details follows. They were all chosen as the correct answer is typically eluded for a standard mistake.

The three-item Cognitive Reflection Test (CRT) was used as introduced by Frederick [ 16 ]. This test was devised in line with the theory that there are two general types of cognitive activity: one that operates quickly and without reflection, and another that requires not only conscious thought and effort, but also an ability to reflect on one’s own cognition by including a step of suppression of the first to reach it. The three items in the test involve an incorrect “gut” response and further cognitive skill is deemed required to reach the correct answer (although see [ 17 ] for evidence that correct responses can result from “intuition”, which could be related to intelligence [ 18 ]).

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

Bat and ball

A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost?

The solutions are: 47 days for the Lily Pads problem, 5 minutes for the Widgets problem and 5 cents for the Bat and Ball problem. The considered intuitive, but wrong, answers are 24 days, 100 minutes and 10 cents, respectively. These wrong answers are attributed to participants becoming over focused on the numbers so as to ignore the exponential growth pattern in the Lily Pads problem, merely complete a pattern in numbers in the Widgets problem, and neglect the relationship “more than” in the Bat and Ball problem [ 19 ]. The original study by Frederick [ 16 ] provides a composite measure of the performance on these three items, with only 17% of those studied (n = 3428) reaching the perfect score. The CRT has since been studied extensively [ 19 – 21 ]. Research using the CRT tends not to report performance on the individual items of the test, but rather a composite measure of performance. Attridge and Inglis [ 22 ] used the CRT as a test for thinking disposition of mathematics students as one way to attempt to disentangle the issue of filtering according to prior thinking styles rather than transference of knowledge in successful problem solving. They repeat tested 16-year old pre-university mathematics students and English literature students without mathematics subjects at a one-year interval and found no difference between groups.

Three problems were included that test the ability to reason about probability. All three problems were originally discussed by Kahneman and Tversky [ 23 ], with the typically poor performance on these problems explained by participants relying not on probability knowledge, but a short-cut method of thinking known as the representativeness heuristic. In the late 1980s, Richard Nisbett and colleagues showed that graduate level training in statistics, while not revealing any improvement in logical reasoning, did correlate with higher-quality statistical answers [ 24 ]. Their studies lead in particular to the conclusion that comprehension of, what is known as the law of large numbers, did show improvement with training. The first of our next three problems targeted this law directly.

• (a). the larger hospital
• (b). the smaller hospital
• (c). about the same (that is, within 5 percent of each other)

Kahneman and Tversky [ 23 ] reported that, of 50 participants, 12 chose (a), 10 chose (b), and 28 chose (c). The correct answer is (b), for the reason that small samples are more likely to exhibit extreme events than large samples from the same population. The larger the sample, the more likely it will exhibit characteristics of the parent population, such as the proportion of boys to girls. However, people tend to discount or be unaware of this feature of sampling statistics, which Kahneman and Tversky refer to as the law of large numbers. Instead, according to Kahneman and Tversky, people tend to adhere to a fallacious law of small numbers, where even small samples are expected to exhibit properties of the parent population, as illustrated by the proportion of participants choosing the answer (c) in their 1972 study. Such thinking reflects use of the representativeness heuristic, whereby someone will judge the likelihood of an uncertain event based on how similar it is to characteristics of the parent population of events.

Birth order

• (a). What is your estimate of the number of families surveyed in which the exact order of births was BGBBBB?
• (b). In the same survey set, which, if any, of the following two sequences would be more likely: BBBGGG or GBBGBG?

All of the events listed in the problem have an equal probability, so the correct answer to (a) is 72, and to (b) is “neither is more likely”. Kahneman and Tversky [ 23 ] reported that 75 of 92 participants judged the sequence in (a) as less likely than the given sequence. A similar number (unspecified by Kahneman and Tversky, but the statistical effect was reported to be of the same order as in (a)) reported that GBBGBG was the more likely sequence. Again, Kahneman and Tversky suggested that these results reflected use of the representativeness heuristic. In the context of this problem, the heuristic would have taken the following form: some birth orders appear less patterned than others, and less patterned is to be associated with the randomness of birth order, making them more likely.

