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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.
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Critical Thinking Skills: A Guide for Problem-Solving
Feeling challenged by the problems in your business? Looking for creative and strategic ways of solving problems? Your journey can start with critical thinking and problem-solving training . In a business environment, you are always searching for opportunities. Problems are opportunities in disguise. To become a problem-solver, you are on a mission to learn the art of thinking critically and creatively.
You need to find innovative solutions to your problems which will derive from teamwork and collaboration. Let’s explore the key concepts of critical thinking and problem-solving skills.
In this article ....
What is critical thinking, critical thinking and problem-solving: why should you have the skills.
- Improves flexibility and learning skills . With the evolutionary changes in technology, you have to learn and adapt faster to new environments and procedures. Critical thinking helps us to be more flexible to changes.
- Students can reflect on their learning experiences critically and make effective decisions.
- With critical thinking, you can take apart facts from opinionated facts . You start considering all possible options for reaching a prospective solution.
- In the field of education, students tend to become more interactive if the teacher encourages them to think critically. With critical thinking, students can align their subjects with their own lives. In the process, learners become active participants in the whole learning process.
- While solving problems, students also learn other important skills such as creativity, collaboration, and cooperation .
- Encourages the practice of reasoning that helps us to overcome biases and prejudices.
- Critical thinking skills enhance performance as you are self-directed in your learning and decision-making.
How relevant is critical thinking to your job?
Managers are role models for their teams. As a manager, your ability to analyse problems critically influence your team members in the long run.
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Business analyst, marketing associate.
Marketing associates gather and analyse a wide range of information regarding the target audience for their organisations. The ability to think critically can influence them to work out different solutions for successful marketing campaigns.
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Creative ways of solving problems: the problem-solving method.
Start identifying your goals, desires or challenges. Don’t make wild assumptions about your problem. Define your objectives clearly for clarity. Gather data about the problem. You can interview people, conduct surveys and collect statistics. Try to understand everyone’s opinions and feelings. Formulate open-ended questions based on your awareness of the problems. Visualise the challenges and opportunities regarding the problem.
It’s time for brainstorming, brain writing, mind mapping or other forms of idea generating techniques. This is where creativity matters. When you get tired of the continuous process, take a break and return with fresh ideas. Problem Solving Skills discusses elaborately on the preparation for brainstorming.
Now you are moving to the convergent stage of creative problem-solving. Your focus shifts to the evaluation of all the ideas generated before. Analyse the potential solutions, and think of the rationale behind the implementation of the solution.
You have to plan the course of action for the implementation stage. Identify your resources, communicate with the stakeholders and explain everything to the implementer.
Some ways of generating ideas creatively
Brainwriting: Brainwriting is a complementary technique to brainstorming. It can be considered a graphic version of brainstorming. Horst Geschka and his colleagues gave the idea as part of their research on the innovation management method.
Mind mapping: Mind maps are a visual representation of ideas on a piece of paper. You put the central idea in the middle and the associated ideas surrounding the central concept. Afterwards, you connect the ideas.
Duncker diagram: A comparative flowchart of the present state and desired state side by side with general solutions, functional solutions and specific solutions in three different levels.
How can a course on critical thinking help you to solve problems?
From our course on critical thinking and problem-solving , you will familiarise with the following concepts:
- Understanding and defining problems for creative problem-solving
- Using your existing resources more productively to generate ideas
- Thinking outside the box overcoming personal limitations
- Gaining knowledge on the different phases of the creative problem-solving process
- Utilising popular models in your way to gather information about problems and solutions
- Working with team members and implementing established brainstorming techniques for practical solutions to problems.
The modules of the course cover topics like problem-solving methods, information-gathering techniques, defining problems for clarity, getting ready for effective brainstorming, generating solutions maintaining a specific sequence, solutions analysis and planning the implementation phase.
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Critical, Lateral, & Creative Thinking
Critical thinking & problem-solving, introduction.
