critical thinking and inference

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TIP Sheet INFERENCES

We all make inferences; that is, we draw conclusions by using information to create new information. When you make an inference, you connect the dots from the known to the unknown, from the stated to the unstated. An inference is a logical conclusion based on an analysis of objects, sensations, events, facts, and ideas that seems likely in light of what is known. We can reach factual, that is, verifiable, inferences from factual information. For example, given the following facts, the conclusions are logical:

Fact: A lion can run 50 miles per hour. Fact: A cheetah can run faster than a lion. Conclusion: A cheetah can run faster than 50 miles per hour.

We reach non-factual inferences based on non-factual, even non-verbal, information, such as facial express and body language.

Active reading, listening, and note taking require us to make inferences, which are partly based on information the author or speaker has not supplied. To improve our ability to make valid inferences, it helps to understand the following:

our background knowledge affects our inferences our assumptions affect our inferences we draw inferences even from implied facts, implications connotation creates implications

Background knowledge College textbook authors expect you to have a certain amount of background knowledge–knowledge about people, history, arts, sciences, mathematics, and current events, for example–to draw meaningful inferences as you read. Students whose prior reading and breadth of experience have been limited find it more difficult to use textbooks and classroom instruction to reach valid conclusions. We acquire our background knowledge by reading, talking to people, traveling, watching the news, learning job skills–in fact, everything we have seen and done contributes to our background knowledge.

Inferences are everyday events. Suppose early one Friday morning you see your neighbor load a suitcase into his car. You infer he is going on a trip, and not a long one, either, with just that one suitcase. Later, at 11:30 a.m., you notice it has started to rain. You infer that the noon school picnic will be canceled. In each case, you do not know for sure, but your conclusion is based on what you observe and on your background knowledge. Depending on what facts you know, you could draw other inferences. For example, if you know the picnic area is covered, you may infer that the picnic will take place as planned despite the rain. Likewise, there may be another explanation for the suitcase-perhaps your neighbor is taking it out to be repaired. Maybe he has decided to use it to store his jumper cables and flashlight. Regardless, your inference at least is logical in light of what you do know.

Assumptions It is an important part of developing critical thinking skills to distinguish our inferences, or conclusions, both from the raw facts and from our assumptions. Assumptions are the unstated and frequently unexamined beliefs we take for granted–that we ourselves, and most other people we know, will not gladly picnic on wet grass, for example. But it is possible for someone, somewhere, to hold a different view–that picnicking in the rain is quirky and fun. A frequent reason for disagreements between people who hold different opinions is that the people began with different assumptions.

For example, suppose Phong assumes that a capitalistic market society strengthens a democracy and leads to innovative solutions to social problems. He brings that underlying belief to bear on everyday matters, such as the price of textbooks in the student bookstore. Phong does not complain about the high price of his textbooks because he feels (a little vaguely, perhaps) it would be un-American; instead, he cheerfully cancels his cable subscription and puts the money he saves toward purchasing books. On the other hand, Karla assumes that capitalism weakens America, quashing innovation and impoverishing the greater part of society for the benefit of a rich and powerful few. Karla buys her textbooks because she must, but she is bitter and feels that the textbook producers are not acting like real Americans–in fact, she suspects they are not Americans at all, but some kind of supra-national cabal systematically preying on students and the intelligentsia. (See the TIP Sheet " Conspiracy Theories .")

Their different assumptions about the value of capitalism and what it means to be a "real" American lead Phong and Karla to different conclusions. Phong and Karla may have examined their assumptions and consciously affirmed them, but it's far likelier they have not. Therefore, neither Phong nor Karla can understand the other's attitude about buying textbooks: Why is he so passive, fumes Karla. Why is she so angry, wonders Phong. Their misunderstanding will probably continue until they realize they have different assumptions and discuss that.

Implications Not all inferences are based on facts. We often make inferences based on a best guess or on implications. When a statement is only suggested or hinted at, it is an implication . We draw inferences and reach conclusions from implications just as we do from direct statements. The problem with drawing conclusions from implications is that the language of implications is slippery, sometimes intentionally so.

This can lead to shaky conclusions. Political mud-slinging is often based on implications constructed using misleading language that, in a pinch, can be disavowed ("I never said that!"). It is especially important to examine any inference based on implication; it may well be faulty, since the authors of implications tend to be selective about which facts to include and often use language chosen for "loaded" connotations.

(See the TIP Sheet " Deductive, Inductive, & Abductive Reasoning " for more information on "best guess" reasoning.)

