critical thinking logic problems

7 Puzzles to Challenge Your Critical Thinking

Can you spot the connections and sort these items.

Posted March 5, 2015 | Reviewed by Ekua Hagan

The theme of this post is critical thinking—and the kinds of puzzles that can be constructed around it. This term is used frequently in psychology and education . There are various definitions, but the one that best suits our purpose and which is, in the end, perhaps the best, is the ability to comprehend the logical connections among ideas, words, phrases, and concepts . In the relevant scientific literature, of course, the term is used much more broadly as a framework for understanding human cognition . But in my opinion, the best way to understand things is to construct puzzles to illustrate their basic essence.

Critical thinking involves skill at recognizing a pattern in given information and especially recognizing how the information is connected to the real world. Here are a couple of very simple examples. First, consider the five words below:

• Cruise ship
• Walking on foot
• Automobile (not a race car)

Now, put them in order from the slowest to the fastest, when they are going at maximum speed. The solution, of course, is: 4-2-5-1-3.

As with all such puzzles, there might be slightly different solutions—one could claim that some automobiles go faster than cruise ships. This “indeterminacy” characterizes this kind of thinking. However, some puzzles are straightforward. For instance, what do the following five things have in common?

The answer? These are all words referring to shades of blue.

The seven puzzles below are to the ones above, though hopefully more challenging. Some involve knowledge of facts, but critical thinking is still involved in such cases because the organization of the facts according to some principle is always involved—for example, a puzzle may ask you to put five items in order of their dates of invention.

The following tongue-in-cheek definition of critical thinking by Richard W. Paul, a leading expert on critical thinking theory, says it all: “Critical thinking is thinking about your thinking while you’re thinking in order to make your thinking better.”

I. What do the following 5 things have in common?

• Orange juice

II. Put the following buildings or structures in order of height, from the shortest to the tallest.

• Typical camping tent

III. What do the following animals have in common?

IV. Put the following inventions in order from earliest to most recent.

V. What feature do the following words have in common?

• Imagination

VI. Put these bodies of water in order in terms of volume, from smallest to largest .

VII. What do the following landmasses have in common?

I. They are all drinkable liquids. II. 5-1-4-3-2 III. They all have a tail. They are also all quadrupeds. IV. To the best of my knowledge: 5-4-3-1-2 V. They start with a vowel: a, e, i, o, u VI. 4-2-1-5-3 VII. They are all peninsulas.

Marcel Danesi, Ph.D. , is a professor of semiotics and anthropology at Victoria College, University of Toronto. His books include The Puzzle Instinct and The Total Brain Workout .

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Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Copyright Year: 2016

Publisher: Matthew J. Van Cleave

Language: English

Formats Available

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Learn more about reviews.

Reviewed by "yusef" Alexander Hayes, Professor, North Shore Community College on 6/9/21

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness. read more

Comprehensiveness rating: 5 see less

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness.

Content Accuracy rating: 5

The book is accurate.

Relevance/Longevity rating: 5

While many modern examples are used, and they are helpful, they are not necessarily needed. The usefulness of logical principles and skills have proved themselves, and this text presents them clearly with many examples.

Clarity rating: 5

It is obvious that the author cares about their subject, audience, and students. The text is comprehensible and interesting.

Consistency rating: 5

The format is easy to understand and is consistent in framing.

Modularity rating: 5

This text would be easy to adapt.

Organization/Structure/Flow rating: 5

The organization is excellent, my one suggestion would be a concluding chapter.

Interface rating: 5

I accessed the PDF version and it would be easy to work with.

Grammatical Errors rating: 5

The writing is excellent.

Cultural Relevance rating: 5

This is not an offensive text.

Reviewed by Susan Rottmann, Part-time Lecturer, University of Southern Maine on 3/2/21

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it... read more

Comprehensiveness rating: 4 see less

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it fits better for a general critical thinking course than for a true logic course. I'm not sure that I'd agree. I have been using Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," and I think that book is a better introduction to critical thinking for non-philosophy majors. However, the latter is not open source so I will figure out how to get by without it in the future. Overall, the book seems comprehensive if the subject is logic. The index is on the short-side, but fine. However, one issue for me is that there are no page numbers on the table of contents, which is pretty annoying if you want to locate particular sections.

Content Accuracy rating: 4

I didn't find any errors. In general the book uses great examples. However, they are very much based in the American context, not for an international student audience. Some effort to broaden the chosen examples would make the book more widely applicable.

Relevance/Longevity rating: 4

I think the book will remain relevant because of the nature of the material that it addresses, however there will be a need to modify the examples in future editions and as the social and political context changes.

Clarity rating: 3

The text is lucid, but I think it would be difficult for introductory-level students who are not philosophy majors. For example, in Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," the sub-headings are very accessible, such as "Experts cannot rescue us, despite what they say" or "wishful thinking: perhaps the biggest single speed bump on the road to critical thinking." By contrast, Van Cleave's "Introduction to Logic and Critical Thinking" has more subheadings like this: "Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form" or "Propositional logic and the four basic truth functional connectives." If students are prepared very well for the subject, it would work fine, but for students who are newly being introduced to critical thinking, it is rather technical.

It seems to be very consistent in terms of its terminology and framework.

Modularity rating: 4

The book is divided into 4 chapters, each having many sub-chapters. In that sense, it is readily divisible and modular. However, as noted above, there are no page numbers on the table of contents, which would make assigning certain parts rather frustrating. Also, I'm not sure why the book is only four chapter and has so many subheadings (for instance 17 in Chapter 2) and a length of 242 pages. Wouldn't it make more sense to break up the book into shorter chapters? I think this would make it easier to read and to assign in specific blocks to students.

Organization/Structure/Flow rating: 4

The organization of the book is fine overall, although I think adding page numbers to the table of contents and breaking it up into more separate chapters would help it to be more easily navigable.

Interface rating: 4

The book is very simply presented. In my opinion it is actually too simple. There are few boxes or diagrams that highlight and explain important points.

The text seems fine grammatically. I didn't notice any errors.

The book is written with an American audience in mind, but I did not notice culturally insensitive or offensive parts.

Overall, this book is not for my course, but I think it could work well in a philosophy course.

Reviewed by Daniel Lee, Assistant Professor of Economics and Leadership, Sweet Briar College on 11/11/19

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument read more

Comprehensiveness rating: 3 see less

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument

To the best of my ability, I regard this content as accurate, error-free, and unbiased

The book is broadly relevant and up-to-date, with a few stray temporal references (sydney olympics, particular presidencies). I don't view these time-dated examples as problematic as the logical underpinnings are still there and easily assessed

Clarity rating: 4

My only pushback on clarity is I didn't find the distinction between argument and explanation particularly helpful/useful/easy to follow. However, this experience may have been unique to my class.

To the best of my ability, I regard this content as internally consistent

I found this text quite modular, and was easily able to integrate other texts into my lessons and disregard certain chapters or sub-sections

The book had a logical and consistent structure, but to the extent that there are only 4 chapters, there isn't much scope for alternative approaches here

No problems with the book's interface

The text is grammatically sound

Cultural Relevance rating: 4

Perhaps the text could have been more universal in its approach. While I didn't find the book insensitive per-se, logic can be tricky here because the point is to evaluate meaningful (non-trivial) arguments, but any argument with that sense of gravity can also be traumatic to students (abortion, death penalty, etc)

No additional comments

Reviewed by Lisa N. Thomas-Smith, Graduate Part-time Instructor, CU Boulder on 7/1/19

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text,... read more

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text, and the index is very thorough.

The content is excellent. The text is thorough and accurate with no errors that I could discern. The terminology and exercises cover the material nicely and without bias.

The text should easily stand the test of time. The exercises are excellent and would be very helpful for students to internalize correct critical thinking practices. Because of the logical arrangement of the text and the many sub-sections, additional material should be very easy to add.

The text is extremely clearly and simply written. I anticipate that a diligent student could learn all of the material in the text with little additional instruction. The examples are relevant and easy to follow.

The text did not confuse terms or use inconsistent terminology, which is very important in a logic text. The discipline often uses multiple terms for the same concept, but this text avoids that trap nicely.

The text is fairly easily divisible. Since there are only four chapters, those chapters include large blocks of information. However, the chapters themselves are very well delineated and could be easily broken up so that parts could be left out or covered in a different order from the text.

The flow of the text is excellent. All of the information is handled solidly in an order that allows the student to build on the information previously covered.

The PDF Table of Contents does not include links or page numbers which would be very helpful for navigation. Other than that, the text was very easy to navigate. All the images, charts, and graphs were very clear

I found no grammatical errors in the text.

Cultural Relevance rating: 3

The text including examples and exercises did not seem to be offensive or insensitive in any specific way. However, the examples included references to black and white people, but few others. Also, the text is very American specific with many examples from and for an American audience. More diversity, especially in the examples, would be appropriate and appreciated.

Reviewed by Leslie Aarons, Associate Professor of Philosophy, CUNY LaGuardia Community College on 5/16/19

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an... read more

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an argument and an explanation; validity; soundness; and the distinctions between an inductive and a deductive argument in accessible terms in the first chapter. It also does a good job introducing and discussing informal fallacies (Chapter 4). The incorporation of opportunities to evaluate real-world arguments is also very effective. Chapter 2 also covers a number of formal methods of evaluating arguments, such as Venn Diagrams and Propositional logic and the four basic truth functional connectives, but to my mind, it is much more thorough in its treatment of Informal Logic and Critical Thinking skills, than it is of formal logic. I also appreciated that Van Cleave’s book includes exercises with answers and an index, but there is no glossary; which I personally do not find detracts from the book's comprehensiveness.

Overall, Van Cleave's book is error-free and unbiased. The language used is accessible and engaging. There were no glaring inaccuracies that I was able to detect.

Van Cleave's Textbook uses relevant, contemporary content that will stand the test of time, at least for the next few years. Although some examples use certain subjects like former President Obama, it does so in a useful manner that inspires the use of critical thinking skills. There are an abundance of examples that inspire students to look at issues from many different political viewpoints, challenging students to practice evaluating arguments, and identifying fallacies. Many of these exercises encourage students to critique issues, and recognize their own inherent reader-biases and challenge their own beliefs--hallmarks of critical thinking.

As mentioned previously, the author has an accessible style that makes the content relatively easy to read and engaging. He also does a suitable job explaining jargon/technical language that is introduced in the textbook.

Van Cleave uses terminology consistently and the chapters flow well. The textbook orients the reader by offering effective introductions to new material, step-by-step explanations of the material, as well as offering clear summaries of each lesson.

This textbook's modularity is really quite good. Its language and structure are not overly convoluted or too-lengthy, making it convenient for individual instructors to adapt the materials to suit their methodological preferences.

The topics in the textbook are presented in a logical and clear fashion. The structure of the chapters are such that it is not necessary to have to follow the chapters in their sequential order, and coverage of material can be adapted to individual instructor's preferences.

The textbook is free of any problematic interface issues. Topics, sections and specific content are accessible and easy to navigate. Overall it is user-friendly.

I did not find any significant grammatical issues with the textbook.

The textbook is not culturally insensitive, making use of a diversity of inclusive examples. Materials are especially effective for first-year critical thinking/logic students.

I intend to adopt Van Cleave's textbook for a Critical Thinking class I am teaching at the Community College level. I believe that it will help me facilitate student-learning, and will be a good resource to build additional classroom activities from the materials it provides.

Reviewed by Jennie Harrop, Chair, Department of Professional Studies, George Fox University on 3/27/18

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters... read more

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters that are dense with statistical analyses and critical vocabulary. These topics are likely better broached in manageable snippets rather than hefty single chapters.

The ideas addressed in Introduction to Logic and Critical Thinking are accurate but at times notably political. While politics are effectively used to exemplify key concepts, some students may be distracted by distinct political leanings.

The terms and definitions included are relevant, but the examples are specific to the current political, cultural, and social climates, which could make the materials seem dated in a few years without intentional and consistent updates.

While the reasoning is accurate, the author tends to complicate rather than simplify -- perhaps in an effort to cover a spectrum of related concepts. Beginning readers are likely to be overwhelmed and under-encouraged by his approach.

Consistency rating: 3

The four chapters are somewhat consistent in their play of definition, explanation, and example, but the structure of each chapter varies according to the concepts covered. In the third chapter, for example, key ideas are divided into sub-topics numbering from 3.1 to 3.10. In the fourth chapter, the sub-divisions are further divided into sub-sections numbered 4.1.1-4.1.5, 4.2.1-4.2.2, and 4.3.1 to 4.3.6. Readers who are working quickly to master new concepts may find themselves mired in similarly numbered subheadings, longing for a grounded concepts on which to hinge other key principles.

Modularity rating: 3

The book's four chapters make it mostly self-referential. The author would do well to beak this text down into additional subsections, easing readers' accessibility.

The content of the book flows logically and well, but the information needs to be better sub-divided within each larger chapter, easing the student experience.

The book's interface is effective, allowing readers to move from one section to the next with a single click. Additional sub-sections would ease this interplay even further.

Grammatical Errors rating: 4

Some minor errors throughout.

For the most part, the book is culturally neutral, avoiding direct cultural references in an effort to remain relevant.

