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Sudoku for Beginners: How to Improve Your Problem-Solving Skills

Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.

Understanding the Basics of Sudoku

Before we dive into the strategies and techniques, let’s first understand the basics of Sudoku. A Sudoku puzzle is a 9×9 grid that is divided into nine smaller 3×3 grids. The objective is to fill in each row, column, and smaller grid with numbers 1-9 without repeating any numbers.

Starting Strategies for Beginners

As a beginner, it can be overwhelming to look at an empty Sudoku grid. But don’t worry. There are simple starting strategies that can help you get started. First, look for any rows or columns that only have one missing number. Fill in that number and move on to the next row or column with only one missing number. Another strategy is looking for any smaller grids with only one missing number and filling in that number.

Advanced Strategies for Beginner/Intermediate Level

Once you’ve mastered the starting strategies, it’s time to move on to more advanced techniques. One technique is called “pencil marking.” This involves writing down all possible numbers in each empty square before making any moves. Then use logic and elimination techniques to cross off impossible numbers until you are left with the correct answer.

Another advanced technique is “hidden pairs.” Look for two squares within a row or column that only have two possible numbers left. If those two possible numbers exist in both squares, then those two squares must contain those specific numbers.

Benefits of Solving Sudoku Puzzles

Not only is solving Sudoku puzzles fun and challenging, but it also has many benefits for your brain health. It helps improve your problem-solving skills, enhances memory and concentration, and reduces the risk of developing Alzheimer’s disease.

In conclusion, Sudoku is a great way to improve your problem-solving skills while also providing entertainment. With these starting and advanced strategies, you’ll be able to solve even the toughest Sudoku puzzles. So grab a pencil and paper and start sharpening those brain muscles.

This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.


ability to use reasoning skills to solve problems

Problem Solving Technique, Skills & Examples (2023 Guide)

What Is Problem Solving?

Examples of problem solving in the workplace, what are problem solving interview questions, why do employers want problem solving skills, how to answer problem solving interview questions in 2023 with examples, how to highlight problem-solving skills in your cv or cover letter in 2023, problem solving technique, skills & examples (2023 guide).

Updated August 20, 2023

Edward Melett

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There are many definitions of problem solving – but at a basic level, it focuses on the ability to accurately assess a situation and arrive at a positive solution.

Problem solving is an analytical skill that many employers look for when reviewing candidate application forms.

This particular skill isn’t restricted to a single sector, industry or role, though employers in the engineering and legal industries, in particular, tend to look for proficiency.

Consequently, questions about your problem-solving ability are commonplace in interviews.

Strong problem solving skills can be hugely beneficial for your career. In every sector, problems are inevitable and will arise in one form or another as you go about your day-to-day duties.

When problems do occur, employees are expected to use their initiative and develop suitable solutions to avoid the situation escalating into something more serious.

There are many situations where problems could present themselves in the workplace, from a client's concern through to assisting a technical team resolve a website or database error.

The issues that you come across will often vary in complexity, with some situations requiring a simple solution and others demanding more thought and skill to overcome.

Business managers will spend a lot of their time solving problems and consequently require their employees to be creative and intuitive when it comes to addressing them.

Being confident in your problem solving approach is really important, and as you learn which processes are most effective to overcome obstacles, so your confidence will grow.

Without suitable processes in place, your solutions may fail or they could even create additional problems.

A good problem solving process involves four fundamental stages: problem definition , devising alternatives , evaluating alternatives and then implementing the most viable solutions .

ability to use reasoning skills to solve problems

Managers are looking for recruits who can be creative and intuitive when it comes to addressing business problems.

How to Improve Problem Solving Skills in 2023: Step By Step

There are several ways you can improve problem solving skills. It helps to approach each problem through a series of logical steps.

Step 1: Define the Problem with the 5 Whys Technique

First, identify what the problem is. This requires examining a particular situation to determine what specifically is causing the problem.

Rather than looking at a problematic situation as a whole (for example, a customer is upset), try to break it down and determine the cause of the problem (why is the customer upset?).

The Five Whys (or 5 Whys) technique can be helpful here, which essentially involves asking 'why' five times to determine the root of a problem.

There may be several elements causing the problem or one specific element. Either way, breaking a problem down into smaller parts makes it much easier to solve each of the elements or issues contributing to the problem.

Step 2: Generate and Select an Alternative

Next, come up with a range of potential solutions. Techniques such as problem tree analysis and mind mapping can help to lay out problem elements and potential solutions.