Coin tosses

• (a). H T H T H T H T
• (b). H H H H T T T T
• (c). T T H H T T H H
• (d). H T T H T H H T
• (e). all of the above are equally likely

The correct answer in this problem is (e). Kahneman and Tversky [ 23 ] reported that participants tend to choose less patterned looking sequences (e.g., H T T H T H H T) as more likely than more systematic looking sequences (e.g., H T H T H T H T). This reasoning again reflects the representativeness heuristic.

Three further questions from the literature were included to test problem solving skill.

Two drivers

• (a). Driver A would win the race
• (b). Driver B would win the race
• (c). the two drivers would arrive at the same time (within a few seconds of one another)

This problem was developed by Pelham and Neter [ 25 ]. The correct answer is (a), which can be determined by calculations of driving times for each Driver, using time = distance/velocity. Pelham and Neter argue, however, that (c) is intuitively appealing, on the basis that both drivers appear to have the same overall average speed. Pelham and Neter reported that 67% of their sample gave this incorrect response to the problem, and a further 13% selected (b).

Petrol station

Imagine that you are driving along the road and you notice that your car is running low on petrol. You see two petrol stations next to each other, both advertising their petrol prices. Station A’s price is 65c/litre; Station B’s price is 60c/litre. Station A’s sign also announces: “5c/litre discount for cash!” Station B’s sign announces “5c/litre surcharge for credit cards.” All other factors being equal (for example, cleanliness of the stations, number of cars waiting at each etc), to which station would you choose to go, and why?

This problem was adapted from one described by Galotti [ 26 ], and is inspired by research reported by Thaler [ 27 ]. According to Thaler’s research, most people prefer Station A, even though both stations are offering the same deal: 60c/litre for cash, and 65c/litre for credit. Tversky and Kahneman [ 28 ] explain this preference by invoking the concept of framing effects. In the context of this problem, such an effect would involve viewing the outcomes as changes from some initial point. The initial point frames the problem, and provides a context for viewing the outcome. Thus, depending on the starting point, outcomes in this problem can be viewed as either a gain (in Station A, you gain a discount if you use cash) or a loss (in Station B, you are charged more (a loss) for using credit). Given that people are apparently more concerned about a loss than a gain [ 29 ], the loss associated with Station B makes it the less attractive option, and hence the preference for Station A. The correct answer, though, is that the stations are offering the same deal and so no station should be preferred.

And finally, a question described by Stanovich [ 30 , 31 ] as testing our predisposition for cognitive operations that require the least computational effort.

Jack looking at Anne

• (c). Cannot be determined

Stanovich reported that over 80% of people choose the “lazy” answer (c). The correct answer is (a).

The above questions survey, in a clear problem solving setting, an ability to engage advanced cognitive processing in order to critically evaluate and possibly override initial gut reasoning, an ability to reason about probability within the framework of the law of large numbers and the relationship between randomness and patterning, an ability to isolate salient features of a problem and, with the last question in particular, an ability to map logical relations. It might be hypothesised that according to degrees of mathematical training, in line with the knowledge base provided and the claims of associated broad and enhanced problem-solving abilities in general, that participants with greater degrees of such training would outperform others on these questions. This hypothesis was investigated in this study. In addition, given that no previous study on this issue has examined the variety of problems used in this study, we also undertook an exploratory analysis to investigate whether there exist any associations between the problems in terms of their likelihood of correct solution. Similarities between problems might indicate which problem solving domains could be susceptible to the effects of mathematics training.

• Introductory—First year, second semester, university students with weak high school mathematical results, only enrolled in the current unit as a compulsory component for their chosen degree, a unit not enabling any future mathematical pathway, a typical student may be enrolled in a Biology or Geography major;
• Standard—First year, second semester, university students with fair to good high school mathematical results, enrolled in the current mathematics unit as a compulsory component for their chosen degree with the possibility of including some further mathematical units in their degree pathway, a typical student may be enrolled in an IT or Computer Science major;
• Advanced1—First year, second semester, university mathematics students with very strong interest as well as background in mathematics, all higher year mathematical units are included as possible future pathway, a typical student may be enrolled in a Mathematics or Physics major;
• Advanced2—Second year, second semester, university mathematics students with strong interest as well as background in mathematics, typically a direct follow on from the previously mentioned Advanced1 cohort;
• Academic—Research academics in the mathematical sciences.