Reviewed by Yoichi Ishida, Assistant Professor of Philosophy, Ohio University on 2/1/18

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic,... read more

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic, this textbook does not cover suppositional arguments, such as conditional proof and reductio ad absurdum. But other standard argument forms are covered. Chapter 3 covers inductive logic, and here this textbook introduces probability and its relationship with cognitive biases, which are rarely discussed in other textbooks. Chapter 4 introduces common informal fallacies. The answers to all the exercises are given at the end. However, the last set of exercises is in Chapter 3, Section 5. There are no exercises in the rest of the chapter. Chapter 4 has no exercises either. There is index, but no glossary.

The textbook is accurate.

The content of this textbook will not become obsolete soon.

The textbook is written clearly.

The textbook is internally consistent.

The textbook is fairly modular. For example, Chapter 3, together with a few sections from Chapter 1, can be used as a short introduction to inductive logic.

The textbook is well-organized.

There are no interface issues.

I did not find any grammatical errors.

This textbook is relevant to a first semester logic or critical thinking course.

Reviewed by Payal Doctor, Associate Professro, LaGuardia Community College on 2/1/18

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner... read more

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner book, but seems to be a good text for a course that needs a foundation for arguments. There are exercises on creating truth tables and proofs, so it could work as a logic primer in short sessions or with the addition of other course content.

The books is accurate in the information it presents. It does not contain errors and is unbiased. It covers the essential vocabulary clearly and givens ample examples and exercises to ensure the student understands the concepts

The content of the book is up to date and can be easily updated. Some examples are very current for analyzing the argument structure in a speech, but for this sort of text understandable examples are important and the author uses good examples.

The book is clear and easy to read. In particular, this is a good text for community college students who often have difficulty with reading comprehension. The language is straightforward and concepts are well explained.

The book is consistent in terminology, formatting, and examples. It flows well from one topic to the next, but it is also possible to jump around the text without loosing the voice of the text.

The books is broken down into sub units that make it easy to assign short blocks of content at a time. Later in the text, it does refer to a few concepts that appear early in that text, but these are all basic concepts that must be used to create a clear and understandable text. No sections are too long and each section stays on topic and relates the topic to those that have come before when necessary.

The flow of the text is logical and clear. It begins with the basic building blocks of arguments, and practice identifying more and more complex arguments is offered. Each chapter builds up from the previous chapter in introducing propositional logic, truth tables, and logical arguments. A select number of fallacies are presented at the end of the text, but these are related to topics that were presented before, so it makes sense to have these last.

The text is free if interface issues. I used the PDF and it worked fine on various devices without loosing formatting.

1. The book contains no grammatical errors.

The text is culturally sensitive, but examples used are a bit odd and may be objectionable to some students. For instance, President Obama's speech on Syria is used to evaluate an extended argument. This is an excellent example and it is explained well, but some who disagree with Obama's policies may have trouble moving beyond their own politics. However, other examples look at issues from all political viewpoints and ask students to evaluate the argument, fallacy, etc. and work towards looking past their own beliefs. Overall this book does use a variety of examples that most students can understand and evaluate.

My favorite part of this book is that it seems to be written for community college students. My students have trouble understanding readings in the New York Times, so it is nice to see a logic and critical thinking text use real language that students can understand and follow without the constant need of a dictionary.

Reviewed by Rebecca Owen, Adjunct Professor, Writing, Chemeketa Community College on 6/20/17

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current... read more

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current events, funny scenarios, or other interesting ways to evaluate argument structure and validity. The third section, which deals with logical fallacies, is very clear and comprehensive. My only critique of the material included in the book is that the middle section may be a bit dense and math-oriented for learners who appreciate the more informal, informative style of the first and third section. Also, the book ends rather abruptly--it moves from a description of a logical fallacy to the answers for the exercises earlier in the text.

The content is very reader-friendly, and the author writes with authority and clarity throughout the text. There are a few surface-level typos (Starbuck's instead of Starbucks, etc.). None of these small errors detract from the quality of the content, though.

One thing I really liked about this text was the author's wide variety of examples. To demonstrate different facets of logic, he used examples from current media, movies, literature, and many other concepts that students would recognize from their daily lives. The exercises in this text also included these types of pop-culture references, and I think students will enjoy the familiarity--as well as being able to see the logical structures behind these types of references. I don't think the text will need to be updated to reflect new instances and occurrences; the author did a fine job at picking examples that are relatively timeless. As far as the subject matter itself, I don't think it will become obsolete any time soon.

The author writes in a very conversational, easy-to-read manner. The examples used are quite helpful. The third section on logical fallacies is quite easy to read, follow, and understand. A student in an argument writing class could benefit from this section of the book. The middle section is less clear, though. A student learning about the basics of logic might have a hard time digesting all of the information contained in chapter two. This material might be better in two separate chapters. I think the author loses the balance of a conversational, helpful tone and focuses too heavily on equations.

Consistency rating: 4

Terminology in this book is quite consistent--the key words are highlighted in bold. Chapters 1 and 3 follow a similar organizational pattern, but chapter 2 is where the material becomes more dense and equation-heavy. I also would have liked a closing passage--something to indicate to the reader that we've reached the end of the chapter as well as the book.

I liked the overall structure of this book. If I'm teaching an argumentative writing class, I could easily point the students to the chapters where they can identify and practice identifying fallacies, for instance. The opening chapter is clear in defining the necessary terms, and it gives the students an understanding of the toolbox available to them in assessing and evaluating arguments. Even though I found the middle section to be dense, smaller portions could be assigned.

The author does a fine job connecting each defined term to the next. He provides examples of how each defined term works in a sentence or in an argument, and then he provides practice activities for students to try. The answers for each question are listed in the final pages of the book. The middle section feels like the heaviest part of the whole book--it would take the longest time for a student to digest if assigned the whole chapter. Even though this middle section is a bit heavy, it does fit the overall structure and flow of the book. New material builds on previous chapters and sub-chapters. It ends abruptly--I didn't realize that it had ended, and all of a sudden I found myself in the answer section for those earlier exercises.

The simple layout is quite helpful! There is nothing distracting, image-wise, in this text. The table of contents is clearly arranged, and each topic is easy to find.

Tiny edits could be made (Starbuck's/Starbucks, for one). Otherwise, it is free of distracting grammatical errors.

This text is quite culturally relevant. For instance, there is one example that mentions the rumors of Barack Obama's birthplace as somewhere other than the United States. This example is used to explain how to analyze an argument for validity. The more "sensational" examples (like the Obama one above) are helpful in showing argument structure, and they can also help students see how rumors like this might gain traction--as well as help to show students how to debunk them with their newfound understanding of argument and logic.

The writing style is excellent for the subject matter, especially in the third section explaining logical fallacies. Thank you for the opportunity to read and review this text!

Reviewed by Laurel Panser, Instructor, Riverland Community College on 6/20/17

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as... read more

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as the 13th edition with the same title. Lori Watson is the second author on the 13th edition.

Competing with Hurley is difficult with respect to comprehensiveness. For example, Van Cleave’s book is comprehensive to the extent that it probably covers at least two-thirds or more of what is dealt with in most introductory, one-semester logic courses. Van Cleave’s chapter 1 provides an overview of argumentation including discerning non-arguments from arguments, premises versus conclusions, deductive from inductive arguments, validity, soundness and more. Much of Van Cleave’s chapter 1 parallel’s Hurley’s chapter 1. Hurley’s chapter 3 regarding informal fallacies is comprehensive while Van Cleave’s chapter 4 on this topic is less extensive. Categorical propositions are a topic in Van Cleave’s chapter 2; Hurley’s chapters 4 and 5 provide more instruction on this, however. Propositional logic is another topic in Van Cleave’s chapter 2; Hurley’s chapters 6 and 7 provide more information on this, though. Van Cleave did discuss messy issues of language meaning briefly in his chapter 1; that is the topic of Hurley’s chapter 2.

Van Cleave’s book includes exercises with answers and an index. A glossary was not included.

Reviews of open source textbooks typically include criteria besides comprehensiveness. These include comments on accuracy of the information, whether the book will become obsolete soon, jargon-free clarity to the extent that is possible, organization, navigation ease, freedom from grammar errors and cultural relevance; Van Cleave’s book is fine in all of these areas. Further criteria for open source books includes modularity and consistency of terminology. Modularity is defined as including blocks of learning material that are easy to assign to students. Hurley’s book has a greater degree of modularity than Van Cleave’s textbook. The prose Van Cleave used is consistent.

Van Cleave’s book will not become obsolete soon.

Van Cleave’s book has accessible prose.

Van Cleave used terminology consistently.

Van Cleave’s book has a reasonable degree of modularity.

Van Cleave’s book is organized. The structure and flow of his book is fine.

Problems with navigation are not present.

Grammar problems were not present.

Van Cleave’s book is culturally relevant.

Van Cleave’s book is appropriate for some first semester logic courses.

Table of Contents

Chapter 1: Reconstructing and analyzing arguments

• 1.1 What is an argument?
• 1.2 Identifying arguments
• 1.3 Arguments vs. explanations
• 1.4 More complex argument structures
• 1.5 Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form
• 1.6 Validity
• 1.7 Soundness
• 1.8 Deductive vs. inductive arguments
• 1.9 Arguments with missing premises
• 1.10 Assuring, guarding, and discounting
• 1.11 Evaluative language
• 1.12 Evaluating a real-life argument

Chapter 2: Formal methods of evaluating arguments

• 2.1 What is a formal method of evaluation and why do we need them?
• 2.2 Propositional logic and the four basic truth functional connectives
• 2.3 Negation and disjunction
• 2.4 Using parentheses to translate complex sentences
• 2.5 “Not both” and “neither nor”
• 2.6 The truth table test of validity
• 2.7 Conditionals
• 2.8 “Unless”
• 2.9 Material equivalence
• 2.10 Tautologies, contradictions, and contingent statements
• 2.11 Proofs and the 8 valid forms of inference
• 2.12 How to construct proofs
• 2.13 Short review of propositional logic
• 2.14 Categorical logic
• 2.15 The Venn test of validity for immediate categorical inferences
• 2.16 Universal statements and existential commitment
• 2.17 Venn validity for categorical syllogisms

Chapter 3: Evaluating inductive arguments and probabilistic and statistical fallacies

• 3.1 Inductive arguments and statistical generalizations
• 3.2 Inference to the best explanation and the seven explanatory virtues
• 3.3 Analogical arguments
• 3.4 Causal arguments
• 3.5 Probability
• 3.6 The conjunction fallacy
• 3.7 The base rate fallacy
• 3.8 The small numbers fallacy
• 3.9 Regression to the mean fallacy
• 3.10 Gambler's fallacy

Chapter 4: Informal fallacies

• 4.1 Formal vs. informal fallacies
• 4.1.1 Composition fallacy
• 4.1.2 Division fallacy
• 4.1.3 Begging the question fallacy
• 4.1.4 False dichotomy
• 4.1.5 Equivocation
• 4.2 Slippery slope fallacies
• 4.2.1 Conceptual slippery slope
• 4.2.2 Causal slippery slope
• 4.3 Fallacies of relevance
• 4.3.1 Ad hominem
• 4.3.2 Straw man
• 4.3.3 Tu quoque
• 4.3.4 Genetic
• 4.3.5 Appeal to consequences
• 4.3.6 Appeal to authority

Answers to exercises Glossary/Index

Ancillary Material

About the book.

This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a “critical thinking textbook.”

About the Contributors

Matthew Van Cleave ,   PhD, Philosophy, University of Cincinnati, 2007.  VAP at Concordia College (Moorhead), 2008-2012.  Assistant Professor at Lansing Community College, 2012-2016. Professor at Lansing Community College, 2016-

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Become a better critical thinker with these 7 critical thinking exercises

Critical thinking is a skill you can use in any situation. Whether you're a student, entrepreneur, or business executive, critical thinking can help you make better decisions and solve problems.

But learning critical thinking skills isn't always an easy task. Many tools, techniques, and strategies are available, and choosing the right one can be challenging. Vague suggestions on the internet like "read more" aren't very helpful, and elaborate business examples don’t apply to many of us.

As average problem-solvers, we need actionable thinking exercises to improve our critical thinking skills and enhance our thinking processes. Regularly performing exercises that specifically stretch our decision-making and reasoning skills is the most effective method of improving our thinking abilities.

This article will explore several exercises that will help you develop critical thinking skills. Whether you are preparing for an exam, making an influential decision for your business, or going about your daily life, these fun activities can build your reasoning skills and creative problem-solving abilities.

Boost your logical thinking skills and start practicing a critical mindset with these 10 critical thinking exercises.

A Quick Look at Critical Thinking

As a thoughtful learner, you likely already understand the basics of critical thinking, but here's a quick refresher.

Critical thinking involves analyzing problems or issues objectively and rationally. Critical thinkers are able to understand their own biases and assumptions, as well as those of others. They’re also able to see the world from a different point of view and understand how their experiences impact their thinking.

Developing critical thinking skills is essential because it allows us to see things from multiple perspectives, identify biases and errors in reasoning, and be open to possible solutions. Making informed decisions is easier when we have a better understanding of the world around us.

Why We Need to Practice Critical Thinking

We aren't born with critical thinking skills, and they don’t naturally develop beyond survival-level thinking. To master critical thinking, we must practice it and develop it over time.

However, learning to think critically isn't as easy as learning to ride a bicycle. There aren't any step-by-step procedures to follow or supportive guides to fall back on, and it is not taught in public schools consistently or reliably. To ensure students' success, teachers must know higher-order thinking skills (HOTS) and how to teach them, research says.