Connotations One of the reasons we can make implications is that words have connotation . Denotation is the dictionary meaning of a word. Connotation is its "color" or emotional feel. Some words have negative connotations, some positive. Would you rather be called sensitive or touchy ? Liberal or progressive? Religious or spiritual ? We interpret connotation unconsciously, making inferences about both the author and material based partly on the "color" of the words.

Connotation is largely cultural. Students new to English, or students who lack background knowledge, often find it difficult to accurately sense connotations. Students whose range of vocabulary is limited also have a more difficult time "reading" connotation. Connotation can also vary among groups within a society. For example, to Karla's group, above, the word profit carried negative connotations, and to Phong's group, positive. (This is why, in polarized political issues for example, the statements of one group can sound so nonsensical–or even sinister-to the other group: the connotations of political messages are "colored" for particular audiences.)

Your awareness of these factors that enable–or constrain–your ability to draw valid inferences can help you begin to read beyond the words. The result will be greater empathy for the ideas of others and greater comprehension of complex topics.

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Reading & Writing Purposes

Introduction: critical thinking, reading, & writing, critical thinking.

The phrase “critical thinking” is often misunderstood. “Critical” in this case does not mean finding fault with an action or idea. Instead, it refers to the ability to understand an action or idea through reasoning. According to the website SkillsYouNeed [1]:

Critical thinking might be described as the ability to engage in reflective and independent thinking.

In essence, critical thinking requires you to use your ability to reason. It is about being an active learner rather than a passive recipient of information.

Critical thinkers rigorously question ideas and assumptions rather than accepting them at face value. They will always seek to determine whether the ideas, arguments, and findings represent the entire picture and are open to finding that they do not.

Critical thinkers will identify, analyze, and solve problems systematically rather than by intuition or instinct.

Someone with critical thinking skills can:

• Understand the links between ideas.
• Determine the importance and relevance of arguments and ideas.
• Recognize, build, and appraise arguments.
• Identify inconsistencies and errors in reasoning.
• Approach problems in a consistent and systematic way.
• Reflect on the justification of their own assumptions, beliefs and values.

Read more at:  https://www.skillsyouneed.com/learn/critical-thinking.html

Critical thinking—the ability to develop your own insights and meaning—is a basic college learning goal. Critical reading and writing strategies foster critical thinking, and critical thinking underlies critical reading and writing.

Critical Reading

Critical reading builds on the basic reading skills expected for college.

College Readers’ Characteristics

• College readers are willing to spend time reflecting on the ideas presented in their reading assignments. They know the time is well-spent to enhance their understanding.
• College readers are able to raise questions while reading. They evaluate and solve problems rather than merely compile a set of facts to be memorized.
• College readers can think logically. They are fact-oriented and can review the facts dispassionately. They base their judgments on ideas and evidence.
• College readers can recognize error in thought and persuasion as well as recognize good arguments.
• College readers are skeptical. They understand that not everything in print is correct. They are diligent in seeking out the truth.

Critical Readers’ Characteristics

• Critical readers are open-minded. They seek alternative views and are open to new ideas that may not necessarily agree with their previous thoughts on a topic. They are willing to reassess their views when new or discordant evidence is introduced and evaluated.
• Critical readers are in touch with their own personal thoughts and ideas about a topic. Excited about learning, they are eager to express their thoughts and opinions.
• Critical readers are able to identify arguments and issues. They are able to ask penetrating and thought-provoking questions to evaluate ideas.
• Critical readers are creative. They see connections between topics and use knowledge from other disciplines to enhance their reading and learning experiences.
• Critical readers develop their own ideas on issues, based on careful analysis and response to others’ ideas.

The video below, although geared toward students studying for the SAT exam (Scholastic Aptitude Test used for many colleges’ admissions), offers a good, quick overview of the concept and practice of critical reading.

Critical Reading & Writing

College reading and writing assignments often ask you to react to, apply, analyze, and synthesize information. In other words, your own informed and reasoned ideas about a subject take on more importance than someone else’s ideas, since the purpose of college reading and writing is to think critically about information.

Critical thinking involves questioning. You ask and answer questions to pursue the “careful and exact evaluation and judgment” that the word “critical” invokes (definition from The American Heritage Dictionary ). The questions simply change depending on your critical purpose. Different critical purposes are detailed in the next pages of this text.

However, here’s a brief preview of the different types of questions you’ll ask and answer in relation to different critical reading and writing purposes.

When you react to a text you ask:

• “What do I think?” and
• “Why do I think this way?”

e.g., If I asked and answered these “reaction” questions about the topic assimilation of immigrants to the U.S. , I might create the following main idea statement, which I could then develop in an essay:  I think that assimilation has both positive and negative effects because, while it makes life easier within the dominant culture, it also implies that the original culture is of lesser value.