Participants

123 first year university students volunteered during “help on demand” tutorial times containing up to 30 students. These are course allocated times that are supervised yet self-directed by students. This minimised disruption and discouraged coercion. 44 second year university students completed the questionnaire during a weekly one-hour time slot dedicated to putting the latest mathematical concepts to practice with the lecturer (whereby contrast to what occurs in tutorial times the lecturer does most of the work and all students enrolled are invited). All these university students completed the questionnaire in normal classroom conditions; they were not placed under strict examination conditions. The lead author walked around to prevent discussion and coercion and there was minimum disruption. 30 research academics responded to local advertising and answered the questionnaire in their workplace while supervised.

The questionnaires were voluntary, anonymous and confidential. Participants were free to withdraw from the study at any time and without any penalty. No participant took this option however. The questionnaires gathered demographic information which included age, level of education attained and current qualification pursued, name of last qualification and years since obtaining it, and an option to note current speciality for research academics. Each problem task was placed on a separate page. Participants were not placed under time constraint, but while supervised, were asked to write their start and finish times on the front page of the survey to note approximate completion times. Speed of completion was not incentivised. Participants were not allowed to use calculators. A final “Comments Page” gave the option for feedback including specifically if the participants had previously seen any of the questions. Questionnaires were administered in person and supervised to avoid collusion or consulting of external sources.

The responses were coded four ways: A) correct; B) standard error (the errors discussed above in The Study); C) other error; D) left blank.

The ethical aspects of the study were approved by the Human Research Ethics Committee of the University of Sydney, protocol number [2016/647].

The first analysis examined the total number of correct responses provided by the participants as a function of group. Scores ranged from 1 to 11 out of a total possible of 11 (Problem 6 had 2 parts) ( Fig 1 ). An ANOVA of this data indicated a significant effect of group (F(4, 192) = 20.426, p < .001, partial η 2 = .299). Pairwise comparisons using Tukey’s HSD test indicated that the Introductory group performed significantly worse than the Advanced1, Advanced2 and Academic groups. There were no significant differences between the Advanced1, Advanced2 and Academic groups.

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Error bars are one standard error of the mean.

https://doi.org/10.1371/journal.pone.0236153.g001

Overall solution time, while recorded manually and approximately, was positively correlated with group, such that the more training someone had received, the longer were these solution times (r(180) = 0.247, p = .001). However, as can be seen in Fig 2 , this relationship is not strong.

https://doi.org/10.1371/journal.pone.0236153.g002

A series of chi-squared analyses, and their Bayesian equivalents, were performed on each problem, to determine whether the distribution of response types differed as a function of group. To minimise the number of cells in which expected values in some of these analyses were less than 5, the Standard Error, Other Error and Blank response categories were collapsed into one category (Incorrect Response). For three of the questions, the expected values of some cells did fall below 5, and this was due to most people getting the problem wrong (Four Cards), or most people correctly responding to the problem (Bat and Ball, Coin Tosses). In these cases, the pattern of results was so clear that a statistical analysis was barely required. Significant chi-squared results were examined further with pairwise posthoc comparisons (see Table 1 ).

https://doi.org/10.1371/journal.pone.0236153.t001

The three groups with the least amount of training in mathematics were far less likely than the other groups to give the correct solution (χ 2 (4) = 31.06, p < .001; BF 10 = 45,045) ( Table 1 ). People in the two most advanced groups (Advanced2 and Academic) were more likely to solve the card problem correctly, although it was still less than half of the people in these groups who did so. Further, these people were less likely to give the standard incorrect solution, so that most who were incorrect suggested some more cognitively elaborate answer, such as turning over all cards. The proportion of people in the Advanced2 and Academic groups (39 and 37%) who solved the problem correctly far exceeded the typical proportion observed with this problem (10%). Of note, also, is the relatively high proportion of those in the higher training groups who, when they made an error, did not make the standard error, a similar result to the one reported by Inglis and Simpson [ 11 ].