Unfortunately, although teachers understand the importance of HOTS and attempt to teach it, studies show that their capacity to measure students' HOTS is low. Educator and author Dr. Kulvarn Atwal says, "It seems that we are becoming successful at producing students who are able to jump through hoops and pass tests."

As critical thinking skills become more important in higher grades, some students find it challenging to understand the concept of critical thinking. To develop necessary thinking skills, we must set aside our assumptions and beliefs. This allows us to explore and question topics from a "blank page" point of view and distinguish fact from opinion.

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7 Critical Thinking Exercises To Improve Your Critical Thinking Skills

The good news is that by assessing, analyzing, and evaluating our thought processes, we can improve our skills. Critical thinking exercises are key to this improvement. Our critical thinking builds and improves with regular practice, just like a muscle that gets stronger with use.

If you want to become a better critical thinker , here are some critical thinking exercises to try:

Exercise #1: The Ladder of Inference

You can exercise your critical thinking skills by using the Ladder of Inference model . This thinking model was developed by renowned organizational psychologist Chris Argyris. Each rung on the ladder of inference represents a step you take to arrive at your conclusions.

The decision-making process starts when we are faced with a problem or situation. As soon as we observe something problematic or important, we presume what is causing it, and then we use that assumption to draw conclusions. Based on those conclusions, we take action.

For example, say you're at a party and see a friend across the room. You catch their eye and wave, but they turn and walk away. Using the ladder, you might climb the rungs as follows:

• Observe that your friend walked away.
• Select a few details of the situation, including your wave and your assumption that they saw you.
• Meaning is attached based on the environment, making you think your friend must have other people to talk to at the party.
• Assumptions are made based on that meaning, assuming that means your friend doesn’t like you as much as them.
• Conclusions are drawn from the assumption, and you determine that your friend must be mad at you or doesn't want you to be at the party.
• Beliefs are formed, making you think you're not welcome.
• Action is taken, and you leave the party.

In this example, you started with a situation (someone walking away at a crowded party) and made a series of inferences to arrive at a conclusion (that the person is mad at you and doesn't want you there).

The Ladder of Inference can be a helpful tool to frame your thinking because it encourages you to examine each step of your thought process and avoid jumping to conclusions. It's easy to make assumptions without realizing it, as in this scene. Perhaps your friend never even saw you wave from across the crowded room.

Exercise #2: The Five Whys

The "Five Whys" technique is an analytical skill that can help you uncover the source of a problem. The activity was created by Sakichi Toyoda, the founder of Toyota, and consists of repeatedly asking “why?” when a problem is encountered to determine its root cause.

This exercise can be difficult because knowing if you've discovered the source of your problem is challenging. The "five" in "Five Whys" is just a guideline — you may need to ask more. When you can't ask anything else, and your response is related to the original issue, you've probably arrived at the end.

Even if you need several rounds of questioning, just keep going. The important part that helps you practice critical thinking is the process of asking "why?" and uncovering the deeper issues affecting the situation.

For instance, say you're trying to figure out why your computer keeps crashing.

• You ask " why ," and the answer is that there's a software problem.
• Why? Because the computer keeps running out of memory.
• Why? Because too many programs are running at the same time.
• Why? Because too many browser tabs are open .
• Why? Because multitasking is fragmenting your focus, you're doing too many things at once.

In this example, working through the "why's" revealed the underlying cause. As a result, you can find the best solution, which is concentrating on just one thing at a time.

Exercise #3: Inversion

Inversion is another critical thinking exercise that you can use in any situation. Inversion is sort of like taking on the role of the devil's advocate. In this exercise, adopt the opposite view of whatever issue you're exploring and consider the potential arguments for that side. This will help broaden your critical thinking skills and enable you to see other perspectives on a situation or topic more clearly.

For example, let's say you're thinking about starting your own business. Using inversion, you would explore all of the potential arguments for why starting your own business is bad. This might include concerns like:

• You could end up in debt.
• The business might fail.
• It's a lot of work.
• You might not have time for anything else.

By exploring these potentially adverse outcomes, you can identify the potential risks involved in starting your own business and make a more sound decision. You might realize that now is not the right time for you to become an entrepreneur. And if you do start the company, you'll be better prepared to deal with the issues you identified when they occur.

Exercise #4: Argument Mapping

Argument mapping can be a beneficial exercise for enhancing critical thinking skills. Like mind mapping, argument mapping is a method of visually representing an argument's structure. It helps analyze and evaluate ideas as well as develop new ones.

In critical thinking textbooks, argument diagramming is often presented to introduce students to argument constructions. It can be an effective way to build mental templates or schema for argument structures, which researchers think may make critical evaluation easier .

Argument maps typically include the following:

• Conclusion: What is being argued for or against
• Premises: The reasons given to support the conclusion
• Inferences: The connections made between the premises and conclusion

The argument map should be as clear and concise as possible, with a single word or phrase representing each element. This will help you make connections more easily. After the map is completed, you can use it to identify any weak points in the argument. If any areas aren't well-supported, additional premises can be added.

Argument mapping can be applied to any situation that requires critical thinking skills. The more time you take to map out an argument, the better you'll understand how the pieces fit together. Ultimately, this will help you think more creatively and critically, and make more informed decisions.

Exercise #5: Opinion vs. Fact

Critical thinking activities that focus on opinions and facts are particularly valuable and relevant new learning opportunities. Our constantly-connected world makes it easy to confuse opinions and facts , especially with sensationalist news articles and click-bait headlines.

How can you tell a fact from an opinion? Facts are generally objective and established, whereas opinions are subjective and unproven. For example, "the cloud is in the air" is a fact. "That dress looks good on you" is an opinion.

Practice your critical thinking skills by reading or listening to the news. See if you can identify when someone is stating an opinion rather than a fact. Ask yourself the following questions:

• Who is saying what? What reasons might be behind their statements?
• Does the claim make sense? Who would disagree with it and why?
• How can you tell if the data is reliable? Can it be fact-checked? Has it been shared by other credible publishers?
• How do you know whether or not the presenter is biased? What kind of language is being used?

This powerful exercise can train your mind to start asking questions whenever presented with a new claim. This will help you think critically about the information you're taking in and question what you're hearing before accepting it as truth.

Exercise #6: Autonomy of an Object

In her book " The Critical Thinking Tool Kit ," Dr. Marlene Caroselli describes a critical thinking exercise called "Living Problems, Lively Solutions." This exercise uses the autonomy of an object as a problem-solving tool to find a possible solution.

To do this, you'll personify your problem and place it in another context — a different time or place. This allows you to uncover unique solutions to the problem that might be tied to your mental associations with that setting.

For example, if your problem is poor time management , you might personify the issue as a thief of your time. The idea of a thief could make you think of jail, which might prompt thoughts of locking up specific distractions in your life. The idea of jail could also make you think of guards and lead you to the possible solution of checking in with an accountability buddy who can make sure you're sticking to your schedule.

The autonomy-of-object technique works because it stimulates thoughts you wouldn’t have considered without the particular context in which you place the problem.

Exercise #7: The Six Thinking Hats

Designed by Edward de Bono, the Six Thinking Hats is a critical thinking exercise that was created as a tool for groups to use when exploring different perspectives on an issue. When people use other thinking processes, meetings can become challenging rather than beneficial.

To help teams work more productively and mindfully, de Bono suggests dividing up different styles of thinking into six categories, represented as hats:

• The white hat is objective and focuses on facts and logic
• The red hat is intuitive, focusing on emotion and instinct
• The black hat is cautious and predicts negative outcomes
• The yellow hat is optimistic and encourages positive outcomes
• The green hat is creative, with numerous ideas and little criticism
• The blue hat is the control hat used for management and organization

With each team member wearing a different hat, a group can examine an issue or problem from many different angles, preventing one viewpoint (or individual) from dominating the meeting or discussion. This means that decisions and solutions reached using the Six Thinking Hats approach will likely be more robust and effective, and everyone’s creative thinking skills will benefit.

Train Your Brain With Critical Thinking Exercises

Using critical thinking regularly in various situations can improve our ability to evaluate and analyze information. These seven critical thinking exercises train your brain for better critical thinking skills . With daily practice, they can become habits that will help you think more critically each day.

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What are critical thinking skills?

How to develop critical thinking skills: 12 tips, how to practice critical thinking skills at work, become your own best critic.

A client requests a tight deadline on an intense project. Your childcare provider calls in sick on a day full of meetings. Payment from a contract gig is a month behind. 

Your day-to-day will always have challenges, big and small. And no matter the size and urgency, they all ask you to use critical thinking to analyze the situation and arrive at the right solution. 

Critical thinking includes a wide set of soft skills that encourage continuous learning, resilience , and self-reflection. The more you add to your professional toolbelt, the more equipped you’ll be to tackle whatever challenge presents itself. Here’s how to develop critical thinking, with examples explaining how to use it.

Critical thinking skills are the skills you use to analyze information, imagine scenarios holistically, and create rational solutions. It’s a type of emotional intelligence that stimulates effective problem-solving and decision-making . 

When you fine-tune your critical thinking skills, you seek beyond face-value observations and knee-jerk reactions. Instead, you harvest deeper insights and string together ideas and concepts in logical, sometimes out-of-the-box , ways. 

Imagine a team working on a marketing strategy for a new set of services. That team might use critical thinking to balance goals and key performance indicators , like new customer acquisition costs, average monthly sales, and net profit margins. They understand the connections between overlapping factors to build a strategy that stays within budget and attracts new sales. 

Looking for ways to improve critical thinking skills? Start by brushing up on the following soft skills that fall under this umbrella: 

• Analytical thinking: Approaching problems with an analytical eye includes breaking down complex issues into small chunks and examining their significance. An example could be organizing customer feedback to identify trends and improve your product offerings. 
• Open-mindedness: Push past cognitive biases and be receptive to different points of view and constructive feedback . Managers and team members who keep an open mind position themselves to hear new ideas that foster innovation . 
• Creative thinking: With creative thinking , you can develop several ideas to address a single problem, like brainstorming more efficient workflow best practices to boost productivity and employee morale . 
• Self-reflection: Self-reflection lets you examine your thinking and assumptions to stimulate healthier collaboration and thought processes. Maybe a bad first impression created a negative anchoring bias with a new coworker. Reflecting on your own behavior stirs up empathy and improves the relationship. 
• Evaluation: With evaluation skills, you tackle the pros and cons of a situation based on logic rather than emotion. When prioritizing tasks , you might be tempted to do the fun or easy ones first, but evaluating their urgency and importance can help you make better decisions. 

There’s no magic method to change your thinking processes. Improvement happens with small, intentional changes to your everyday habits until a more critical approach to thinking is automatic. 

Here are 12 tips for building stronger self-awareness and learning how to improve critical thinking: 

1. Be cautious

There’s nothing wrong with a little bit of skepticism. One of the core principles of critical thinking is asking questions and dissecting the available information. You might surprise yourself at what you find when you stop to think before taking action. 

Before making a decision, use evidence, logic, and deductive reasoning to support your own opinions or challenge ideas. It helps you and your team avoid falling prey to bad information or resistance to change .

2. Ask open-ended questions

“Yes” or “no” questions invite agreement rather than reflection. Instead, ask open-ended questions that force you to engage in analysis and rumination. Digging deeper can help you identify potential biases, uncover assumptions, and arrive at new hypotheses and possible solutions. 

3. Do your research

No matter your proficiency, you can always learn more. Turning to different points of view and information is a great way to develop a comprehensive understanding of a topic and make informed decisions. You’ll prioritize reliable information rather than fall into emotional or automatic decision-making. 

4. Consider several opinions

You might spend so much time on your work that it’s easy to get stuck in your own perspective, especially if you work independently on a remote team . Make an effort to reach out to colleagues to hear different ideas and thought patterns. Their input might surprise you.

If or when you disagree, remember that you and your team share a common goal. Divergent opinions are constructive, so shift the focus to finding solutions rather than defending disagreements. 

5. Learn to be quiet

Active listening is the intentional practice of concentrating on a conversation partner instead of your own thoughts. It’s about paying attention to detail and letting people know you value their opinions, which can open your mind to new perspectives and thought processes.

If you’re brainstorming with your team or having a 1:1 with a coworker , listen, ask clarifying questions, and work to understand other peoples’ viewpoints. Listening to your team will help you find fallacies in arguments to improve possible solutions.

6. Schedule reflection

Whether waking up at 5 am or using a procrastination hack, scheduling time to think puts you in a growth mindset . Your mind has natural cognitive biases to help you simplify decision-making, but squashing them is key to thinking critically and finding new solutions besides the ones you might gravitate toward. Creating time and calm space in your day gives you the chance to step back and visualize the biases that impact your decision-making. 

7. Cultivate curiosity

With so many demands and job responsibilities, it’s easy to seek solace in routine. But getting out of your comfort zone helps spark critical thinking and find more solutions than you usually might.

If curiosity doesn’t come naturally to you, cultivate a thirst for knowledge by reskilling and upskilling . Not only will you add a new skill to your resume , but expanding the limits of your professional knowledge might motivate you to ask more questions. 

You don’t have to develop critical thinking skills exclusively in the office. Whether on your break or finding a hobby to do after work, playing strategic games or filling out crosswords can prime your brain for problem-solving. 