Some of the potential solutions won't be as effective as others, and that's okay. The goal at this stage is to evaluate each potential solution and determine which one is likely to be the most effective at solving the problem. You may require several different solutions to solve different elements of the problem as a whole.

Step 3: Implement and Follow Up on the Solution

Once you have decided on a solution, follow a step-by-step plan to implement that solution. Just as breaking down a problem into key elements makes it easier to identify solutions, an action plan with various steps makes it easier to implement those solutions.

Questions about problem solving will typically arise within a competency -based interview and will require you to demonstrate your particular approach.

Problem solving interview questions can be asked in a range of different ways, but some common examples of problem-solving are:

  • How do you solve problems?
  • Give me an example of a problem you have faced in the past, either as part of a team or as an individual. How did you solve the problem?
  • What do you do when you can't solve a problem?

Effective problem-solving requires a combination of creative thinking and sound analytical skills . Employers look for hires who can demonstrate each of these skills in the workplace to deliver positive outcomes.

Managers would far rather employ a member of staff who can take action to resolve a problem than someone who doesn't act and relies on someone else to think of a solution. Even if it isn't outlined as a requirement in a job description, many employers will still be evaluating your problem-solving ability throughout the application process.

Effective problem solvers are those who can apply logic and imagination to make sense of the situation and develop a solution that works. Even if it doesn't prove as successful as you had hoped, resilience is important, so you can reassess the situation and try an alternative.

To find out which jobs fit your personality best, visit our partner CareerFitter and take the Career Test for FREE .

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What Form Do Problem-Solving Questions Take?

If problem-solving skills are an integral part of your role, it is likely that you will have to complete some kind of assessment during the application process. There are a number of forms that a problem-solving question can take, but the majority of them will be scenario-based .

Employers may base problem-solving questions around three main areas:

  • How you have approached situations in the past
  • How you would manage a problem that would arise as part of the job
  • How you handle problems throughout the application process

Past Challenges

Some employers believe that the way you approached a situation in the past is a good indicator of how you will approach a challenging situation in the future. Therefore the best way to understand how someone would respond to a specific scenario is to ask a question such as 'explain an occasion when…’

As the employer wants to assess your problem-solving skills, they may ask you to outline a situation where something went wrong and what happened. This could be an example of a time when you faced something unexpected, or you were approached by a client about a concern.

Situations Specific to the Job

Managers will often relate one or more questions to the role you are applying for. Sometimes this may take the form of a question about what the applicant would do if they had too much or too little work to complete.

These types of questions usually begin with the recruiter asking how you would deal with a specific situation followed by some kind of challenge. For example, how you would deal with a colleague who was relying on you to do all of the work or falling short of a target.

Questions Throughout the Application Process

Although these aren't questions as such, they may be used by some recruiters to see how you handle unexpected changes. This could be rearranging the time of your interview or sending an email without attaching something important. Both of these - even if they are unintentional - could be used as a way to assess how you approach something that is unforeseen.

If you know that you are likely to face problem-solving questions in the application process, it’s good practice to research the typical questions and scenarios that candidates are presented with.

This will not only increase your confidence but also help you to refine your answers and provide a stronger response.

In this section we provide three problem solving scenarios of common questions and suitable responses:

Problem Solving Skills & Examples (2023 Guide)

Problem Solving Question 1

You have been asked to schedule in a rush project but you cannot complete the piece of work you need to, since you require information from another colleague who is not currently available. How would you deal with the situation?

Problem Solving Question 2

You are working on a project and halfway through you realise that you have made a significant mistake that may require you to restart the project to resolve it. How would you approach this so you still met the deadline?

Problem Solving Question 3

How would you deal with a customer who wasn't happy with your service, even though you haven't done anything wrong and it is the customer who has made the mistake?

Problem Solving Skills - Tips, Common Mistakes and Further Practice

When it comes to answering questions about problem-solving skills, we recommend the following;

Select a strong example that truly demonstrates your problem-solving ability in a positive manner.

Choose examples that are relevant to the job you are applying for . If you are applying for a project-based position, give an example of how you resolved a problem with a work or academic project.

Be specific with your responses and use an example with enough detail to show how you approach situations and the way you think. Take the time to come up with possible answers and scenarios before the interview .

Make sure the problem is unique . If you have a problem, simply calling someone else to solve it is not impressive. The best answers will show tailored solutions to tasks that may seem mundane.