The cognitive reflection test

In the Lily Pads problem, although most people in the Standard, Advanced1, Advanced2 and Academic groups were likely to select the correct solution, it was also the case that the less training someone had received in mathematics, the more likely they were to select an incorrect solution (χ 2 (4) = 27.28, p < .001; BF 10 = 15,554), with the standard incorrect answer being the next most prevalent response for the two lower ability mathematics groups ( Table 1 ).

Performance on the Widgets problem was similar to performance on the Lily Pads problem in that most people in the Standard, Advanced1, Advanced2 and Academic groups were likely to select the correct solution, but that the less training someone had received in mathematics, the more likely they were to select an incorrect solution (χ 2 (4) = 23.76, p< .001; BF 10 = 516) ( Table 1 ). As with the Lily Pads and Widget problems, people in the Standard, Advanced1, Advanced2 and Academic groups were highly likely to solve the Bat and Ball problem (χ 2 (4) = 35.37, p < .001; BF 10 = 208,667). Errors were more likely from the least mathematically trained people (Introductory, Standard) than the other groups ( Table 1 ).

To compare performance on the CRT with previously published results, performance on the three problems (Lily Pads, Widgets, Bat and Ball) were combined. The number of people in each condition that solved 0, 1, 2, or 3 problems correctly is presented in Table 2 . The Introductory group were evenly distributed amongst the four categories, with 26% solving all three problems correctly. Around 70% of the rest of the groups solved all 3 problems correctly, which is vastly superior to the 17% reported by Frederick [ 16 ].

https://doi.org/10.1371/journal.pone.0236153.t002

Responses to the Hospitals problem were almost universally split between correct and standard errors in the Standard, Advanced1, Advanced2 and Academic groups. Although this pattern of responses was also evident in the Introductory group, this group also exhibited more non-standard errors and non-responses than the other groups. However, the differences between the groups were not significant (χ 2 (4) = 4.93, p = .295; BF 10 = .068) ( Table 1 ). Nonetheless, the performance of all groups exceeds the 20% correct response rate reported by Kahneman and Tversky [ 23 ].

The two versions of the Birth Order problem showed similar results, with correct responses being more likely in the groups with more training (i.e., Advanced1, Advanced2 and Academic), and responses being shared amongst the various categories in the Introductory and Standard groups (χ a 2 (4) = 24.54, p < .001; BF 10 = 1,303; χ b 2 (4) = 25.77, p < .001; BF 10 = 2,970) ( Table 1 ). Nonetheless, performance on both versions of the problem in this study was significantly better than the 82% error rate reported by Kahneman and Tversky [ 23 ].

The Coin Tosses problem was performed well by all groups, with very few people in any condition committing errors. There were no obvious differences between the groups (χ 2 (4) = 3.70, p = .448; BF 10 = .160) ( Table 1 ). Kahneman and Tversky [ 23 ] reported that people tend to make errors on this type of problem by choosing less patterned looking sequences, but they did not report relative proportions of people making errors versus giving correct responses. Clearly the sample in this study did not perform like those in Kahneman and Tversky’s study.

Responses on the Two Drivers problem were clearly distinguished by a high chance of error in the Introductory and Standard groups (over 80%), and a fairly good chance of being correct in the Advanced1, Advanced2 and Academic groups (χ 2 (4) = 46.16, p < .001; BF 10 = 1.32 x 10 8 ) ( Table 1 ). Academics were the standout performers on this problem, although over a quarter of this group produced an incorrect response. Thus, the first two groups performed similarly to the participants in the Pelham and Neter [ 25 ] study, 80% of whom gave an incorrect response.