9. Write it down

Recording your thoughts with pen and paper can lead to stronger brain activity than typing them out on a keyboard. If you’re stuck and want to think more critically about a problem, writing your ideas can help you process information more deeply.

The act of recording ideas on paper can also improve your memory . Ideas are more likely to linger in the background of your mind, leading to deeper thinking that informs your decision-making process. 

10. Speak up

Take opportunities to share your opinion, even if it intimidates you. Whether at a networking event with new people or a meeting with close colleagues, try to engage with people who challenge or help you develop your ideas. Having conversations that force you to support your position encourages you to refine your argument and think critically. 

11. Stay humble

Ideas and concepts aren’t the same as real-life actions. There may be such a thing as negative outcomes, but there’s no such thing as a bad idea. At the brainstorming stage , don’t be afraid to make mistakes.

Sometimes the best solutions come from off-the-wall, unorthodox decisions. Sit in your creativity , let ideas flow, and don’t be afraid to share them with your colleagues. Putting yourself in a creative mindset helps you see situations from new perspectives and arrive at innovative conclusions. 

12. Embrace discomfort

Get comfortable feeling uncomfortable . It isn’t easy when others challenge your ideas, but sometimes, it’s the only way to see new perspectives and think critically.

By willingly stepping into unfamiliar territory, you foster the resilience and flexibility you need to become a better thinker. You’ll learn how to pick yourself up from failure and approach problems from fresh angles. 

Thinking critically is easier said than done. To help you understand its impact (and how to use it), here are two scenarios that require critical thinking skills and provide teachable moments. 

Scenario #1: Unexpected delays and budget

Imagine your team is working on producing an event. Unexpectedly, a vendor explains they’ll be a week behind on delivering materials. Then another vendor sends a quote that’s more than you can afford. Unless you develop a creative solution, the team will have to push back deadlines and go over budget, potentially costing the client’s trust. 

Here’s how you could approach the situation with creative thinking:

• Analyze the situation holistically: Determine how the delayed materials and over-budget quote will impact the rest of your timeline and financial resources . That way, you can identify whether you need to build an entirely new plan with new vendors, or if it’s worth it to readjust time and resources. 
• Identify your alternative options: With careful assessment, your team decides that another vendor can’t provide the same materials in a quicker time frame. You’ll need to rearrange assignment schedules to complete everything on time. 
• Collaborate and adapt: Your team has an emergency meeting to rearrange your project schedule. You write down each deliverable and determine which ones you can and can’t complete by the deadline. To compensate for lost time, you rearrange your task schedule to complete everything that doesn’t need the delayed materials first, then advance as far as you can on the tasks that do. 
• Check different resources: In the meantime, you scour through your contact sheet to find alternative vendors that fit your budget. Accounting helps by providing old invoices to determine which vendors have quoted less for previous jobs. After pulling all your sources, you find a vendor that fits your budget. 
• Maintain open communication: You create a special Slack channel to keep everyone up to date on changes, challenges, and additional delays. Keeping an open line encourages transparency on the team’s progress and boosts everyone’s confidence. 

Scenario #2: Differing opinions 

A conflict arises between two team members on the best approach for a new strategy for a gaming app. One believes that small tweaks to the current content are necessary to maintain user engagement and stay within budget. The other believes a bold revamp is needed to encourage new followers and stronger sales revenue. 

Here’s how critical thinking could help this conflict:

• Listen actively: Give both team members the opportunity to present their ideas free of interruption. Encourage the entire team to ask open-ended questions to more fully understand and develop each argument. 
• Flex your analytical skills: After learning more about both ideas, everyone should objectively assess the benefits and drawbacks of each approach. Analyze each idea's risk, merits, and feasibility based on available data and the app’s goals and objectives. 
• Identify common ground: The team discusses similarities between each approach and brainstorms ways to integrate both idea s, like making small but eye-catching modifications to existing content or using the same visual design in new media formats. 
• Test new strategy: To test out the potential of a bolder strategy, the team decides to A/B test both approaches. You create a set of criteria to evenly distribute users by different demographics to analyze engagement, revenue, and customer turnover. 
• Monitor and adapt: After implementing the A/B test, the team closely monitors the results of each strategy. You regroup and optimize the changes that provide stronger results after the testing. That way, all team members understand why you’re making the changes you decide to make.

You can’t think your problems away. But you can equip yourself with skills that help you move through your biggest challenges and find innovative solutions. Learning how to develop critical thinking is the start of honing an adaptable growth mindset. 

Now that you have resources to increase critical thinking skills in your professional development, you can identify whether you embrace change or routine, are open or resistant to feedback, or turn to research or emotion will build self-awareness. From there, tweak and incorporate techniques to be a critical thinker when life presents you with a problem.

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Elizabeth Perry, ACC

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

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Critical Thinking Brain Teasers: Enhance Your Cognitive Skills Today

Critical thinking brain teasers are an engaging way to challenge one’s cognitive abilities and improve problem-solving skills. These mind-bending puzzles come in various forms, such as logic puzzles, visual puzzles, and rebus puzzles, each designed to test one’s ability to analyze, evaluate, and think outside the box. Incorporating critical thinking brain teasers into daily routines or educational settings helps develop key cognitive skills, fostering creativity and enhancing overall intellectual capacity.

Key Takeaways

Understanding critical thinking.

A significant aspect of critical thinking is the ability to approach problems from multiple angles. This skill allows individuals to consider various perspectives, enhancing the quality and accuracy of their judgments. It also aids in identifying biases and misleading information, fostering an open and clear-minded approach to complex issues.

In the realm of education, critical thinking is crucial for promoting independent thought and fostering a deeper understanding of complex topics. Educators can encourage the development of these skills by incorporating various critical thinking activities into lesson plans, such as debates, analysis of case studies, and group problem-solving exercises. This not only helps students become more insightful individuals but also equips them with the tools necessary for lifelong learning and adaptation in an ever-changing world.

Role of Critical Thinking in Problem-Solving

Developing problem-solving skills begins with understanding the importance of reasoning and logic. Critical thinking encourages individuals to avoid relying solely on intuition and assumptions. Instead, they should seek evidence, identify biases, and consider various perspectives before reaching a conclusion.

Brain Teasers and Their Importance

Brain teasers play a significant role in developing and maintaining cognitive skills. They come in various forms, ranging from simple puzzles that provide a sense of joy to more hard challenges that require extensive critical thinking. These mind-boggling exercises often require creativity, analytical thinking, and logical reasoning to solve.

In summary, brain teasers offer a range of advantages, from improving critical thinking skills to providing mental stimulation and enjoyment. By incorporating these engaging exercises into daily routines, individuals can enhance their cognitive abilities and contribute to overall personal growth and success.

Logic Puzzles

Sudoku is another popular type of logic puzzle that challenges a player’s logic and deduction skills. In a Sudoku puzzle, the player is presented with a partially filled 9×9 grid, with each row, column, and 3×3 subgrid containing the numbers 1 to 9 exactly once. The objective is to fill in the remaining cells in the grid using the provided information and the rules of the game, without guessing.

Enhancing Cognitive Skills and Creativity with Brain Teasers

Brain teasers offer a fun and engaging way to sharpen cognitive skills and boost creativity. They are designed to challenge the way individuals think, analyze information, and solve problems. Utilizing brain teasers as a part of one’s daily routine can foster intellectual growth, improve memory, and stimulate new ideas.

Moreover, brain teasers can be an excellent tool for mental training, keeping the mind sharp and focused. They can help in reducing cognitive decline associated with age, and even have the potential to improve productivity in various aspects of life. By maintaining an active mind, individuals are more likely to excel in their personal and professional pursuits.

Critical Thinking Brain Teasers

One type of critical thinking brain teaser involves a match-stick puzzle. In these puzzles, participants are given a specific number of matchsticks, and the objective is to rearrange them to form a new shape only by moving the specified number of matchsticks. These puzzles require a good spatial sense, attention to detail, and an understanding of geometric principles.

Another category of critical thinking brain teasers includes logic puzzles and grid-based challenges, where participants must deduce relationships between objects, people, or events based on a set of clues. For example, in a puzzle involving five houses of different heights and colors, participants must determine which house is the tallest and who lives in each house.

Strategies to Solve Brain Teasers

First, take the time to carefully read and understand the information provided in the brain teaser. Identify the key details and relevant information that will help in reaching the solution. It is essential to have a clear understanding of the problem before diving into solving it.

Another useful strategy is to approach the brain teaser from different angles or perspectives. Explore multiple possibilities and consider alternative interpretations of the information provided. This can help in identifying potential solutions that might not have been apparent at first glance.

Benefits of Brain Teasers in Real World

Brain teasers offer a wide range of benefits in the real world. They not only provide entertainment but also enhance your cognitive abilities in various aspects of life.

Furthermore, brain teasers often require a strong command of language skills. Puzzles based on wordplay, riddles, or anagrams can be particularly beneficial for expanding vocabulary, improving reading comprehension, and honing language abilities. This expertise in language assists you in more effective communication, both written and verbal, in various personal and professional settings.

Visual Puzzles and Rebus Puzzles

Visual puzzles are logic or reasoning problems that are expressed and solved using drawings or images. They can be found in various forms, such as finding differences between two pictures, identifying hidden objects in a scene, or determining the number of geometrical shapes in a given pattern. Some popular examples of visual puzzles are mentioned in this article titled “ Visual Puzzles & Brain Teasers That Will Challenge Your Mind .”

In conclusion, both visual puzzles and rebus puzzles are valuable tools for exercising critical thinking and cognitive skills. These challenges offer an engaging and entertaining way to promote mental agility while enhancing language and problem-solving abilities.

Educational Games and Worksheets

In addition to worksheets, teachers may also utilize visual brain teasers in their lessons. These activities encourage students to use critical thinking skills by solving problems through visual cues and patterns. This engaging form of game-based learning can be a fun way to develop logical thinking and problem-solving abilities among students.

Engaging in brain teasers is a valuable activity to develop and improve critical thinking abilities. They offer a way to sharpen the mind, making it more efficient and effective when facing complex challenges. Examples of such brain teasers can be found on websites like gcfglobal and Psychology Today .

Frequently Asked Questions

What is half of 2+2.

The first step in solving this is understanding that the equation should be read as “half of (2+2).” In this case, you have to perform the addition first: 2+2 equals 4. Now, find half of 4, which equals 2. Therefore, half of 2+2 is 2.

Which tire doesn’t move when a car takes a left turn?

You walk into a room with one match, a stove, a candle, and a fireplace; which do you light first, a man gave one of his three children one coin each. how many coins are left.

To solve this, it’s essential to realize that the man has three children and gave each of them one coin. Therefore, all three of the coins are given away, and none are left.

What is full of holes but still holds water?

What word becomes shorter when you add two letters to it, you may also like, what is logical thinking, critical thinking vs creative thinking, divergent vs convergent thinking – what are they and how are they different, critical reading strategies, download this free ebook.

PHIL102: Introduction to Critical Thinking and Logic

Course introduction.

• Time: 40 hours
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The course touches upon a wide range of reasoning skills, from verbal argument analysis to formal logic, visual and statistical reasoning, scientific methodology, and creative thinking. Mastering these skills will help you become a more perceptive reader and listener, a more persuasive writer and presenter, and a more effective researcher and scientist.

The first unit introduces the terrain of critical thinking and covers the basics of meaning analysis, while the second unit provides a primer for analyzing arguments. All of the material in these first units will be built upon in subsequent units, which cover informal and formal logic, Venn diagrams, scientific reasoning, and strategic and creative thinking.

Course Syllabus

First, read the course syllabus. Then, enroll in the course by clicking "Enroll me". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.

Unit 1: Introduction and Meaning Analysis

Critical thinking is a broad classification for a diverse array of reasoning techniques. In general, critical thinking works by breaking arguments and claims down to their basic underlying structure so we can see them clearly and determine whether they are rational. The idea is to help us do a better job of understanding and evaluating what we read, what we hear, and what we write and say.

In this unit, we will define the broad contours of critical thinking and learn why it is a valuable and useful object of study. We will also introduce the fundamentals of meaning analysis: the difference between literal meaning and implication, the principles of definition, how to identify when a disagreement is merely verbal, the distinction between necessary and sufficient conditions, and problems with the imprecision of ordinary language.

Completing this unit should take you approximately 5 hours.

Unit 2: Argument Analysis

Arguments are the fundamental components of all rational discourse: nearly everything we read and write, like scientific reports, newspaper columns, and personal letters, as well as most of our verbal conversations, contain arguments. Picking the arguments out from the rest of our often convoluted discourse can be difficult. Once we have identified an argument, we still need to determine whether or not it is sound. Luckily, arguments obey a set of formal rules that we can use to determine whether they are good or bad.

In this unit, you will learn how to identify arguments, what makes an argument sound as opposed to unsound or merely valid, the difference between deductive and inductive reasoning, and how to map arguments to reveal their structure.

Completing this unit should take you approximately 7 hours.

Unit 3: Basic Sentential Logic

This unit introduces a topic that many students find intimidating: formal logic. Although it sounds difficult and complicated, formal (or symbolic) logic is actually a fairly straightforward way of revealing the structure of reasoning. By translating arguments into symbols, you can more readily see what is right and wrong with them and learn how to formulate better arguments. Advanced courses in formal logic focus on using rules of inference to construct elaborate proofs. Using these techniques, you can solve many complicated problems simply by manipulating symbols on the page. In this course, however, you will only be looking at the most basic properties of a system of logic. In this unit, you will learn how to turn phrases in ordinary language into well-formed formulas, draw truth tables for formulas, and evaluate arguments using those truth tables.