Make sure the problem is simple . If you have switched from a legal career to an engineering career and your problem is legal in nature, ensure your problem is easy to understand and explain it to your interviewer without using jargon.

Choose a weak or boring problem , or one that reflects you in a negative way.

Generalise your answers with responses such as ‘you consider yourself to be a great problem solver’ or ‘you regularly solve problems’. You need to demonstrate how you solve problems effectively.

Raise any areas of concern by giving examples of negative situations that were a result of your own actions , even if you solved a problem successfully.

No matter how interesting the story that you have to tell is, don’t spend too much time providing too much detail , because the recruiter will soon get bored. Keep your answer short and to the point.

During your written application and at interview, employers will expect you to evidence your problem-solving skills. In your written application you should demonstrate them via relevant keywords, statements and achievements. If you solved a problem and it had a positive impact on the business – such as improved customer service standards or resource savings – say so on your CV.

If you are invited to an interview try to use the STAR technique to structure your answers. This technique focuses your responses on a Situation, Task, Action and Result. Following this process will help your answers to be focused, concise and strong.

Where problem-solving is a main element of your role, an employer may incorporate a relevant psychometric test and/or an activity to carefully assess your problem-solving skills.

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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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Problem solving: the mark of an independent employee

Abigail Lewis

Last updated: 24 Aug 2023, 08:40

Problem-solving abilities are essential in virtually any graduate role you can think of. Discover how to develop your problem-solving skills and demonstrate them to eagle-eyed recruiters.

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Interviewers will be interested to discover how you'd approach problems that could arise in the workplace.

Problem solving is all about using logic, as well as imagination, to make sense of a situation and come up with an intelligent solution. In fact, the best problem solvers actively anticipate potential future problems and act to prevent them or to mitigate their effects.

Problem-solving abilities are connected to a number of other skills, including:

  • analytical skills
  • innovative and creative thinking
  • a lateral mindset
  • adaptability and flexibility
  • level-headedness
  • resilience (in order to reassess when your first idea doesn’t work)
  • teamworking (if problem solving is a team effort)
  • influencing skills (to get colleagues, clients and bosses to adopt your solutions).

Identifying a problem is often the kernel for a new business or product idea – and, as such, problem solving is an essential ingredient of entrepreneurialism . It is also a key component of good leadership .

Short on time? Watch our one-minute guide to problem solving

  • how to answer problem-solving interview questions
  • how to think of examples of your problem-solving skills
  • a problem-solving technique you can use in any work or life situation.


Our targetjobs careers expert gives you a quick guide to showing off your problem-solving skills in a job interview.

Why all graduates require problem-solving skills in the workplace

Some graduate careers revolve around finding solutions – for example, engineering , management consulting , scientific research and technology . Graduates in other careers, meanwhile, will be expected to solve problems that crop up in the course of their jobs: for example, trainee managers should deal with operational problems (such as delays in the supply chain) or resolve conflict between team members.

In fact, the ability to solve problems is an essential part of any employee’s skill set, even if it isn’t specified on the job description.

Get the insights and skills you need to shape your career journey with Pathways. Learn and practise a selection of simple yet effective reasoning strategies to take your problem solving to the next level.

How to improve your problem-solving skills

How will employers assess your problem-solving skills?

Your problem-solving abilities can be assessed in three ways: by asking for examples of times when you previously solved a problem; by presenting you with certain hypothetical situations and asking how you would respond to them; and by seeing how you apply your problem-solving skills to different tests and exercises.

Competency-based application and interview questions about problem solving

You may be asked for an example of when you solved a problem on an application form – for instance, an engineering firm’s application form has previously included the question ‘Please tell us about a time when you have used your technical skills and knowledge to solve a problem’. But these questions are more likely at interview. Typical problem-solving competency-based questions include:

  • Give me an example of a time when you ran into a problem on a project. What did you do?
  • Give me an example of a difficult problem you had to solve outside of your course. How did you approach it?
  • Tell me about a time you worked through a problem as a team.
  • Have you ever had a disagreement with a team member? How was it resolved?
  • Give me an example of a time when you spotted a potential problem and took steps to stop it becoming one.
  • Give me an example of a time when you handled a major crisis.
  • Give me an example of your lateral thinking.