Critical thinking is self-directed, self-disciplined, self-monitored, and self-corrected. In other words, it is a thought process that involves the evaluation, assessment, and reinterpretation of your own or others’ ideas and thought processes. Critical thinking requires effort and dedication, but pays dividends for the time invested.
Critical thinking comes into play in a wide variety of circumstances. As a citizen of a democracy, it is important to think critically and do background research each time an election is coming up or when there is a news story about which you want to be more informed. As a student, you want to think critically about near term options, such as what courses to take, and longer term decisions, such as how to plan your degree and whether the degree you’re planning should be directed toward current employment, future employment, or your own academic interest that may or may not be related to a current or potential career.
Critical thinking involves analysis, or breaking something (a concept, an argument, a piece of information) down into its parts in order to understand and evaluate it, as a prelude to accepting or rejecting it. You’re expected to think critically when you’re asked to analyze an article for a college assignment, for example, and offer your own opinion on its validity. You also think critically when you analyze real-life situations such as moving your residence, changing jobs, or buying a car.
View the following videos on critical thinking, which further define the concept and offer some steps to apply in order to think critically and solve problems.
What are the key concepts of this video?
What examples do you have of the following?
- creating your own solution to an unexpected problem
- using pros and cons to make a decision
- making assumptions about a person
- unthinkingly applying a bias
The first two concepts often have positive outcomes, while the last two concepts may result in negative outcomes. Most likely you will have done all four of these things subconsciously in the workplace or other situations.
This video offers one (of many) ways to consider something critically:
- formulate your question
- gather your information
- apply the information (consider biases, assumptions)
- consider the implications
- explore other points of view
Both videos emphasize the need to consider a question, problem, action, or issue consciously and planfully, breaking it into its parts and considering the parts, before putting them back together with a reasoned solution or multiple potential, reasoned solutions.
Just for fun, here’s a short video on assumptions, a concept related to critical thinking.
initial learning activity
First, read and view information on the Lateral & Creative Thinking page of this text.
Then, write a brief essay (4-5 pages) applying critical, lateral, and creative thinking skills to the solution of a real problem. Use the following format:
- Identify a problem at work or with a community group, or any group or situation in which you are involved (family, friends, daily commuters on the same bus, etc.). In a few paragraphs, explain the problem.
- In another few paragraphs, analyze the problem. What are the component parts of the problem? Are there inherent assumptions and/or biases involved?
- In another few paragraphs, offer some possible solutions that you can identify immediately and logically. Identify and discuss the pros and cons of each immediate and logical solution.
- Then, try to think differently about the problem by applying lateral and creative approaches. You may want to identify the positives, negatives, and interesting aspects of the problem. You may want to consider solutions that could only happen “in your wildest dreams.” Brainstorm, and/or create a persona and ask yourself “how would X approach this problem?” Apply these and techniques suggested by the article and videos to posit at least one or more different solutions to the problem. Explain these different solutions in another few paragraphs, and posit what would need to be in place in order to enact this more creative solution.
- Conclude by reflecting on this exercise in a final few paragraphs. What did you learn about your own thought processes by completing this activity? How might you apply what you learned to your academic studies?
Submit: essay applying thinking skills
in-depth learning activity
Then, read the publication, Robot-Ready: Human + Skills for the Future of Work . (You may have read excerpts from this in other sections of this text.)
The authors of Robot-Ready assert a number of things, including that:
- Human skills will be more valued in the workplace of the future.
- Human skills are often best taught through liberal arts courses in college.
- Educators and employers do not yet have a common language for discussing the same skill sets.
- Education needs to become more problem-based in order to help develop the “both/and” that will be required in the workplace of the future (both technical knowledge and human skills).
Consider these assertions critically. Do you accept the evidence provided? What assumptions, if any, are inherent in the information? What biases, if any, are inherent in the information? Is there enough data to back up the assertion, and is that data valid?