Responses on the Petrol Station problem were marked by good performance by the Academic group (73% providing a correct response), and just over half of each of the other groups correctly solving the problem. This difference was not significant (χ 2 (4) = 4.68, p = .322: BF 10 = .059) ( Table 1 ). Errors were fairly evenly balanced between standard and other, except for the Academic group, who were more likely to provide a creative answer if they made an error. Thaler [ 27 ] reported that most people get this problem wrong. In this study, however, on average, most people got this problem correct, although this average was boosted by the Academic group.

Responses on the Jack looking at Anne problem generally were standard errors, except for the Advanced2 and Academic groups, which were evenly split between standard errors and correct responses (χ 2 (4) = 18.03, p = .001; BF 10 = 46) ( Table 1 ). Thus, apart from these two groups, the error rate in this study was similar to that reported by Stanovich [ 30 ], where 80% of participants were incorrect.

A series of logistic regression analyses were performed in order to examine whether the likelihood of solving a particular problem correctly could be predicted on the basis of whether other problems were solved correctly. Each analysis involved selecting performance (correct or error) on one problem as the outcome variable, and performance on the other problems as predictor variables. Training (amount of training) was also included as a predictor variable in each analysis. A further logistic regression was performed with training as the outcome variable, and performance on all of the problems as predictor variables. The results of these analyses are summarised in Table 3 . There were three multi-variable relationships observed in these analyses, which can be interpreted as the likelihood of solving one problem in each group being associated with solving the others in the set. These sets were: (1) Lily Pads, Widgets and Petrol Station; (2) Hospitals, Four Cards and Two Drivers; (3) Birth Order and Coin Tosses. Training also featured in each of these sets, moderating the relationships as per the results presented above for each problem.

https://doi.org/10.1371/journal.pone.0236153.t003

The final “Comments Page” revealed the participants as overwhelmingly enjoying the questions. Any analysis of previous exposure to the tasks proved impossible as there was little to no alignment on participant’s degree of recall, if any, and even perceptions of what exposure entailed. For example, some participants confused being exposed to the particular tasks with being habitually exposed to puzzles, or even mathematics problems, more broadly.

In general, the amount of mathematics training a group had received predicted their performance on the overall set of problems. The greater the training, the more problems were answered correctly, and the slower the recorded response times. There was not an obvious difference between the Advanced1, Advanced2 and Academic groups on either of these measures, however there were clear differences between this group and the Introductory and Standard groups, with the former exhibiting clearly superior accuracy. While time records were taken approximately, so as to avoid adding time pressure as a variable, that the Advanced1, Advanced2 and Academic groups recorded more time in their consideration of the problems, may suggest a “pause and consider” approach to such problems is a characteristic of the advanced groups. This is in line with what was suggested by an eye-movement tracking study of mathematically trained students attempting the Four Cards Problem; where participants that had not chosen the standard error had spent longer considering the card linked to the matching bias effect [ 14 ]. It is important to note, however, that longer response times may reflect other cognitive processes than deliberation [ 32 ].

Performance on some problems was associated with performance on other problems. That is, if someone correctly answered a problem in one of these sets, they were also highly likely to correctly answer the other problems in the set. These sets were: (1) Lily Pads, Widgets and Petrol Station; (2) Hospitals, Four Cards and Two Drivers; (3) Birth Order and Coin Tosses. This is different with how these problems have been typically clustered a priori in the research literature: (I) Lily Pads, Widgets and Bat and Ball (CRT); (II) Hospitals and Two Drivers (explained below); (III) Hospitals, Birth Order and Coin Tosses (representativeness heuristic); (IV) Birth Order and Coin Tosses (probability theory). Consideration of these problem groupings follows.

Correctly answering all three problems in (I) entailed not being distracted by particular pieces of information in the problems so as to stay focused on uncovering the real underlying relationships. The Lily Pads and Widget problems can mislead if attention is over focused on the numbers, and conversely, the Petrol Station problem can mislead if there is too much focus on the idea of a discount. While the Lily Pads and Widget problems are traditionally paired with the Bat and Ball problem in the CRT, it may be that performance on the Bat and Ball problem did not appear as part of this set due to an added level of difficulty. With the problems in (I), avoiding being distracted by certain parts of the questions at the expense of others almost leads directly to the correct answer. However, with the Bat and Ball problem, further steps in mathematical reasoning still need to occur in answering which two numbers add together to give a result while also subtracting one from the other for another.