When you apply text information you ask:

• “How does this information relate to the real world?”

e.g., If I asked and answered this “application” question about the topic assimilation , I might create the following main idea statement, which I could then develop in an essay:  During the past ten years, a group of recent emigrants has assimilated into the local culture; the process of their assimilation followed certain specific stages.

When you analyze text information you ask:

• “What is the main idea?”
• “What do I want to ‘test’ in the text to see if the main idea is justified?” (supporting ideas, type of information, language), and
• “What pieces of the text relate to my ‘test?'”

e.g., If I asked and answered these “analysis” questions about the topic immigrants to the United States , I might create the following main idea statement, which I could then develop in an essay: Although Lee (2009) states that “segmented assimilation theory asserts that immigrant groups may assimilate into one of many social sectors available in American society, instead of restricting all immigrant groups to adapting into one uniform host society,” other theorists have shown this not to be the case with recent immigrants in certain geographic areas.

When you synthesize information from many texts you ask:

• “What information is similar and different in these texts?,” and
• “What pieces of information fit together to create or support a main idea?”

e.g., If I asked and answered these “synthesis” questions about the topic immigrants to the U.S. , I might create the following main idea statement, which I could then develop by using examples and information from many text articles as evidence to support my idea: Immigrants who came to the United States during the immigration waves in the early to mid 20th century traditionally learned English as the first step toward assimilation, a process that was supported by educators. Now, both immigrant groups and educators are more focused on cultural pluralism than assimilation, as can be seen in educators’ support of bilingual education. However, although bilingual education heightens the child’s reasoning and ability to learn, it may ultimately hinder the child’s sense of security within the dominant culture if that culture does not value cultural pluralism as a whole.

Critical reading involves asking and answering these types of questions in order to find out how the information “works” as opposed to just accepting and presenting the information that you read in a text. Critical writing involves recording your insights into these questions and offering your own interpretation of a concept or issue, based on the meaning you create from those insights.

• Crtical Thinking, Reading, & Writing. Authored by : Susan Oaks, includes material adapted from TheSkillsYouNeed and Reading 100; attributions below. Project : Introduction to College Reading & Writing. License : CC BY-NC: Attribution-NonCommercial
• Critical Thinking. Provided by : TheSkillsYouNeed. Located at : https://www.skillsyouneed.com/ . License : Public Domain: No Known Copyright . License Terms : Quoted from website: The use of material found at skillsyouneed.com is free provided that copyright is acknowledged and a reference or link is included to the page/s where the information was found. Read more at: https://www.skillsyouneed.com/
• The Reading Process. Authored by : Scottsdale Community College Reading Faculty. Provided by : Maricopa Community College. Located at : https://learn.maricopa.edu/courses/904536/files/32966438?module_item_id=7198326 . Project : Reading 100. License : CC BY: Attribution
• image of person thinking with light bulbs saying -idea- around her head. Authored by : Gerd Altmann. Provided by : Pixabay. Located at : https://pixabay.com/photos/light-bulb-idea-think-education-3704027/ . License : CC0: No Rights Reserved
• video What is Critical Reading? SAT Critical Reading Bootcamp #4. Provided by : Reason Prep. Located at : https://www.youtube.com/watch?v=5Hc3hmwnymw . License : Other . License Terms : YouTube video
• image of man smiling and holding a lightbulb. Authored by : africaniscool. Provided by : Pixabay. Located at : https://pixabay.com/photos/man-african-laughing-idea-319282/ . License : CC0: No Rights Reserved

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• What Is Critical Thinking? | Definition & Examples

What Is Critical Thinking? | Definition & Examples

Published on May 30, 2022 by Eoghan Ryan . Revised on May 31, 2023.

Critical thinking is the ability to effectively analyze information and form a judgment .

To think critically, you must be aware of your own biases and assumptions when encountering information, and apply consistent standards when evaluating sources .

Critical thinking skills help you to:

• Identify credible sources
• Evaluate and respond to arguments
• Assess alternative viewpoints
• Test hypotheses against relevant criteria

Table of contents

Why is critical thinking important, critical thinking examples, how to think critically, other interesting articles, frequently asked questions about critical thinking.

Critical thinking is important for making judgments about sources of information and forming your own arguments. It emphasizes a rational, objective, and self-aware approach that can help you to identify credible sources and strengthen your conclusions.

Critical thinking is important in all disciplines and throughout all stages of the research process . The types of evidence used in the sciences and in the humanities may differ, but critical thinking skills are relevant to both.