Completing this unit should take you approximately 13 hours.

Unit 4: Venn Diagrams

In addition to using predicate logic, the limitations of sentential logic can also be overcome by using Venn diagrams to illustrate statements and arguments. Statements that include general words like "some" or "few" as well as absolute words like "every" and "all" – so-called categorical statements – lend themselves to being represented on paper as circles that may or may not overlap.

Venn diagrams are especially helpful when dealing with logical arguments called syllogisms. Syllogisms are a special type of three-step argument with two premises and a conclusion, which involve quantifying terms. In this unit, you will learn the basic principles of Venn diagrams, how to use them to represent statements, and how to use them to evaluate arguments.

Completing this unit should take you approximately 6 hours.

Unit 5: Fallacies

Now that you have studied the necessary structure of a good argument and can represent its structure visually, you might think it would be simple to pick out bad arguments. However, identifying bad arguments can be very tricky in practice. Very often, what at first appears to be ironclad reasoning turns out to contain one or more subtle errors.

Fortunately, there are many easily identifiable fallacies (mistakes of reasoning) that you can learn to recognize by their structure or content. In this unit, you will learn about the nature of fallacies, look at a couple of different ways of classifying them, and spend some time dealing with the most common fallacies in detail.

Completing this unit should take you approximately 3 hours.

Unit 6: Scientific Reasoning

Unlike the syllogistic arguments you explored in the last unit, which are a form of deductive argument, scientific reasoning is empirical. This means that it depends on observation and evidence, not logical principles. Although some principles of deductive reasoning do apply in science, such as the principle of contradiction, scientific arguments are often inductive. For this reason, science often deals with confirmation and disconfirmation.

Nonetheless, there are general guidelines about what constitutes good scientific reasoning, and scientists are trained to be critical of their inferences and those of others in the scientific community. In this unit, you will investigate some standard methods of scientific reasoning, some principles of confirmation and disconfirmation, and some techniques for identifying and reasoning about causation.

Completing this unit should take you approximately 4 hours.

Unit 7: Strategic Reasoning and Creativity

While most of this course has focused on the types of reasoning necessary to critique and evaluate existing knowledge or to extend our knowledge following correct procedures and rules, an enormous branch of our reasoning practice runs in the opposite direction. Strategic reasoning, problem-solving, and creative thinking all rely on an ineffable component of novelty supplied by the thinker.

Despite their seemingly mystical nature, problem-solving and creative thinking are best approached by following tried and tested procedures that prompt our cognitive faculties to produce new ideas and solutions by extending our existing knowledge. In this unit, you will investigate problem-solving techniques, representing complex problems visually, making decisions in risky and uncertain scenarios, and creative thinking in general.

Completing this unit should take you approximately 2 hours.

Study Guide

This study guide will help you get ready for the final exam. It discusses the key topics in each unit, walks through the learning outcomes, and lists important vocabulary terms. It is not meant to replace the course materials!

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Certificate Final Exam

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Saylor Direct Credit

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1 Introduction to Critical Thinking

I. what is c ritical t hinking [1].

Critical thinking is the ability to think clearly and rationally about what to do or what to believe.  It includes the ability to engage in reflective and independent thinking. Someone with critical thinking skills is able to do the following:

• Understand the logical connections between ideas.
• Identify, construct, and evaluate arguments.
• Detect inconsistencies and common mistakes in reasoning.
• Solve problems systematically.
• Identify the relevance and importance of ideas.
• Reflect on the justification of one’s own beliefs and values.

Critical thinking is not simply a matter of accumulating information. A person with a good memory and who knows a lot of facts is not necessarily good at critical thinking. Critical thinkers are able to deduce consequences from what they know, make use of information to solve problems, and to seek relevant sources of information to inform themselves.

Critical thinking should not be confused with being argumentative or being critical of other people. Although critical thinking skills can be used in exposing fallacies and bad reasoning, critical thinking can also play an important role in cooperative reasoning and constructive tasks. Critical thinking can help us acquire knowledge, improve our theories, and strengthen arguments. We can also use critical thinking to enhance work processes and improve social institutions.

Some people believe that critical thinking hinders creativity because critical thinking requires following the rules of logic and rationality, whereas creativity might require breaking those rules. This is a misconception. Critical thinking is quite compatible with thinking “out-of-the-box,” challenging consensus views, and pursuing less popular approaches. If anything, critical thinking is an essential part of creativity because we need critical thinking to evaluate and improve our creative ideas.

II. The I mportance of C ritical T hinking

Critical thinking is a domain-general thinking skill. The ability to think clearly and rationally is important whatever we choose to do. If you work in education, research, finance, management or the legal profession, then critical thinking is obviously important. But critical thinking skills are not restricted to a particular subject area. Being able to think well and solve problems systematically is an asset for any career.

Critical thinking is very important in the new knowledge economy.  The global knowledge economy is driven by information and technology. One has to be able to deal with changes quickly and effectively. The new economy places increasing demands on flexible intellectual skills, and the ability to analyze information and integrate diverse sources of knowledge in solving problems. Good critical thinking promotes such thinking skills, and is very important in the fast-changing workplace.

Critical thinking enhances language and presentation skills. Thinking clearly and systematically can improve the way we express our ideas. In learning how to analyze the logical structure of texts, critical thinking also improves comprehension abilities.

Critical thinking promotes creativity. To come up with a creative solution to a problem involves not just having new ideas. It must also be the case that the new ideas being generated are useful and relevant to the task at hand. Critical thinking plays a crucial role in evaluating new ideas, selecting the best ones and modifying them if necessary.

Critical thinking is crucial for self-reflection. In order to live a meaningful life and to structure our lives accordingly, we need to justify and reflect on our values and decisions. Critical thinking provides the tools for this process of self-evaluation.

Good critical thinking is the foundation of science and democracy. 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.

Critical thinking is a   metacognitive skill . What this means is that it is a higher-level cognitive skill that involves thinking about thinking. We have to be aware of the good principles of reasoning, and be reflective about our own reasoning. In addition, we often need to make a conscious effort to improve ourselves, avoid biases, and maintain objectivity. This is notoriously hard to do. We are all able to think but to think well often requires a long period of training. The mastery of critical thinking is similar to the mastery of many other skills. There are three important components: theory, practice, and attitude.

III. Improv ing O ur T hinking S kills

If we want to think correctly, we need to follow the correct rules of reasoning. Knowledge of theory includes knowledge of these rules. These are the basic principles of critical thinking, such as the laws of logic, and the methods of scientific reasoning, etc.

Also, it would be useful to know something about what not to do if we want to reason correctly. This means we should have some basic knowledge of the mistakes that people make. First, this requires some knowledge of typical fallacies. Second, psychologists have discovered persistent biases and limitations in human reasoning. An awareness of these empirical findings will alert us to potential problems.

However, merely knowing the principles that distinguish good and bad reasoning is not enough. We might study in the classroom about how to swim, and learn about the basic theory, such as the fact that one should not breathe underwater. But unless we can apply such theoretical knowledge through constant practice, we might not actually be able to swim.

Similarly, to be good at critical thinking skills it is necessary to internalize the theoretical principles so that we can actually apply them in daily life. There are at least two ways to do this. One is to perform lots of quality exercises. These exercises don’t just include practicing in the classroom or receiving tutorials; they also include engaging in discussions and debates with other people in our daily lives, where the principles of critical thinking can be applied. The second method is to think more deeply about the principles that we have acquired. In the human mind, memory and understanding are acquired through making connections between ideas.

Good critical thinking skills require more than just knowledge and practice. Persistent practice can bring about improvements only if one has the right kind of motivation and attitude. The following attitudes are not uncommon, but they are obstacles to critical thinking:

• I prefer being given the correct answers rather than figuring them out myself.
• I don’t like to think a lot about my decisions as I rely only on gut feelings.
• I don’t usually review the mistakes I have made.
• I don’t like to be criticized.

To improve our thinking we have to recognize the importance of reflecting on the reasons for belief and action. We should also be willing to engage in debate, break old habits, and deal with linguistic complexities and abstract concepts.

The  California Critical Thinking Disposition Inventory  is a psychological test that is used to measure whether people are disposed to think critically. It measures the seven different thinking habits listed below, and it is useful to ask ourselves to what extent they describe the way we think:

• Truth-Seeking—Do you try to understand how things really are? Are you interested in finding out the truth?
• Open-Mindedness—How receptive are you to new ideas, even when you do not intuitively agree with them? Do you give new concepts a fair hearing?
• Analyticity—Do you try to understand the reasons behind things? Do you act impulsively or do you evaluate the pros and cons of your decisions?
• Systematicity—Are you systematic in your thinking? Do you break down a complex problem into parts?
• Confidence in Reasoning—Do you always defer to other people? How confident are you in your own judgment? Do you have reasons for your confidence? Do you have a way to evaluate your own thinking?
• Inquisitiveness—Are you curious about unfamiliar topics and resolving complicated problems? Will you chase down an answer until you find it?
• Maturity of Judgment—Do you jump to conclusions? Do you try to see things from different perspectives? Do you take other people’s experiences into account?

Finally, as mentioned earlier, psychologists have discovered over the years that human reasoning can be easily affected by a variety of cognitive biases. For example, people tend to be over-confident of their abilities and focus too much on evidence that supports their pre-existing opinions. We should be alert to these biases in our attitudes towards our own thinking.

IV. Defining Critical Thinking

There are many different definitions of critical thinking. Here we list some of the well-known ones. You might notice that they all emphasize the importance of clarity and rationality. Here we will look at some well-known definitions in chronological order.

1) Many people trace the importance of critical thinking in education to the early twentieth-century American philosopher John Dewey. But Dewey did not make very extensive use of the term “critical thinking.” Instead, in his book  How We Think (1910), he argued for the importance of what he called “reflective thinking”:

…[when] the ground or basis for a belief is deliberately sought and its adequacy to support the belief examined. This process is called reflective thought; it alone is truly educative in value…

Active, persistent and careful consideration of any belief or supposed form of knowledge in light of the grounds that support it, and the further conclusions to which it tends, constitutes reflective thought.

There is however one passage from How We Think where Dewey explicitly uses the term “critical thinking”:

The essence of critical thinking is suspended judgment; and the essence of this suspense is inquiry to determine the nature of the problem before proceeding to attempts at its solution. This, more than any other thing, transforms mere inference into tested inference, suggested conclusions into proof.

2) The  Watson-Glaser Critical Thinking Appraisal  (1980) is a well-known psychological test of critical thinking ability. The authors of this test define critical thinking as:

…a composite of attitudes, knowledge and skills. This composite includes: (1) attitudes of inquiry that involve an ability to recognize the existence of problems and an acceptance of the general need for evidence in support of what is asserted to be true; (2) knowledge of the nature of valid inferences, abstractions, and generalizations in which the weight or accuracy of different kinds of evidence are logically determined; and (3) skills in employing and applying the above attitudes and knowledge.

3) A very well-known and influential definition of critical thinking comes from philosopher and professor Robert Ennis in his work “A Taxonomy of Critical Thinking Dispositions and Abilities” (1987):

Critical thinking is reasonable reflective thinking that is focused on deciding what to believe or do.

4) The following definition comes from a statement written in 1987 by the philosophers Michael Scriven and Richard Paul for the  National Council for Excellence in Critical Thinking (link), an organization promoting critical thinking in the US:

Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. 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. It entails the examination of those structures or elements of thought implicit in all reasoning: purpose, problem, or question-at-issue, assumptions, concepts, empirical grounding; reasoning leading to conclusions, implications and consequences, objections from alternative viewpoints, and frame of reference.

The following excerpt from Peter A. Facione’s “Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction” (1990) is quoted from a report written for the American Philosophical Association:

We understand critical thinking to be purposeful, self-regulatory judgment which results in interpretation, analysis, evaluation, and inference, as well as explanation of the evidential, conceptual, methodological, criteriological, or contextual considerations upon which that judgment is based. CT is essential as a tool of inquiry. As such, CT is a liberating force in education and a powerful resource in one’s personal and civic life. While not synonymous with good thinking, CT is a pervasive and self-rectifying human phenomenon. The ideal critical thinker is habitually inquisitive, well-informed, trustful of reason, open-minded, flexible, fairminded in evaluation, honest in facing personal biases, prudent in making judgments, willing to reconsider, clear about issues, orderly in complex matters, diligent in seeking relevant information, reasonable in the selection of criteria, focused in inquiry, and persistent in seeking results which are as precise as the subject and the circumstances of inquiry permit. Thus, educating good critical thinkers means working toward this ideal. It combines developing CT skills with nurturing those dispositions which consistently yield useful insights and which are the basis of a rational and democratic society.

V. Two F eatures of C ritical T hinking

A. how not what .

Critical thinking is concerned not with what you believe, but rather how or why you believe it. Most classes, such as those on biology or chemistry, teach you what to believe about a subject matter. In contrast, critical thinking is not particularly interested in what the world is, in fact, like. Rather, critical thinking will teach you how to form beliefs and how to think. It is interested in the type of reasoning you use when you form your beliefs, and concerns itself with whether you have good reasons to believe what you believe. Therefore, this class isn’t a class on the psychology of reasoning, which brings us to the second important feature of critical thinking.