With the problems in (II) it is of interest that the Two Drivers problem was created specifically to be paired with the Hospitals problem to test for motivation in problem solving [ 23 ]. Within this framework further transparent versions of these problems were successfully devised to manipulate for difficulty. The Two Drivers problem was amended to have Driver B travelling at exactly 5 mph during the first half of the race and at exactly 95 mph during the last half of the race. The Hospitals problem was amended so the smaller hospital would have “only 2” babies born each day and where for a period of one year the hospitals recorded the number of days on which all of the babies born were boys. Could the association in (II) be pointing to how participants overcome initial fictitious mathematical rules? Maybe they reframe the question in simpler terms to see the pattern. The Four Cards Problem also elicited a high number of incorrect answers where, associated with mathematical training, the standard incorrect solution was avoided for more cognitively elaborate ones. Indeed, a gradation effect appeared across the groups where the standard error of the “D and 3” cards becomes “D only” ( Table 4 ). Adrian Simpson and Derrick Watson found a comparable result across their two groups [14 p61]. This could again be pointing to having avoided an initial fictitious rule of simply concentrating on items directly found in the question, participants then seek to reframe the question to unearth the logical rule to be deduced. An added level of difficulty with this question may be why participants become trapped in a false answer. The eye-movement tracking study mentioned above supports this theory.

https://doi.org/10.1371/journal.pone.0236153.t004

The problems in (III) fit naturally together as part of basic probability theory, a topic participants would have assimilated, or not, as part of various education curricula. While the equal likelihood of all possible outcomes with respect to a coin toss may be culturally assimilated, the same may not be as straightforward for birth gender outcomes where such assumptions could be swayed by biological hypothesis or folk wisdom [ 33 ]. The gradation of the results in terms of mathematical training does not support this possibility.

The effect of training on performance accuracy was more obvious in some problems compared to others, and to some extent, this was related to the type of problem. For instance, most of the problems in which performance was related to training (Four Cards, CRT [Lily Pads, Widgets, Bat and Ball], Two Drivers, Jack looking at Anne) could be classed as relying on logical and/or critical thinking. The one exception was the Birth Order problems, which are probability related.

In contrast, two of the three problems in which training did not appear to have much impact on performance (Hospitals and Coin Tosses) require domain-specific knowledge. The Hospitals problem requires a degree of knowledge about sampling statistics. This is a topic of quite distinct flavour that not all mathematically trained individuals gain familiarity with. On the other hand, all groups having performed well on the Coin Tosses problem is in line with a level of familiarity with basic probability having been originally presented at high school. While the questioning of patterning as negatively correlated with randomness is similar to that appearing in the Birth Order question, in the Birth Order question this aspect is arguably more concealed. These results and problem grouping (III) could be pointing to an area for improvement in teaching where the small gap in knowledge required to go from answering the Coin Tosses problem correctly to achieving similarly with the Birth Order problem could be easily addressed. A more formal introduction to sampling statistics in mathematical training could potentially bridge this gap as well as further be extended towards improvement on the Hospitals problem.

The other problem where performance was unrelated to training, the Petrol Station problem, cannot be characterised similarly. It is more of a logical/critical thinking type problem, where there remains some suggestion that training may have impacted performance, as the Academic group seemed to perform better than the rest of the sample. An alternate interpretation of this result is therefore that this problem should not be isolated but grouped with the other problems where performance is affected by training.