In academic writing , critical thinking can help you to determine whether a source:

• Is free from research bias
• Provides evidence to support its research findings
• Considers alternative viewpoints

Outside of academia, critical thinking goes hand in hand with information literacy to help you form opinions rationally and engage independently and critically with popular media.

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Critical thinking can help you to identify reliable sources of information that you can cite in your research paper . It can also guide your own research methods and inform your own arguments.

Outside of academia, critical thinking can help you to be aware of both your own and others’ biases and assumptions.

Academic examples

However, when you compare the findings of the study with other current research, you determine that the results seem improbable. You analyze the paper again, consulting the sources it cites.

You notice that the research was funded by the pharmaceutical company that created the treatment. Because of this, you view its results skeptically and determine that more independent research is necessary to confirm or refute them. Example: Poor critical thinking in an academic context You’re researching a paper on the impact wireless technology has had on developing countries that previously did not have large-scale communications infrastructure. You read an article that seems to confirm your hypothesis: the impact is mainly positive. Rather than evaluating the research methodology, you accept the findings uncritically.

Nonacademic examples

However, you decide to compare this review article with consumer reviews on a different site. You find that these reviews are not as positive. Some customers have had problems installing the alarm, and some have noted that it activates for no apparent reason.

You revisit the original review article. You notice that the words “sponsored content” appear in small print under the article title. Based on this, you conclude that the review is advertising and is therefore not an unbiased source. Example: Poor critical thinking in a nonacademic context You support a candidate in an upcoming election. You visit an online news site affiliated with their political party and read an article that criticizes their opponent. The article claims that the opponent is inexperienced in politics. You accept this without evidence, because it fits your preconceptions about the opponent.

There is no single way to think critically. How you engage with information will depend on the type of source you’re using and the information you need.

However, you can engage with sources in a systematic and critical way by asking certain questions when you encounter information. Like the CRAAP test , these questions focus on the currency , relevance , authority , accuracy , and purpose of a source of information.

When encountering information, ask:

• Who is the author? Are they an expert in their field?
• What do they say? Is their argument clear? Can you summarize it?
• When did they say this? Is the source current?
• Where is the information published? Is it an academic article? Is it peer-reviewed ?
• Why did the author publish it? What is their motivation?
• How do they make their argument? Is it backed up by evidence? Does it rely on opinion, speculation, or appeals to emotion ? Do they address alternative arguments?

Critical thinking also involves being aware of your own biases, not only those of others. When you make an argument or draw your own conclusions, you can ask similar questions about your own writing:

• Am I only considering evidence that supports my preconceptions?
• Is my argument expressed clearly and backed up with credible sources?
• Would I be convinced by this argument coming from someone else?

If you want to know more about ChatGPT, AI tools , citation , and plagiarism , make sure to check out some of our other articles with explanations and examples.

• ChatGPT vs human editor
• ChatGPT citations
• Is ChatGPT trustworthy?
• Using ChatGPT for your studies
• What is ChatGPT?
• Chicago style
• Paraphrasing

 Plagiarism

• Types of plagiarism
• Self-plagiarism
• Avoiding plagiarism
• Academic integrity
• Consequences of plagiarism
• Common knowledge

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Critical thinking refers to the ability to evaluate information and to be aware of biases or assumptions, including your own.

Like information literacy , it involves evaluating arguments, identifying and solving problems in an objective and systematic way, and clearly communicating your ideas.

Critical thinking skills include the ability to:

You can assess information and arguments critically by asking certain questions about the source. You can use the CRAAP test , focusing on the currency , relevance , authority , accuracy , and purpose of a source of information.

Ask questions such as:

• Who is the author? Are they an expert?
• How do they make their argument? Is it backed up by evidence?

A credible source should pass the CRAAP test  and follow these guidelines:

• The information should be up to date and current.
• The author and publication should be a trusted authority on the subject you are researching.
• The sources the author cited should be easy to find, clear, and unbiased.
• For a web source, the URL and layout should signify that it is trustworthy.

Information literacy refers to a broad range of skills, including the ability to find, evaluate, and use sources of information effectively.

Being information literate means that you:

• Know how to find credible sources
• Use relevant sources to inform your research
• Understand what constitutes plagiarism
• Know how to cite your sources correctly

Confirmation bias is the tendency to search, interpret, and recall information in a way that aligns with our pre-existing values, opinions, or beliefs. It refers to the ability to recollect information best when it amplifies what we already believe. Relatedly, we tend to forget information that contradicts our opinions.

Although selective recall is a component of confirmation bias, it should not be confused with recall bias.

On the other hand, recall bias refers to the differences in the ability between study participants to recall past events when self-reporting is used. This difference in accuracy or completeness of recollection is not related to beliefs or opinions. Rather, recall bias relates to other factors, such as the length of the recall period, age, and the characteristics of the disease under investigation.