Hypothetical interview questions about problem solving

Interviewers will also be interested to know how you would approach problems that could arise when you are in the workplace. The precise interview questions will vary according to the job, but common ones include:

  • How would you deal with conflict in the workplace? (This is especially likely to be asked of trainee managers and graduate HR professionals.)
  • What would you do if there is an unexpected delay to one of your projects because of supply chain issues? (This is particularly likely to be asked in construction, logistics or retail interviews).
  • What would you do if a client or customer raised a complaint?
  • What would you do if you noticed that a colleague was struggling with their work?
  • How would you react if given negative feedback by a manager on an aspect of your performance?
  • How would you judge whether you should use your own initiative on a task or ask for help?

Problem-solving exercises and tests for graduate jobs

Different tests that employers could set to gauge your problem-solving skills include:

  • Online aptitude, psychometric and ability tests . These are normally taken as part of the application stage, although they may be repeated at an assessment centre. The tests that are most likely to assess your problem-solving skills are situational judgement tests and any that assess your reasoning, such as inductive reasoning or diagrammatic reasoning tests.
  • Video ‘immersive experiences’ , game-based recruitment exercises or virtual reality assessments. Not all of these methods are widely used yet but they are becoming more common. They are usually the recruitment stage before a face-to-face interview or assessment centre.
  • Case study exercises. These are common assessment centre tasks. You’d be set a business problem, typically related to the sector in which you’d be working, and asked to make recommendations for solving it, either individually or in groups. You’ll also usually be asked to outline your recommendations in either a presentation or in written form , a task that assesses your ability to explain your problem-solving approach.
  • In-tray (or e-tray) exercises. These always used to be set at an assessment centre but nowadays can also be part of the online testing stage. In-tray exercises primarily test your time management skills, but also assess your ability to identify a potential problem and take actions to solve it.
  • Job-specific or task-specific exercises, given at an assessment centre or at an interview. If set, these will be related to the role you are applying for and will either require you to devise a solution to a problem or to spot errors. Civil and structural engineering candidates , for example, will often be required to sketch a design in answer to a client’s brief and answer questions on it, while candidates for editorial roles may be asked to proofread copy or spot errors in page proofs (fully designed pages about to be published).

How to develop and demonstrate your problem-solving skills

Here are some tips on how to develop the problem-solving techniques employers look for.

Seek out opportunities to gain problem-solving examples

Dealing with any of the following situations will help you gain problem-solving skills, perhaps without even realising it:

  • Sorting out a technical problem with your phone, device or computer.
  • Resolving a dispute with a tricky landlord in order to get your deposit back.
  • Carrying out DIY.
  • Serving a demanding customer or resolving a complaint.
  • Finding a way round a funding shortfall in order to pay for travel or a gap year.
  • Turning around the finances or increasing the membership of a struggling student society.
  • Organising a student society’s trip overseas, overcoming unforeseen difficulties on the way.
  • Acting as a course rep or as a mentor for other students.

There should also be opportunities for you to develop problem-solving skills through your studies. Many assignments in subjects such as engineering and computer science are explicitly based around solving a problem in a way that, for example, essay topics in English literature aren’t. But, then, English literature students may also encounter academic problems, such as difficulties in tracking down the best source material.

Some professional bodies (for example, those in construction) run competitions for students, which often ask students to suggest solutions for problems facing the industry; entering these can provide good evidence of your problem-solving skills.

Games such as Sudoku and chess can also strengthen your ability to think strategically and creatively.

Practise recruitment exercises beforehand

Any candidate, no matter how high-flying, may be thrown by undertaking an online test or attending an assessment centre for the first time, so do everything you can to practise beforehand. Access our links to free and paid-for practice tests. Contact your careers service and book in for a mock-interview or mock-assessment centre.

Keep in mind this problem-solving technique

If you’re provided with a scenario or a case study during the graduate recruitment process, you could try using the IDEAL model, described by Bransford and Stein in their book Ideal Problem Solver . It breaks down what you need to do to solve a problem into stages:

  • Identify the issue
  • Define the obstacles
  • Examine your options
  • Act on an agreed course of action
  • Look at how it turns out, and whether any changes need to be made.

Give detail in your answers

You will need to explain how you identified the problem, came up with a solution and implemented it. Quantifiable results are good, and obviously the more complex the situation, the more impressive a successful result is. Follow the STAR technique outlined in our article on competency-based interview questions .

If you tackled a problem as part of a team, explain how your role was important in ensuring the positive solution, but also explain how your group worked together. This could be an opportunity to promote your teamworking skills as well.

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This describes editorially independent and impartial content, which has been written and edited by the targetjobs content team. Any external contributors featuring in the article are in line with our non-advertorial policy, by which we mean that we do not promote one organisation over another.