• The Introductory group’s mathematics high school syllabus studied prior to first semester course entry covered: Functions, Trigonometric Functions, Calculus (Introduction to Differentiation, Applications of the Derivative, Antiderivatives, Areas and the Definite Integral), Financial Mathematics, Statistical Analysis. The Introductory group then explored concepts in mathematical modelling with emphasis on the importance of calculus in their first semester of mathematical studies.
• The Standard group’s mathematics high school syllabus studied prior to first semester course entry covered: Functions, Trigonometric Functions, Calculus (Rates of Change, Integration including the method of substitution, trigonometric identities and inverse trigonometric functions, Areas and Volumes of solids of revolution, some differential equations), Combinatorics, Proof (with particular focus on Proof by Mathematical Induction), Vectors (with application to projectile motion), Statistical Analysis. In first semester their mathematical studies then covered a number of topics the Advanced1 group studied prior to gaining entrance at university; further details on this are given below.
• The Advanced1 group’s mathematics high school syllabus studied prior to first semester course entry covered: the same course content the Standard group covered at high school plus extra topics on Proof (develop rigorous mathematical arguments and proofs, specifically in the context of number and algebra and further develop Proof by Mathematical Induction), Vectors (3 dimensional vectors, vector equations of lines), Complex Numbers, Calculus (Further Integration techniques with partial fractions and integration by parts), Mechanics (Application of Calculus to Mechanics with simple harmonic motion, modelling motion without and with resistance, projectiles and resisted motion). The Standard group cover these topics in their first semester university studies in mathematics with the exclusion of further concepts of Proof or Mechanics. In first semester the Advanced1 group have built on their knowledge with an emphasis on both theoretical and foundational aspects, as well as developing the skill of applying mathematical theory to solve practical problems. Theoretical topics include a host of theorems relevant to the study of Calculus.

In summary, at the point of our study, the Advanced1 group had more knowledge and practice on rigorous mathematical arguments and proofs in the context of number and algebra, and more in-depth experience with Proofs by Induction, but the bulk of extra knowledge rests with a much deeper knowledge of Calculus. They have had longer experience with a variety of integration techniques, and have worked with a variety of applications of calculus to solve practical problems, including a large section on mechanics at high school. In first semester at university there has been a greater focus on theoretical topics including a host of theorems and associated proofs relevant to the topics studied. As compared to the Introductory and Standard groups, the Advanced1 group have only widened the mathematics knowledge gap since their choice of post-compulsory mathematics at high school. The Advanced2 group come directly from an Advanced1 cohort. And the Academics group would have reached the Advanced1 group’s proficiency as part of their employment. So, are specific reasoning skills resulting from this level of abstract reasoning? Our findings suggest this should certainly be an area of investigation and links in interestingly with other research work. In studying one of the thinking tasks in particular (the Four Cards Problem) and its context of conditional inference more specifically, Inglis and Simpson [ 15 ] found a clear difference between undergraduates in mathematics and undergraduates in other university disciplines, yet also showed a lack of development over first-year university studies on conditional inference measures. A follow up study by Attridge and Inglis [ 22 ] then zeroed in on post-compulsory high school mathematical training and found that students with such training did develop their conditional reasoning to a greater extent than their control group over the course of a year, despite them having received no explicit tuition in conditional logic. The development though, whilst demonstrated as not being the result of a domain-general change in cognitive capacity or thinking disposition, and most likely associated with the domain-specific study of mathematics, revealed a complex pattern of endorsing more of some inferences and less of others. The study here focused on a much broader problem set associated with logical and critical thinking and it too is suggestive of a more complex picture in how mathematics training may be contributing to problem solving styles. A more intricate pattern to do with the impact of mathematical training on problem solving techniques is appearing as required for consideration.

There is also a final interpretation to consider: that people in the Advanced 1, Advanced2 and Academic groups did not gain anything from their mathematics training in terms of their ability to solve these problems. Instead, with studies denying any correlation of many of these problems with what is currently measured as intelligence [ 30 ], they might still be people of a particular intelligence or thinking disposition to start with, who have been able to use that intelligence to not only solve these problems, but also survive the challenges of their mathematics training.

That the CRT has been traditionally used as a measure of baseline thinking disposition and that performance has been found to be immutable across groups tested is of particular interest since our results show a clear possible training effect on these questions. CRT is tied with a willingness to engage in effortful thinking which presents as a suitable ability for training. It is beyond the scope of this study, but a thorough review of CRT testing is suggestive of a broader appreciation and better framework to understand thinking disposition, ability and potential ability.