B. Ought N ot Is ( or Normative N ot Descriptive )

There is a difference between normative and descriptive theories. Descriptive theories, such as those provided by physics, provide a picture of how the world factually behaves and operates. In contrast, normative theories, such as those provided by ethics or political philosophy, provide a picture of how the world should be. Rather than ask question such as why something is the way it is, normative theories ask how something should be. In this course, we will be interested in normative theories that govern our thinking and reasoning. Therefore, we will not be interested in how we actually reason, but rather focus on how we ought to reason.

In the introduction to this course we considered a selection task with cards that must be flipped in order to check the validity of a rule. We noted that many people fail to identify all the cards required to check the rule. This is how people do in fact reason (descriptive). We then noted that you must flip over two cards. This is how people ought to reason (normative).

• Section I-IV are taken from http://philosophy.hku.hk/think/ and are in use under the creative commons license. Some modifications have been made to the original content. ↵

Critical Thinking Copyright © 2019 by Brian Kim is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Exploring Logic Problem Worksheets

Incorporating logic puzzle worksheets into your teaching or parenting repertoire is a great way to engage students, exercise their minds, and foster critical thinking skills. Whether you're focusing on math challenges, geometry, or general logical thinking, these puzzles offer a free and enjoyable way for students to practice and improve their problem-solving abilities. So, print some riddles worksheets today, and watch your students' logical thinking skills flourish.

Logic Problem Worksheet Ideas

• Geometry Challenge Quest (Geometry Logic Worksheets): High school students solve geometry puzzles using worksheets. They apply geometric knowledge to crack codes and find hidden treasures.
• Logic Olympics (Logic Puzzle Worksheets for High School): High school students compete in solving challenging puzzles, earning points for correct solutions in a friendly Olympics competition.
• Logical Detective Challenge (Proof Worksheet): Students act as detectives, using proof worksheets to solve a fictional crime by constructing logical proofs based on evidence.
• Building Logical Bridges (Logic Model Worksheet): Students use model worksheets to create flowcharts and decision trees, helping them visualize and understand complex processes.
• Escape Room: The Logic Lab (Logic Puzzles for 5th Graders): 5th graders work together to escape a virtual lab by solving puzzles, deciphering clues, and unlocking locks.
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Whether you prefer to engage in problem-solving activities on paper or through digital interfaces, there's a versatile learning tool for you, from traditional pen-and-paper exercises to interactive worksheet logic puzzles. Printable worksheets are an alternative to hands-on interactive experiences, and they differ from solving a logic problem online in that they make students engage in dynamic, real-time challenges that encourage active critical thinking. Storyboard That is the ideal online platform for crafting a wide range of educational materials, including printable logic puzzles worksheets. Whether you need logic problems for high school students or logic problems 3rd-graders can solve Storyboard That's user-friendly interface and pre-made templates streamline the process. You can also adapt these materials for online use, ensuring accessibility and flexibility. Storyboard That also provides the convenience of creating logic problems worksheets that are not only engaging but also easily printable, making it a versatile tool for educators seeking to enhance critical thinking skills in students of all ages.

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Logic problem worksheets help students develop critical thinking, reasoning, and problem-solving skills. They also improve attention to detail, logical deduction, and the ability to work with complex information.

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Yes, there are various types of logic problems, including grid logic puzzles (e.g., Sudoku), cryptic crosswords, logic grid puzzles, and math logic problems. Each type presents unique challenges for students.

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No, logic problem worksheets can cover a wide range of topics and are not limited to math. They can incorporate language, science, history, and more, depending on the chosen theme or scenario.

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41+ Critical Thinking Examples (Definition + Practices)

Critical thinking is an essential skill in our information-overloaded world, where figuring out what is fact and fiction has become increasingly challenging.

But why is critical thinking essential? Put, critical thinking empowers us to make better decisions, challenge and validate our beliefs and assumptions, and understand and interact with the world more effectively and meaningfully.

Critical thinking is like using your brain's "superpowers" to make smart choices. Whether it's picking the right insurance, deciding what to do in a job, or discussing topics in school, thinking deeply helps a lot. In the next parts, we'll share real-life examples of when this superpower comes in handy and give you some fun exercises to practice it.

Critical Thinking Process Outline

Critical thinking means thinking clearly and fairly without letting personal feelings get in the way. It's like being a detective, trying to solve a mystery by using clues and thinking hard about them.

It isn't always easy to think critically, as it can take a pretty smart person to see some of the questions that aren't being answered in a certain situation. But, we can train our brains to think more like puzzle solvers, which can help develop our critical thinking skills.

Here's what it looks like step by step:

Spotting the Problem: It's like discovering a puzzle to solve. You see that there's something you need to figure out or decide.

Collecting Clues: Now, you need to gather information. Maybe you read about it, watch a video, talk to people, or do some research. It's like getting all the pieces to solve your puzzle.

Breaking It Down: This is where you look at all your clues and try to see how they fit together. You're asking questions like: Why did this happen? What could happen next?

Checking Your Clues: You want to make sure your information is good. This means seeing if what you found out is true and if you can trust where it came from.

Making a Guess: After looking at all your clues, you think about what they mean and come up with an answer. This answer is like your best guess based on what you know.

Explaining Your Thoughts: Now, you tell others how you solved the puzzle. You explain how you thought about it and how you answered. 

Checking Your Work: This is like looking back and seeing if you missed anything. Did you make any mistakes? Did you let any personal feelings get in the way? This step helps make sure your thinking is clear and fair.

And remember, you might sometimes need to go back and redo some steps if you discover something new. If you realize you missed an important clue, you might have to go back and collect more information.

Critical Thinking Methods

Just like doing push-ups or running helps our bodies get stronger, there are special exercises that help our brains think better. These brain workouts push us to think harder, look at things closely, and ask many questions.

It's not always about finding the "right" answer. Instead, it's about the journey of thinking and asking "why" or "how." Doing these exercises often helps us become better thinkers and makes us curious to know more about the world.

Now, let's look at some brain workouts to help us think better:

1. "What If" Scenarios

Imagine crazy things happening, like, "What if there was no internet for a month? What would we do?" These games help us think of new and different ideas.

Pick a hot topic. Argue one side of it and then try arguing the opposite. This makes us see different viewpoints and think deeply about a topic.

3. Analyze Visual Data

Check out charts or pictures with lots of numbers and info but no explanations. What story are they telling? This helps us get better at understanding information just by looking at it.

4. Mind Mapping

Write an idea in the center and then draw lines to related ideas. It's like making a map of your thoughts. This helps us see how everything is connected.

There's lots of mind-mapping software , but it's also nice to do this by hand.

5. Weekly Diary

Every week, write about what happened, the choices you made, and what you learned. Writing helps us think about our actions and how we can do better.

6. Evaluating Information Sources

Collect stories or articles about one topic from newspapers or blogs. Which ones are trustworthy? Which ones might be a little biased? This teaches us to be smart about where we get our info.

There are many resources to help you determine if information sources are factual or not.

7. Socratic Questioning

This way of thinking is called the Socrates Method, named after an old-time thinker from Greece. It's about asking lots of questions to understand a topic. You can do this by yourself or chat with a friend.

Start with a Big Question:

"What does 'success' mean?"

Dive Deeper with More Questions:

"Why do you think of success that way?" "Do TV shows, friends, or family make you think that?" "Does everyone think about success the same way?"

"Can someone be a winner even if they aren't rich or famous?" "Can someone feel like they didn't succeed, even if everyone else thinks they did?"

Look for Real-life Examples:

"Who is someone you think is successful? Why?" "Was there a time you felt like a winner? What happened?"

Think About Other People's Views:

"How might a person from another country think about success?" "Does the idea of success change as we grow up or as our life changes?"

Think About What It Means:

"How does your idea of success shape what you want in life?" "Are there problems with only wanting to be rich or famous?"

Look Back and Think:

"After talking about this, did your idea of success change? How?" "Did you learn something new about what success means?"

8. Six Thinking Hats 

Edward de Bono came up with a cool way to solve problems by thinking in six different ways, like wearing different colored hats. You can do this independently, but it might be more effective in a group so everyone can have a different hat color. Each color has its way of thinking:

White Hat (Facts): Just the facts! Ask, "What do we know? What do we need to find out?"

Red Hat (Feelings): Talk about feelings. Ask, "How do I feel about this?"

Black Hat (Careful Thinking): Be cautious. Ask, "What could go wrong?"

Yellow Hat (Positive Thinking): Look on the bright side. Ask, "What's good about this?"

Green Hat (Creative Thinking): Think of new ideas. Ask, "What's another way to look at this?"

Blue Hat (Planning): Organize the talk. Ask, "What should we do next?"

When using this method with a group:

• Explain all the hats.
• Decide which hat to wear first.
• Make sure everyone switches hats at the same time.
• Finish with the Blue Hat to plan the next steps.

9. SWOT Analysis

SWOT Analysis is like a game plan for businesses to know where they stand and where they should go. "SWOT" stands for Strengths, Weaknesses, Opportunities, and Threats.

There are a lot of SWOT templates out there for how to do this visually, but you can also think it through. It doesn't just apply to businesses but can be a good way to decide if a project you're working on is working.

Strengths: What's working well? Ask, "What are we good at?"

Weaknesses: Where can we do better? Ask, "Where can we improve?"

Opportunities: What good things might come our way? Ask, "What chances can we grab?"

Threats: What challenges might we face? Ask, "What might make things tough for us?"

Steps to do a SWOT Analysis:

• Goal: Decide what you want to find out.
• Research: Learn about your business and the world around it.
• Brainstorm: Get a group and think together. Talk about strengths, weaknesses, opportunities, and threats.
• Pick the Most Important Points: Some things might be more urgent or important than others.
• Make a Plan: Decide what to do based on your SWOT list.
• Check Again Later: Things change, so look at your SWOT again after a while to update it.

Now that you have a few tools for thinking critically, let’s get into some specific examples.

Everyday Examples

Life is a series of decisions. From the moment we wake up, we're faced with choices – some trivial, like choosing a breakfast cereal, and some more significant, like buying a home or confronting an ethical dilemma at work. While it might seem that these decisions are disparate, they all benefit from the application of critical thinking.

10. Deciding to buy something

Imagine you want a new phone. Don't just buy it because the ad looks cool. Think about what you need in a phone. Look up different phones and see what people say about them. Choose the one that's the best deal for what you want.

11. Deciding what is true

There's a lot of news everywhere. Don't believe everything right away. Think about why someone might be telling you this. Check if what you're reading or watching is true. Make up your mind after you've looked into it.

12. Deciding when you’re wrong

Sometimes, friends can have disagreements. Don't just get mad right away. Try to see where they're coming from. Talk about what's going on. Find a way to fix the problem that's fair for everyone.

13. Deciding what to eat

There's always a new diet or exercise that's popular. Don't just follow it because it's trendy. Find out if it's good for you. Ask someone who knows, like a doctor. Make choices that make you feel good and stay healthy.

14. Deciding what to do today

Everyone is busy with school, chores, and hobbies. Make a list of things you need to do. Decide which ones are most important. Plan your day so you can get things done and still have fun.

15. Making Tough Choices

Sometimes, it's hard to know what's right. Think about how each choice will affect you and others. Talk to people you trust about it. Choose what feels right in your heart and is fair to others.

16. Planning for the Future

Big decisions, like where to go to school, can be tricky. Think about what you want in the future. Look at the good and bad of each choice. Talk to people who know about it. Pick what feels best for your dreams and goals.

Job Examples

17. solving problems.

Workers brainstorm ways to fix a machine quickly without making things worse when a machine breaks at a factory.

18. Decision Making

A store manager decides which products to order more of based on what's selling best.

19. Setting Goals

A team leader helps their team decide what tasks are most important to finish this month and which can wait.

20. Evaluating Ideas

At a team meeting, everyone shares ideas for a new project. The group discusses each idea's pros and cons before picking one.

21. Handling Conflict

Two workers disagree on how to do a job. Instead of arguing, they talk calmly, listen to each other, and find a solution they both like.

22. Improving Processes

A cashier thinks of a faster way to ring up items so customers don't have to wait as long.

23. Asking Questions

Before starting a big task, an employee asks for clear instructions and checks if they have the necessary tools.

24. Checking Facts

Before presenting a report, someone double-checks all their information to make sure there are no mistakes.

25. Planning for the Future

A business owner thinks about what might happen in the next few years, like new competitors or changes in what customers want, and makes plans based on those thoughts.

26. Understanding Perspectives

A team is designing a new toy. They think about what kids and parents would both like instead of just what they think is fun.

School Examples

27. researching a topic.

For a history project, a student looks up different sources to understand an event from multiple viewpoints.

28. Debating an Issue

In a class discussion, students pick sides on a topic, like school uniforms, and share reasons to support their views.

29. Evaluating Sources

While writing an essay, a student checks if the information from a website is trustworthy or might be biased.

30. Problem Solving in Math

When stuck on a tricky math problem, a student tries different methods to find the answer instead of giving up.

31. Analyzing Literature

In English class, students discuss why a character in a book made certain choices and what those decisions reveal about them.

32. Testing a Hypothesis

For a science experiment, students guess what will happen and then conduct tests to see if they're right or wrong.