Then choose one assertion that you feel is sound, based on your analysis. Apply critical (and lateral and creative) thinking processes to problem-solve and project a way of enacting the concept asserted. For example:
- How might you propose teaching one of the human skills in the workplace?
- How can a liberal arts college course be more obvious in its focus on human skills so that students get a sense of the real-world application of learning gained from that course?
- How might you propose that employers and educators collaborate?
- Consider a college course you already completed, one in which you learned what the authors of Robot-Ready would consider “technical knowledge.” How might you revise a learning activity in the course to make it more problem-based?
- your analysis
- your problem-solving proposal for enacting one of the concepts asserted
Related college Learning Goals
Active Learning: Assess and build upon previous learning and experiences to pursue new learning, independently and in collaboration with others.
Critical Thinking and Problem Solving: Evaluate, analyze, synthesize and critique key concepts and experiences, and apply diverse perspectives to find creative solutions to problems concerning human behavior, society and the natural world.
For more information, see the College Learning Goals Policy .
- Critical Thinking & Problem-Solving. Authored by : Susan Oaks; adapted from team work by Nan Travers (lead), Cathy Davison, Elaine Handley, Linda Jones, Jessica Kindred, Gohar Marikyan, Lynette Nickleberry, Susan Oaks, Eileen O'Connor. Project : Educational Planning. License : CC BY-NC: Attribution-NonCommercial
- first two paragraphs under the heading Critical Thinking. Authored by : Tom Mackey and Trudi Jacobson. Provided by : Metaliteracy.com. Located at : https://sites.google.com/view/metaliteracy/empowered-learner/critical-thinker/reevaluate . Project : Metaliteracy Badges. License : CC BY-NC: Attribution-NonCommercial
- Critical Thinking video. Located at : https://youtu.be/6OLPL5p0fMg . License : Other . License Terms : YouTube video
- 5 Tips to Improve Your Critical Thinking. Authored by : Samantha Agoos. Located at : https://www.youtube.com/watch?v=dItUGF8GdTw&t=5s . License : Other . License Terms : Youtube video
- The Danger of Assumptions. Authored by : Elaine Powell. Located at : https://www.youtube.com/watch?v=rjv_5X9FpVE&t=3s . License : Other . License Terms : YouTube video
- image of male face with question marks. Authored by : geralt. Provided by : Pixabay. Located at : https://pixabay.com/en/man-boy-face-view-direction-479670/ . License : CC0: No Rights Reserved
10 Tips to Succeed with Critical Thinking and Problem-Solving at Work
What are critical thinking and problem-solving skills, how can managers improve their critical thinking and problem-solving skills, how can managers use critical thinking to solve problems, examples of critical thinking and problem-solving for managers , 10 tips for critical thinking & problem-solving for managers.
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- Seek out diverse perspectives: Engage with people with different perspectives and experiences. This can help managers to consider multiple viewpoints and make more informed decisions.
- Read widely: Read books, articles, and other materials from various disciplines and perspectives. It can help managers to broaden their knowledge base and develop new insights and ideas.
- Practice active listening: Listen carefully to others and seek to understand their perspectives. This can help managers to identify potential problems and develop more effective solutions.
- Ask probing questions: Ask questions that challenge assumptions and encourage deeper thinking. It can help managers identify the problem’s root causes and develop more effective solutions.
- Use data to inform decisions: Use data and evidence to inform decision-making . It will help managers to identify patterns and trends and make more informed decisions.
- Embrace uncertainty: Embrace uncertainty and be open to the possibility of failure. This can help managers to take calculated risks and learn from mistakes.
- Engage in reflection: Reflect on past decisions and problem-solving efforts. Consider what worked well and what could have been done differently.
- Practice creativity: Practice creative thinking techniques such as brainstorming , mind-mapping, or lateral thinking. It helps managers to generate new ideas and develop innovative solutions.
- Define the problem: Clearly define the problem or issue that needs to be addressed. Use facts and data to clarify the issue and determine the scope of the problem.
- Gather information: Collect relevant data and information to understand the problem better. Use both internal and external sources to gather insights and perspectives.