Mathematical training appears associated with certain thinking skills, but there are clearly some subtleties that need to be extricated. The thinking tasks here add to the foundational results where the aim is for a firmer platform on which to eventually base more targeted and illustrative inquiry. If thinking skills can be fostered, could first year university mathematics teaching be improved so that all samples from that group reach the Advanced1 group level of reasoning? Do university mathematics courses become purely about domain-specific knowledge from this point on? Intensive training has been shown to impact the brain and cognition across a number of domains from music [ 34 ], to video gaming [ 35 ], to Braille reading [ 36 ]. The hypothesis that mathematics, with its highly specific practice, fits within this list remains legitimate, but simply unchartered. With our current level of understanding it is worth appreciating the careful wording of the NYU Courant Institute on ‘Why Study Math?’ where there is no assumption of causation: “Mathematicians need to have good reasoning ability in order to identify, analyze, and apply basic logical principles to technical problems.” [ 37 ].

Limitations

One possible limitation of the current study is that the problems may have been too easy for the more advanced people, and so we observed a ceiling effect (i.e., some people obtained 100% correct on all problems). This was most obvious in the Advanced1, Advanced2 and Academic groups. It is possible that participants in these groups had developed logical and critical thinking skills throughout their mathematical training that were sufficient to cope with most of the problems used in this study, and so this would support the contention that training in mathematics leads to the development of logical and critical thinking skills useful in a range of domains. Another interpretation is that participants in these groups already possessed the necessary thinking skills for solving the problems in this study, which is why they are able to cope with the material in the advanced units they were enrolled in, or complete a PhD in mathematics and hold down an academic position in a mathematics department. This would then suggest that training in mathematics had no effect on abstract thinking skills—people in this study possessed them to varying extents prior to their studies. This issue might be settled in a future study that used a greater number of problems of varying difficulties to maximise the chances of finding a difference between the three groups with the most amount of training. Alternatively, a longitudinal study that followed people through their mathematics training could determine whether their logical and critical thinking abilities changed throughout their course.

A further limitation of the study may be that several of the reasoning biases examined in this study were measured by only one problem each (i.e., Four Cards Problem, Two Drivers, Petrol Station, Jack looking at Anne). A more reliable measure of these biases could be achieved by including more problems that tap into these biases. This would, however, increase the time required of participants during data collection, and in the context of this study, would mean a different mode of testing would likely be required.

Broad sweeping intuitive claims of the transferable skills endowed by a study of mathematics require evidence. Our study uniquely covers a wide range of participants, from limited mathematics training through to research academics in the mathematical sciences. It furthermore considered performance on 11 well-studied thinking tasks that typically elude participants in psychological studies and on which results have been uncorrelated with general intelligence, education levels and other demographic information [ 15 , 16 , 30 ]. We identified different performances on these tasks with respect to different groups, based on level of mathematical training. This included the CRT which has developed into a method of measuring baseline thinking disposition. We identified different distributions of types of errors for the mathematically trained. We furthermore identified a performance threshold that exists in first year university for those with high level mathematics training. This study then provides insight into possible changes and adjustments to mathematics courses in order for them to fulfil their advertised goal of reaching improved rational and logical reasoning for a higher number of students.

It is central to any education program to have a clear grasp of the nature of what it delivers and how, but arguably especially so for the core discipline that is mathematics. In 2014 the Office of The Chief Scientist of Australia released a report “Australia’s STEM workforce: a survey of employers” where transferable skills attributed to mathematics were also ones that employers deemed as part of the most valuable [ 38 ]. A better understanding of what mathematics delivers in this space is an opportunity to truly capitalise on this historical culture-crossing subject.

Supporting information

https://doi.org/10.1371/journal.pone.0236153.s001

Acknowledgments

The authors would like to thank Jacqui Ramagge for her proof reading and input, as well as support towards data collection.

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