33. Giving Peer Feedback

After reading a classmate's essay, a student offers suggestions for improving it.

34. Questioning Assumptions

In a geography lesson, students consider why certain countries are called "developed" and what that label means.

35. Designing a Study

For a psychology project, students plan an experiment to understand how people's memories work and think of ways to ensure accurate results.

36. Interpreting Data

In a science class, students look at charts and graphs from a study, then discuss what the information tells them and if there are any patterns.

Critical Thinking Puzzles

Not all scenarios will have a single correct answer that can be figured out by thinking critically. Sometimes we have to think critically about ethical choices or moral behaviors. 

Here are some mind games and scenarios you can solve using critical thinking. You can see the solution(s) at the end of the post.

37. The Farmer, Fox, Chicken, and Grain Problem

A farmer is at a riverbank with a fox, a chicken, and a grain bag. He needs to get all three items across the river. However, his boat can only carry himself and one of the three items at a time. 

Here's the challenge:

• If the fox is left alone with the chicken, the fox will eat the chicken.
• If the chicken is left alone with the grain, the chicken will eat the grain.

How can the farmer get all three items across the river without any item being eaten? 

38. The Rope, Jar, and Pebbles Problem

You are in a room with two long ropes hanging from the ceiling. Each rope is just out of arm's reach from the other, so you can't hold onto one rope and reach the other simultaneously. 

Your task is to tie the two rope ends together, but you can't move the position where they hang from the ceiling.

You are given a jar full of pebbles. How do you complete the task?

39. The Two Guards Problem

Imagine there are two doors. One door leads to certain doom, and the other leads to freedom. You don't know which is which.

In front of each door stands a guard. One guard always tells the truth. The other guard always lies. You don't know which guard is which.

You can ask only one question to one of the guards. What question should you ask to find the door that leads to freedom?

40. The Hourglass Problem

You have two hourglasses. One measures 7 minutes when turned over, and the other measures 4 minutes. Using just these hourglasses, how can you time exactly 9 minutes?

41. The Lifeboat Dilemma

Imagine you're on a ship that's sinking. You get on a lifeboat, but it's already too full and might flip over. 

Nearby in the water, five people are struggling: a scientist close to finding a cure for a sickness, an old couple who've been together for a long time, a mom with three kids waiting at home, and a tired teenager who helped save others but is now in danger. 

You can only save one person without making the boat flip. Who would you choose?

42. The Tech Dilemma

You work at a tech company and help make a computer program to help small businesses. You're almost ready to share it with everyone, but you find out there might be a small chance it has a problem that could show users' private info. 

If you decide to fix it, you must wait two more months before sharing it. But your bosses want you to share it now. What would you do?

43. The History Mystery

Dr. Amelia is a history expert. She's studying where a group of people traveled long ago. She reads old letters and documents to learn about it. But she finds some letters that tell a different story than what most people believe. 

If she says this new story is true, it could change what people learn in school and what they think about history. What should she do?

The Role of Bias in Critical Thinking

Have you ever decided you don’t like someone before you even know them? Or maybe someone shared an idea with you that you immediately loved without even knowing all the details. 

This experience is called bias, which occurs when you like or dislike something or someone without a good reason or knowing why. It can also take shape in certain reactions to situations, like a habit or instinct. 

Bias comes from our own experiences, what friends or family tell us, or even things we are born believing. Sometimes, bias can help us stay safe, but other times it stops us from seeing the truth.

Not all bias is bad. Bias can be a mechanism for assessing our potential safety in a new situation. If we are biased to think that anything long, thin, and curled up is a snake, we might assume the rope is something to be afraid of before we know it is just a rope.

While bias might serve us in some situations (like jumping out of the way of an actual snake before we have time to process that we need to be jumping out of the way), it often harms our ability to think critically.

How Bias Gets in the Way of Good Thinking

Selective Perception: We only notice things that match our ideas and ignore the rest. 

It's like only picking red candies from a mixed bowl because you think they taste the best, but they taste the same as every other candy in the bowl. It could also be when we see all the signs that our partner is cheating on us but choose to ignore them because we are happy the way we are (or at least, we think we are).

Agreeing with Yourself: This is called “ confirmation bias ” when we only listen to ideas that match our own and seek, interpret, and remember information in a way that confirms what we already think we know or believe. 

An example is when someone wants to know if it is safe to vaccinate their children but already believes that vaccines are not safe, so they only look for information supporting the idea that vaccines are bad.

Thinking We Know It All: Similar to confirmation bias, this is called “overconfidence bias.” Sometimes we think our ideas are the best and don't listen to others. This can stop us from learning.

Have you ever met someone who you consider a “know it”? Probably, they have a lot of overconfidence bias because while they may know many things accurately, they can’t know everything. Still, if they act like they do, they show overconfidence bias.

There's a weird kind of bias similar to this called the Dunning Kruger Effect, and that is when someone is bad at what they do, but they believe and act like they are the best .

Following the Crowd: This is formally called “groupthink”. It's hard to speak up with a different idea if everyone agrees. But this can lead to mistakes.

An example of this we’ve all likely seen is the cool clique in primary school. There is usually one person that is the head of the group, the “coolest kid in school”, and everyone listens to them and does what they want, even if they don’t think it’s a good idea.

How to Overcome Biases

Here are a few ways to learn to think better, free from our biases (or at least aware of them!).

Know Your Biases: Realize that everyone has biases. If we know about them, we can think better.

Listen to Different People: Talking to different kinds of people can give us new ideas.

Ask Why: Always ask yourself why you believe something. Is it true, or is it just a bias?

Understand Others: Try to think about how others feel. It helps you see things in new ways.

Keep Learning: Always be curious and open to new information.

In today's world, everything changes fast, and there's so much information everywhere. This makes critical thinking super important. It helps us distinguish between what's real and what's made up. It also helps us make good choices. But thinking this way can be tough sometimes because of biases. These are like sneaky thoughts that can trick us. The good news is we can learn to see them and think better.

There are cool tools and ways we've talked about, like the "Socratic Questioning" method and the "Six Thinking Hats." These tools help us get better at thinking. These thinking skills can also help us in school, work, and everyday life.

We’ve also looked at specific scenarios where critical thinking would be helpful, such as deciding what diet to follow and checking facts.

Thinking isn't just a skill—it's a special talent we improve over time. Working on it lets us see things more clearly and understand the world better. So, keep practicing and asking questions! It'll make you a smarter thinker and help you see the world differently.

Critical Thinking Puzzles (Solutions)

The farmer, fox, chicken, and grain problem.

• The farmer first takes the chicken across the river and leaves it on the other side.
• He returns to the original side and takes the fox across the river.
• After leaving the fox on the other side, he returns the chicken to the starting side.
• He leaves the chicken on the starting side and takes the grain bag across the river.
• He leaves the grain with the fox on the other side and returns to get the chicken.
• The farmer takes the chicken across, and now all three items -- the fox, the chicken, and the grain -- are safely on the other side of the river.

The Rope, Jar, and Pebbles Problem

• Take one rope and tie the jar of pebbles to its end.
• Swing the rope with the jar in a pendulum motion.
• While the rope is swinging, grab the other rope and wait.
• As the swinging rope comes back within reach due to its pendulum motion, grab it.
• With both ropes within reach, untie the jar and tie the rope ends together.

The Two Guards Problem

The question is, "What would the other guard say is the door to doom?" Then choose the opposite door.

The Hourglass Problem

• Start both hourglasses. 
• When the 4-minute hourglass runs out, turn it over.
• When the 7-minute hourglass runs out, the 4-minute hourglass will have been running for 3 minutes. Turn the 7-minute hourglass over. 
• When the 4-minute hourglass runs out for the second time (a total of 8 minutes have passed), the 7-minute hourglass will run for 1 minute. Turn the 7-minute hourglass again for 1 minute to empty the hourglass (a total of 9 minutes passed).

The Boat and Weights Problem

Take the cat over first and leave it on the other side. Then, return and take the fish across next. When you get there, take the cat back with you. Leave the cat on the starting side and take the cat food across. Lastly, return to get the cat and bring it to the other side.

The Lifeboat Dilemma

There isn’t one correct answer to this problem. Here are some elements to consider:

• Moral Principles: What values guide your decision? Is it the potential greater good for humanity (the scientist)? What is the value of long-standing love and commitment (the elderly couple)? What is the future of young children who depend on their mothers? Or the selfless bravery of the teenager?
• Future Implications: Consider the future consequences of each choice. Saving the scientist might benefit millions in the future, but what moral message does it send about the value of individual lives?
• Emotional vs. Logical Thinking: While it's essential to engage empathy, it's also crucial not to let emotions cloud judgment entirely. For instance, while the teenager's bravery is commendable, does it make him more deserving of a spot on the boat than the others?
• Acknowledging Uncertainty: The scientist claims to be close to a significant breakthrough, but there's no certainty. How does this uncertainty factor into your decision?
• Personal Bias: Recognize and challenge any personal biases, such as biases towards age, profession, or familial status.

The Tech Dilemma

Again, there isn’t one correct answer to this problem. Here are some elements to consider:

• Evaluate the Risk: How severe is the potential vulnerability? Can it be easily exploited, or would it require significant expertise? Even if the circumstances are rare, what would be the consequences if the vulnerability were exploited?
• Stakeholder Considerations: Different stakeholders will have different priorities. Upper management might prioritize financial projections, the marketing team might be concerned about the product's reputation, and customers might prioritize the security of their data. How do you balance these competing interests?
• Short-Term vs. Long-Term Implications: While launching on time could meet immediate financial goals, consider the potential long-term damage to the company's reputation if the vulnerability is exploited. Would the short-term gains be worth the potential long-term costs?
• Ethical Implications : Beyond the financial and reputational aspects, there's an ethical dimension to consider. Is it right to release a product with a known vulnerability, even if the chances of it being exploited are low?
• Seek External Input: Consulting with cybersecurity experts outside your company might be beneficial. They could provide a more objective risk assessment and potential mitigation strategies.
• Communication: How will you communicate the decision, whatever it may be, both internally to your team and upper management and externally to your customers and potential users?

The History Mystery

Dr. Amelia should take the following steps:

• Verify the Letters: Before making any claims, she should check if the letters are actual and not fake. She can do this by seeing when and where they were written and if they match with other things from that time.
• Get a Second Opinion: It's always good to have someone else look at what you've found. Dr. Amelia could show the letters to other history experts and see their thoughts.
• Research More: Maybe there are more documents or letters out there that support this new story. Dr. Amelia should keep looking to see if she can find more evidence.
• Share the Findings: If Dr. Amelia believes the letters are true after all her checks, she should tell others. This can be through books, talks, or articles.
• Stay Open to Feedback: Some people might agree with Dr. Amelia, and others might not. She should listen to everyone and be ready to learn more or change her mind if new information arises.

Ultimately, Dr. Amelia's job is to find out the truth about history and share it. It's okay if this new truth differs from what people used to believe. History is about learning from the past, no matter the story.

Related posts:

• Experimenter Bias (Definition + Examples)
• Hasty Generalization Fallacy (31 Examples + Similar Names)
• Ad Hoc Fallacy (29 Examples + Other Names)
• Confirmation Bias (Examples + Definition)
• Equivocation Fallacy (26 Examples + Description)

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Critical Thinking Logic Puzzles Puzzle Workbooks for Kids - Updated Each Month!

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The Importance of Logic and Critical Thinking

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"Critical thinking is a desire to seek, patience to doubt, fondness to meditate, slowness to assert, readiness to consider, carefulness to dispose and set in order; and hatred for every kind of imposture." - Francis Bacon (1605)

As parents, we are tasked with instilling a plethora of different values into our children. While some parents in the world choose to instill a lack of values in their kids, those of us that don't want our children growing up to be criminals and various misfits try a bit harder. Values and morality are one piece of the pie. These are important things to mold into a child's mind, but there are also other items in life to focus on as well. It starts with looking both ways to cross the street and either progresses from there, or stops.

If you stopped explaining the world to your children after they learned to cross the street, then perhaps you should stop reading and go back to surfing for funny pictures of cats. I may use some larger words that you might not understand, making you angry and causing you to leave troll-like comments full of bad grammar and moronic thought processes. However, if you looked at the crossing the street issue as I did – as a logical problem with cause and effect and a probable solution – then carry on. You are my target audience.

Or perhaps the opposite is true, as the former are the people that could benefit from letting some critical thinking into their lives. So what exactly is critical thinking? This bit by Linda Elder in a paper on CriticalThinking.org pretty much sums it up:

Through critical thinking, as I understand it, we acquire a means of assessing and upgrading our ability to judge well. It enables us to go into virtually any situation and to figure out the logic of whatever is happening in that situation. It provides a way for us to learn from new experiences through the process of continual self-assessment. Critical thinking, then, enables us to form sound beliefs and judgments, and in doing so, provides us with a basis for a 'rational and reasonable' emotional life. — Inquiry: Critical Thinking Across the Disciplines, Winter, 1996. Vol. XVI, No. 2.

The rationality of the world is what is at risk. Too many people are taken advantage of because of their lack of critical thinking, logic and deductive reasoning. These same people are raising children without these same skills, creating a whole new generation of clueless people.