- Analyze the information: Use critical thinking skills to analyze the data and information collected. Look for patterns, identify cause-and-effect relationships, and consider potential solutions.
- Generate potential solutions: Use creative thinking techniques such as brainstorming to generate a list of potential solutions. Consider multiple options and evaluate them based on their feasibility, impact, and alignment with team goals.
- Evaluate potential solutions: Evaluate each solution using critical thinking skills. Consider the pros and cons of each option, weigh the risks and benefits, and consider potential unintended consequences.
- Choose a solution: Based on evaluating solutions, choose the most appropriate solution. Consider the resources required to implement the solution, the timeline for implementation, and any potential obstacles.
- Implement the solution: Develop a plan for implementing the chosen solution. Communicate the plan to stakeholders, assign roles and responsibilities, and establish a timeline for implementation.
- Evaluate the solution: Monitor the implementation of the solution and evaluate its effectiveness. Collect feedback from stakeholders and make adjustments as necessary.
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- Identifying root causes: A critical-thinking manager might investigate a recurring problem in their department by asking questions to identify the root cause. They might analyze data and seek input from team members to identify potential contributing factors and develop a plan to address the issue.
- Evaluating risks: A manager might use critical thinking to assess the risks associated with a proposed project or initiative. They might consider potential risks and develop contingency plans to mitigate them or decide to postpone the project if the risks are deemed too high.
- Analyzing data: A manager might use critical thinking to analyze data to identify trends and patterns. For example, they might analyze sales data to identify growth opportunities or analyze employee performance data to identify areas for improvement.
- Developing creative solutions: A manager might use critical thinking and problem-solving skills to develop creative solutions to complex problems. For example, they might brainstorm with team members to create innovative products or services that meet customer needs.
- Evaluating proposals: A manager might use critical thinking to assess proposals from vendors or outside consultants. They might ask questions to ensure the proposal aligns with the team’s goals and objectives and consider potential risks and benefits before deciding.
- Develop a growth mindset: Embrace a growth mindset and believe your skills and abilities can improve with effort and practice.
- Challenge your assumptions: Identify them and challenge them by considering alternative perspectives.
- Use logic and reasoning: Use logical reasoning to evaluate arguments and evidence and make informed decisions.
- Practice active listening: Listen carefully to others and ask questions to clarify their perspectives .
- Analyze data: Use data to inform decision-making and analyze trends and patterns.
- Develop creative solutions: Practice creative techniques like brainstorming and lateral thinking to generate new ideas and solutions.
- Consider potential consequences: Evaluate the possible consequences of your decisions and actions, both positive and negative.
- Seek feedback: Seek feedback from others to identify areas for improvement and growth.
- Practice mindfulness: Practice mindfulness to reduce stress and improve focus and clarity.
- Continuously learn: Seek opportunities to learn and develop new skills, such as attending workshops, taking courses, or reading books and articles.
Test your critical thinking skills today to never let any problem stop you
Take the free critical thinking assessment to get started now!
What helps with critical thinking and problem-solving?
What are critical thinking and problem-solving in the workplace, what are critical thinking and problem-solving skills in leadership, what are critical thinking and problem-solving 21st-century skills.
6 Steps to Beat Common Critical Thinking Barriers at Work
How to develop the 8 conceptual skills every manager needs, 7 ways to develop critical thinking skills as a manager, 5 steps to excellent strategic thinking skills for managers.
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Critical thinking and problem solving
Critical thinking is a scope of various complex skills related to a higher level of thinking. It is a self-directed thinking that produces new and innovative ideas and solves problems. It assumes reflecting critically on learning experiences and processes, and making effective decisions by avoiding common pitfalls, for example seeing only one side of an issue, discounting new evidence that disconfirms your ideas, reasoning from passion rather than logic, and failing to support statements with evidence.