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How to assess reasoning skills

How to assess reasoning skills featured image

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.

Why are legal assistant skills important graphic list

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.

Following Instructions test

The Following 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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Fluency, Reasoning and Problem Solving: What This Looks Like In Every Maths Lesson

Neil almond.

Fluency reasoning and problem solving have been central to the new maths national curriculum for primary schools introduced in 2014. Here we look at how these three approaches or elements of maths can be interwoven in a child’s maths education through KS1 and KS2. We look at what fluency, reasoning and problem solving are, how to teach them, and how to know how a child is progressing in each – as well as what to do when they’re not, and what to avoid.

The hope is that this blog will help primary school teachers think carefully about their practice and the pedagogical choices they make around the teaching of reasoning and problem solving in particular.

Before we can think about what this would look like in practice however, we need to understand the background tothese terms.

What is fluency in maths?

Fluency in maths is a fairly broad concept. The basics of mathematical fluency – as defined by the KS1 / KS2 National Curriculum for maths – involve knowing key mathematical facts and being able to recall them quickly and accurately.

But true fluency in maths (at least up to Key Stage 2) means being able to apply the same skill to multiple contexts, and being able to choose the most appropriate method for a particular task.

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

Read more: How the best schools develop maths fluency at KS2 .

What is reasoning in maths?

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

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

Read more: Developing maths reasoning at KS2: the mathematical skills required and how to teach them .

What is problem solving in maths?

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

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

We are all problem solvers

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

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

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

image of baby crying used to illustrate ingrained problem solving skills.

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

Mathematical problem solving is a  learned skill

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

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

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

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

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

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

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

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

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

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

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

In that paper he produces this pyramid:

pyramid diagram showing the link between fluency, reasoning and problem solving

This is important for two reasons:

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

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

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

conical diagram showing the link between fluency, reasoning skills and problem solving

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

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

Performance vs learning: what to avoid when teaching fluency, reasoning, and problem solving

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

At some point schools become obsessed with the ridiculous notion of ‘accelerated progress’. I have heard it used in all manner of educational contexts while training and being a teacher. ‘You will need to show ‘ accelerated progress in maths ’ in this lesson,’ ‘Ofsted will be looking for ‘accelerated progress’ etc.

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

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

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

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

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

twitter poll regarding teaching of problem solving techniques in primary school

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

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

What IS performance vs learning’?

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

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

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

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

Chances are that all they’d need to do is find the numbers in the questions and use the same method they used in the fluency section to get their answers – not exactly high level problem solving skills.

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

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

The pressure for teachers to ‘get through the curriculum’ results in many opportunities to revisit content just not happening in the classroom.

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

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

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

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

Third Space's Ultimate Guide to Problem Solving Techniques

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

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

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

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

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

This blog on mental maths strategies pupils should learn in each year group is a good place to start when thinking about the core aspects of fluency that pupils should achieve.

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

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

Read more: How to teach times tables KS1 and KS2 for total recall .

What about best practice over a longer period?

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

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

example scheme of work

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

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

LY = Last Year

example first lesson of a unit of work targeted towards fluency

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

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

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

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

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

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

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

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

Practise with facts that are secure

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

Now given that much of the content of the KS2 SATs will come from years 5 and 6 it can be hard to stick to this two-year idea as pupils will need to solve problems with content that can be only weeks old to them.

But certainly in other year groups, the argument could be made that content should come from previous years.

You could get pupils in Year 4 to solve complicated place value problems with the numbers they should know from Year 2 or 3. This would lessen the cognitive load, freeing up valuable working memory so they can actually focus on solving the problems using content they are familiar with.

Read more: Cognitive load theory in the classroom

Increase complexity gradually.

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

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

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

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

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

example lesson of a unit using fluency and reasoning to embed problem solving

Fluency, Reasoning and Problem Solving should NOT be taught by rote 

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

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

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

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

Read more: 

  • Maths Mastery Toolkit : A Practical Guide To Mastery Teaching And Learning
  • Year 6 Maths Reasoning Questions and Answers
  • Get to Grips with Maths Problem Solving KS2
  • Mixed Ability Teaching for Mastery: Classroom How To
  • 21 Maths Challenges To Really Stretch Your More Able Pupils
  • Maths Reasoning and Problem Solving CPD Powerpoint
  • Why You Should Be Incorporating Stem Sentences Into Your Primary Maths Teaching

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Subsidised one to one maths tutoring from the UK’s most affordable DfE-approved one to one tutoring provider.

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