To wit, a personal tale of deductive reasoning:

Recently I needed a new transmission for the family van. The warranty on the power train covers the transmission up to 100,000 miles. The van has around 68,000 miles on it. Therefore, even the logic-less dimwit could easily figure that the transmission was covered. Well, this was true until the dealership told me that it wasn't, stating that because we didn't get the scheduled transmission service (which is basically a fluid change) at 30,000 and 60,000 miles the warranty was no longer valid. Now, there are many people that would argue this point, but many more that would shrug, panic, and accept the full cost of repairs.

I read the warranty book. I had a receipt that said the fluid was checked at 60,000 but not replaced. A friend on Twitter pointed out the fact that they were using 100,000 mile transmission fluid. So logically, the fluid would not have to be replaced under 100,000 miles if it wasn't needed, right? So why the stipulation that it needed to be replaced at 60,000 and the loose assumption that not doing that would void the warranty? So I asked the warranty guy to show me in the book where the two items are related. Where it explicitly says that if you don't get the service, the transmission isn't covered. There were portions where it said the service was recommended, but never connecting to actual repairs. Finally the warranty guy shrugged, admitted I was right and said the service was covered.

In this case, valid logic equaled truth and a sound argument. I used very simple reasoning and logic to determine that I was being inadvertently screwed. I say "inadvertently" because I truly believe based on their behavior that they were not intentionally trying to screw me. They believed the two items were related, they had had this argument many times before and were not prepared to be questioned. While both the service manager and the warranty guy seemed at least junior college educated, proving my argument to them took longer than it should have between three adults.

However, valid logic does not always guarantee truth or a sound argument. This is where it gets a little funky. Valid logic is when the structure of logic is correct in the way of syntax and semantics rather than truth. Truth comes from deductive reasoning of said logic. For example:

All transmissions are covered parts. All covered parts are free. Therefore, all transmissions are free. This logic is technically valid, and if the premises are true, then of course the conclusion must be true. You can see here however that it's not always true, though in some situations it could be. While the logic is valid, not all transmissions are free, only those covered by the warranty. So based on that, saying all transmissions are free is not sound logic.

To take it one step further:

All Daleks are brown. Some brown things are Cylons . Therefore, some Daleks are Cylons. Sci-fi fan or not, you probably know that this is not true. The basic lesson here is that, while the logic above might seem valid because of the structure of the statement, it takes a further understanding to figure out why it's not necessarily true: That is, based on the first two statements it's possible that some Daleks are Cylons, but it's not logically concludable. That's where deductive reasoning comes on top of the logic. The underlying lesson here is not to immediately assume everything you read or are told is true, something all children need to and should learn.

This is the direct lesson that needs to be passed on to our children: that of not accepting the immediately visible logic. While not all problems are complex enough to require the scientific method, some of them need some deduction to determine if they are true. Take the example above — how many kids would immediately be satisfied with the false conclusion? Sure, it's a bit geeky with the examples, but switch out bears for Daleks and puppies for Cylons. That makes it easier, and takes the actual research out of it (to find out what Daleks and Cylons are respectively) but many people would just accept that in fact some bears are puppies, if presented with this problem in the context of a textbook or word problem.

Maybe I'm being paranoid or thinking too doomsday, whatever, but I think this is an epidemic. Children are becoming lazier and not as self sufficient because their parents have a problem with watching a three year old cry after they tell her to remove her own jeans, or ask her to put away her own toys (yes, organizational logic falls under the main topic). These are the same parents who do their kid's science project while the kid is playing video games. These kids grow up lacking the simple problem solving skills that make navigating life much easier. Remember when you were growing up and you had the plastic stacking toys ? Well, instead of toys for early development like that, parents are just plopping their kids down in front of the television. While there is some educational type programming on television, it's just not the same as hands-on experience.

My father is an engineer, and he taught me logic and reasoning by making me solve simple, then complex, problems on my own. Or at least giving me the opportunity to solve them on my own. This helped develop critical thinking and problem solving skills, something a lot of children lack these days. Too often I see children that are not allowed to solve problems on their own; instead their parents simply do it for them without argument or discussion. Hell, I am surrounded by adults every day that are unable to solve simple problems, instead choosing to immediately ask me at which point I have to fill the role that their parents never did and – knowing the solution – tell them to solve it themselves, or at least try first.

One of the things I like to work on with my kids is math. There is nothing that teaches deductive reasoning and logic better than math word problems. They are at the age where basic algebra can come into play, which sharpens their reasoning skills because they start to view real world issues with algebraic solutions. Another thing is logic puzzles , crossword puzzles and first person shooters. Actually, not that last one. That's just the reward.

Since I weeded out the folks that don't teach their kids logic in the first two paragraphs, as representatives of the real world it's up to the rest of us to spread the knowledge. It won't be easy. The best thing we can do is teach these thought processes to our children, so that they may look at other children with looks of bewilderment when other children are unable to solve simple tasks. Hopefully, they will not simply do the task for them, but teach them to think. I'm not saying we need to build a whole new generation of project managers and analysts, but it would be better than a generation of task-oriented mindless office drones with untied shoelaces, shoving on a door at the Midvale School for the Gifted .

h/t to @aubreygirl22 for the logical conversation. Image: Flickr user William Notowidagdo. Used under Creative Commons License.

Critical thinking definition

Critical thinking, as described by Oxford Languages, is the objective analysis and evaluation of an issue in order to form a judgement.

Active and skillful approach, evaluation, assessment, synthesis, and/or evaluation of information obtained from, or made by, observation, knowledge, reflection, acumen or conversation, as a guide to belief and action, requires the critical thinking process, which is why it's often used in education and academics.

Some even may view it as a backbone of modern thought.

However, it's a skill, and skills must be trained and encouraged to be used at its full potential.

People turn up to various approaches in improving their critical thinking, like:

• Developing technical and problem-solving skills
• Engaging in more active listening
• Actively questioning their assumptions and beliefs
• Seeking out more diversity of thought
• Opening up their curiosity in an intellectual way etc.

Is critical thinking useful in writing?

Critical thinking can help in planning your paper and making it more concise, but it's not obvious at first. We carefully pinpointed some the questions you should ask yourself when boosting critical thinking in writing:

• What information should be included?
• Which information resources should the author look to?
• What degree of technical knowledge should the report assume its audience has?
• What is the most effective way to show information?
• How should the report be organized?
• How should it be designed?
• What tone and level of language difficulty should the document have?

Usage of critical thinking comes down not only to the outline of your paper, it also begs the question: How can we use critical thinking solving problems in our writing's topic?

Let's say, you have a Powerpoint on how critical thinking can reduce poverty in the United States. You'll primarily have to define critical thinking for the viewers, as well as use a lot of critical thinking questions and synonyms to get them to be familiar with your methods and start the thinking process behind it.

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The Logic Tree: The Ultimate Critical Thinking Framework

Critical Thinking: Problem-Solving

Problem-solving is a central business skill, and yet it's the one many people struggle with most. This course will show you how to apply critical thinking techniques to common business examples, avoid misunderstandings, and get at the root of any problem.

Logical thinking is the most valuable asset any business professional can have. That's why logic trees are such a valuable tool—they can help you identify a problem, break it down, and build it back up to a solution.

MECE Principle

Using the MECE principle can help ensure you categorize without gaps or overlaps. Check out this course from GLOBIS Unlimited for a practical demonstration of how it works!

If you work in business—any aspect of a business, from R&D to sales to back-office data entry—you’ve probably experienced an unpleasant surprise or two. Not every marketing campaign boosts sales the way we want. Not every event has the turnout we hope for. Not every promotion we expect comes our way.

Particularly with problems that have fiscal casualties, you’ll want to do a little analysis and find out what happened. And one of the absolute best tools to apply to your analysis is critical thinking.

Critical thinking applies logic to solve problems systematically. According to the World Economic Forum’s “Future of Jobs Report” in 2020, “The top skills . . . which employers see as rising in prominence in the lead up to 2025 include . . . critical thinking and analysis, as well as problem-solving.”

And 2020 wasn’t the first year critical thinking made the list.

When it comes to problem-solving, logic trees are a go-to critical thinking framework. Done right, they’ll get you to the root of a problem (pun intended) and even help you find solutions.

What is a logic tree?

A logic tree takes a complex problem and breaks it up systematically, drilling down into smaller, more manageable components. If you’ve seen an image like this, you’ve seen a logic tree:

Looks pretty simple, right? It is! But there are some important rules to follow to make sure your logic tree grows up big and strong—and, more importantly, leads you to the answers you seek.

The Logic Tree and the Case of the Missing Sandwich

Logic trees are often used for complex issues, which is why they’re also called “issue trees” or “decision trees.” But consider a simple (though still frustrating) problem faced by many office workers in the days before COVID-19 . . .

It’s lunchtime at your workplace, so you head to the office fridge—only to find your lunch is gone. You stare in disbelief at the empty space where your sandwich should be. A mocking smudge of condensation stares back.

As you are a logical person (not prone to throwing tantrums), you decide to approach this problem with critical thinking . You march back to your desk, grab a pen and paper, and write down four words: “Who took my sandwich?”

You’ve planted your logic tree.

Decide what you really need to know.

Before you jump into the branches, remind yourself that logic trees stem from problems—but knee-jerk responses often misidentify problems. So once you’ve got your initial question down, take a step back. Is there a branch that should have come before the first one you made?

Setting aside the sandwich problem for just a moment, consider you’re exploring a different issue: “How can I get promoted?” Think about the reason you’re asking that question. What’s the actual problem you need to solve?

Maybe you should have asked, “How can I earn more money?” That opens far more possibilities than just getting promoted—you could look for another job, start a side business, or invest in your buddy’s startup. “How can I get promoted?” becomes just one branch on a bigger tree.

This is how logic trees (and critical thinking in general) not only help you identify solutions, but think outside the box —innovate.

Beware emotional bias in the branches.

You decide to start your logic tree with “Who took my sandwich?” From that root problem, you might break up the question into its seemingly logical components: “someone inside the office ate my sandwich” (Mary Anne, maybe? Or Phil?) and “someone came in off the street and stole it” (a hungry ninja, perhaps?).

Already, your logic tree is telling you something important.

The fact that you’ve defined the first two branches of your logic tree as “culprit here or there” means you’re sure there’s a thief in your midst. You’ve (perhaps subconsciously) ruled out the possibility that you forgot your sandwich at home or left it on the bus. The logic tree you’ve started will also not remind you if you didn’t make a lunch at all today because you’ll be eating out with Mary Anne and Phil.

Logic trees will only tell you what you ask them to tell you. They can only answer the questions you lay down. Don’t let your emotions limit the possibilities. Try to be aware of the assumptions you’re baking in.

Next Article

3 Ways the MECE Principle Makes Data Organization Easy

Apply MECE to the branches of your logic tree.

Now that you’ve got your first two branches, you set to work breaking them down further. This is a good time to remember to follow the MECE principle . MECE stands for “mutually exclusive, collectively exhaustive.” In other words, it means you want to build the branches of your logic tree without gaps or duplicates.

Remember, logic trees are a critical thinking tool, and critical thinking is about systematic problem-solving. The MECE component of logic trees helps keep the system clean by eliminating possibilities, which increases efficiency toward finding an answer.

For example, if one branch says, “Someone in the office took my sandwich” and another says, “Someone on this floor took my sandwich,” you’re setting yourself up for some overlap. (Surely, this floor is in the office, no?)

It seems unlikely that someone came in off the street and took your sandwich, so you focus on the other possibility: an inside job. That leads to two new MECE-friendly branches: someone from your team, or someone from another team? Then more branches under those: Someone who decided your lunch looked way more delicious than their own, or someone who innocently mistook your lunch for theirs?

Aha! Looking at the breakdown, the answer strikes you. You bought that sandwich from Sandwich Heaven—the same place your teammate Rick sometimes buys his lunch. You check the fridge again, and sure enough, there’s another sandwich almost identical to yours (except this one has tomato, gross).

Don’t expect logic trees to end with “the answer.”

Logic trees aren’t about quick fixes. They’re about training your mind to reach reliable solutions.

While you may be tempted to rush off and have a chat with Rick about stealing your sandwich, it’ll serve you much better to reflect on why he took your sandwich in the first place. You and Rick bought sandwiches from the same shop, which makes it easy to mix them up. That may be the answer—but is it a solution ?

At the end of your logic tree, pose some further questions: Should you and Rick decide to put your sandwiches on different shelves in the fridge? Should you make it a point to label yours with your name? Or should you stop going to Sandwich Heaven every day?

This follow-up is important, even for logic trees targeting more serious issues. If you’re trying to determine why sales are down, perhaps your logic tree will reveal you’re targeting the wrong customers. In that case, what steps can you take to reset your targets?

The Payoff of Learning Logic Trees

While they might sound like a lot of work (and yes, they can be a bit overwhelming at first), logic trees can actually save you a lot of time once you get the hang of them. Even better, you don’t have to slave away at mastering them on your own. There’s no reason a logic tree needs to be a solitary activity (even if you’re hunting down a sandwich thief).

In fact, if you’re working on a critical business issue, you really shouldn’t try to go it alone. Ask your boss, your team, a consultant, or another colleague to review your work. They don’t even have to understand the problem in depth—the point is to get a fresh pair of eyes on your logic tree and, by extension, your problem.

Finally, keep in mind that there’s no guarantee a logic tree will bring you to the perfect answer. What they will do is train your critical thinking skills and help widen your view of the problems you face.

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