In its exemplary form, it is based on universal intellectual values that transcend subject matter divisions: clarity, accuracy, precision, consistency, relevance, sound evidence, good reasons, depth, breadth, and fairness.
Problem Solving is a mental process involving the ability to analyze and find the solution that best resolves the problem. It describes the process where there is a goal that is blocked for any reason – lack of resources, lack of information and so on – that presents a problem. Whatever is done in order to achieve the set goal is problem solving.
There are routine problems and non-routine problems. Routine problems can be solved using methods familiar to students by replicating previously learned methods in a step-by-step fashion. Non-routine problems are problems for ‘which there is not a predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instructions or a worked-out example’. Everyone needs problem solving skill in everyday life. It assumes a group of skills which, in addition to cognitive, includes social and other skills, helping us to define causes to the problem and to find efficient solutions. We use critical and creative thinking in order to solve problems.
Benefits of learning critical thinking and problem solving skills
Benefits of learning critical thinking.
- Critical thinking improves students’ flexibility and learning skills. We don’t know how technology will change by the time young people leave education. Learning critical thinking and problem solving will prepare them to learn and adapt faster and keep up to date with relevant changes in their fields of study, whatever they may be
- Critical thinking makes education less passive and more interactive. Teaching students how to approach critically any subject makes it more relevant for them. It helps them better understand and get more involved with the subject and its importance in their lives, making them feel as they are active participants
- Critical thinking and problem solving skills enhances academic performance. Rather than relying on teachers and classroom time for instruction and guidance, students with critical thinking skills become more independent, self-directed learners
- Critical thinking is the foundation of science and a liberal democratic society. Science requires the critical use of reason in experimentation and theory confirmation. The proper functioning of a liberal democracy requires citizens who can think critically about social issues to inform their judgments about proper governance and to overcome biases and prejudice.
Benefits of learning problem solving
- Students gain the ability to reflect critically on learning experiences and processes and to make effective decisions
- While solving problems, students also learn other important skills such as creativity, collaboration and cooperation
- Critical thinking enables separation of facts from opinions and helps consider all possible options in solving a problem
- Students are getting prepared for jobs that don’t exist yet. The work environment is changing fast and we simply do not know what jobs will exist and even less so what will be required to do them. Workers will be likely selected based on their ability to learn fast, adapt to changes and work independently, make job-related decisions independently and be able to solve problems on their own.
Critical Thinking and Problem-Solving
What are Critical Thinking & Problem-Solving?
“We can not solve our problems with the same level of thinking that created them.” – Albert Einstein
Critical thinking and problem-solving are core skills that teach students to question or reflect on their own knowledge and information presented to them. These are essential skills for students working on assignments or conducting research. They are the ability to actively use reason to analyze issues, make decisions, and ultimately overcome problems.
Developing critical thinking skills in the workplace is important because it helps students, interns, and employees more effectively diagnose problems and identify possible solutions that aren’t entirely obvious at first. It encourages curiosity and is one of the most valuable skills when it comes to working on a team.
Problem-solving consists of using more general or more precise methods in an orderly fashion to find solutions to problems encountered in life or work. The phrase has a varying meaning depending on the discipline it’s acknowledged under. For example, it is a cognitive process in psychology and a computer-operated process in computer science.
Solving Different Types of Problems
There are two types of problems: imprecise and explicit. Of course, different problem-solving methods are required for each. Explicit problems have specific aims and clear solutions, while imprecise problems do not. Explicit problems permit much better planning and preparation than imprecise problems. Solving problems revolves around dealing with pragmatism, the way that context contributes to meaning, and semantics contribute to the clarification and interpretation of the problem.
The ability to understand what the objective is, and what rules must be implemented represents the key to solving your problem. Sometimes, the problem requires abstract thinking or coming up with a creative solution.
- 7 Ways to Improve Your Critical Thinking Skills
- Most of the time, seeking a solution becomes more difficult and complex than the question or problem originally is. Keep going back to the root of it all and keep yourself grounded on that original issue for better clarity.
- When unsure of something, set aside your assumptions and question them. That is exactly where innovation and ground-breaking discoveries happen! Ask Albert Einstein!
- The human brain naturally uses mental shortcuts to interpret our surroundings. A critical thinker is aware of this cognitive bias and how it evidently influences decisions and solutions that originally appear to be objective and neutral. We all have biases in our thinking process. Being aware of those is precisely what makes critical thinking possible.
- A fun yet efficient way to find a solution to an issue is to try and reverse things. It may appear crystal clear to you that A causes B, but what if B caused A? Even if you end up noticing that the reverse isn’t true, nor is it a solution, considering it can still help you on the right path to discovering a solution.
- When trying to solve an issue, it’s always insightful to look at other people’s work previously done in the same discipline or area of expertise. There’s no purpose to start solving a problem entirely anew when the groundwork has already been laid out for you! Mind you, no copying, only inspiration!
- Thinking for yourself is one of your most powerful tools, yet not so easy to do, precisely because of the outer influences we are constantly subjected to. Of course, do rely on outer sources when lost and in need to build up your knowledge, but remember to do your thinking on your own as well: it is essential in order to answer your difficult questions.
- You can’t critically think all the time and that is perfectly fine. Critical Thinking is merely a tool you whip out when needed: for difficult problems and important decisions.
“It is the mark of an educated mind to be able to entertain a thought without accepting it.” – Aristotle
7 Tips for Effective Problem-Solving
- Understanding your problem clearly is the key to solving it. But that’s not all, you also need to consider that your teammates will have different perspectives on this same problem. Your first mission is to be crystal clear on your issue at hand.
- This is a critical step that is very often forgotten! Interests represent the needs you want to be satisfied by any sort of solution. Hence, the best solution to your problem is the one that satisfies everyone’s interests. The point here is to understand everybody: where they’re coming from and where they’re going.
- This is brainstorming time! Let your creativity run wild and list all the solutions coming to mind. There are no good or bad answers, only solutions that work out or don’t.
- Now that you’ve listed your options, you’ll need to analyse them. Honestly, review all your proposed solutions but mind not to step on the selection of your options! Here, you are only discussing which option is best and balancing the scales.
- Scale your elected solutions: which is best? Can they be jumbled together to better solve the issue at hand?
- While this may seem like a very simple tip, you can’t rely only on memory, as it is a very fickle thing! Better to be safe than sorry and write your solution down. Besides, it will help you finalize the details.
- Last but not least, you will need to think up some contingencies because circumstances may change: plan for the foreseeable future. You also need to think up how to monitor the efficiency of your solution, and finally, evaluate this same solution: does it need to be better tailored, or rather widened?
Improve your Critical Thinking & Problem-Solving Skills with a Course!
Skills course: workplace basics for graduates (now available).
This course is designed to equip all students and recent graduates with the basic skills needed when entering the workplace. There will be a large focus on understanding how to adapt from in-person to remote work in regards to productivity and time management, communication and the use of digital platforms. The course will also provide learners with the skills needed to identify their current skillset, recognise the skills they’re lacking, and provide actionable examples of how to improve these and meet employer’s demands.
Sources & Additional Resources
- TEDx Talk: Encourage Critical Thinking with 3 Questions – Brian Oshiro
- TEDx Talk: Critical Thinking: The Next Step in Human Evolution – Vegard Møller
- TEDx Talk: How Languages Shape the Way We Think – Lera Boroditsky
- TEDx Talk: The Surprising Secret that Solves your Problems Quickly – Collins Key
- TEDx Talk: Find Problem, Solve Problem – Arian Glantz
- TEDx Talk: Working Backward to Solve Problems – Maurice Ashley
- What is Critical Thinking?
- Stanford Encyclopedia of Philosophy – Critical Thinking
- 3 Simple Habits to Improve Your Critical Thinking
- What is Problem Solving?
- Seven Steps for Effective Problem Solving in the Workplace
- The Skills of Problem Solving
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