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Critical Thinking

Critical thinking is a widely accepted educational goal. Its definition is contested, but the competing definitions can be understood as differing conceptions of the same basic concept: careful thinking directed to a goal. Conceptions differ with respect to the scope of such thinking, the type of goal, the criteria and norms for thinking carefully, and the thinking components on which they focus. Its adoption as an educational goal has been recommended on the basis of respect for students’ autonomy and preparing students for success in life and for democratic citizenship. “Critical thinkers” have the dispositions and abilities that lead them to think critically when appropriate. The abilities can be identified directly; the dispositions indirectly, by considering what factors contribute to or impede exercise of the abilities. Standardized tests have been developed to assess the degree to which a person possesses such dispositions and abilities. Educational intervention has been shown experimentally to improve them, particularly when it includes dialogue, anchored instruction, and mentoring. Controversies have arisen over the generalizability of critical thinking across domains, over alleged bias in critical thinking theories and instruction, and over the relationship of critical thinking to other types of thinking.

2.1 Dewey’s Three Main Examples

2.2 dewey’s other examples, 2.3 further examples, 2.4 non-examples, 3. the definition of critical thinking, 4. its value, 5. the process of thinking critically, 6. components of the process, 7. contributory dispositions and abilities, 8.1 initiating dispositions, 8.2 internal dispositions, 9. critical thinking abilities, 10. required knowledge, 11. educational methods, 12.1 the generalizability of critical thinking, 12.2 bias in critical thinking theory and pedagogy, 12.3 relationship of critical thinking to other types of thinking, other internet resources, related entries.

Use of the term ‘critical thinking’ to describe an educational goal goes back to the American philosopher John Dewey (1910), who more commonly called it ‘reflective thinking’. He defined it as

active, persistent and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it, and the further conclusions to which it tends. (Dewey 1910: 6; 1933: 9)

and identified a habit of such consideration with a scientific attitude of mind. His lengthy quotations of Francis Bacon, John Locke, and John Stuart Mill indicate that he was not the first person to propose development of a scientific attitude of mind as an educational goal.

In the 1930s, many of the schools that participated in the Eight-Year Study of the Progressive Education Association (Aikin 1942) adopted critical thinking as an educational goal, for whose achievement the study’s Evaluation Staff developed tests (Smith, Tyler, & Evaluation Staff 1942). Glaser (1941) showed experimentally that it was possible to improve the critical thinking of high school students. Bloom’s influential taxonomy of cognitive educational objectives (Bloom et al. 1956) incorporated critical thinking abilities. Ennis (1962) proposed 12 aspects of critical thinking as a basis for research on the teaching and evaluation of critical thinking ability.

Since 1980, an annual international conference in California on critical thinking and educational reform has attracted tens of thousands of educators from all levels of education and from many parts of the world. Also since 1980, the state university system in California has required all undergraduate students to take a critical thinking course. Since 1983, the Association for Informal Logic and Critical Thinking has sponsored sessions in conjunction with the divisional meetings of the American Philosophical Association (APA). In 1987, the APA’s Committee on Pre-College Philosophy commissioned a consensus statement on critical thinking for purposes of educational assessment and instruction (Facione 1990a). Researchers have developed standardized tests of critical thinking abilities and dispositions; for details, see the Supplement on Assessment . Educational jurisdictions around the world now include critical thinking in guidelines for curriculum and assessment.

For details on this history, see the Supplement on History .

2. Examples and Non-Examples

Before considering the definition of critical thinking, it will be helpful to have in mind some examples of critical thinking, as well as some examples of kinds of thinking that would apparently not count as critical thinking.

Dewey (1910: 68–71; 1933: 91–94) takes as paradigms of reflective thinking three class papers of students in which they describe their thinking. The examples range from the everyday to the scientific.

Transit : “The other day, when I was down town on 16th Street, a clock caught my eye. I saw that the hands pointed to 12:20. This suggested that I had an engagement at 124th Street, at one o’clock. I reasoned that as it had taken me an hour to come down on a surface car, I should probably be twenty minutes late if I returned the same way. I might save twenty minutes by a subway express. But was there a station near? If not, I might lose more than twenty minutes in looking for one. Then I thought of the elevated, and I saw there was such a line within two blocks. But where was the station? If it were several blocks above or below the street I was on, I should lose time instead of gaining it. My mind went back to the subway express as quicker than the elevated; furthermore, I remembered that it went nearer than the elevated to the part of 124th Street I wished to reach, so that time would be saved at the end of the journey. I concluded in favor of the subway, and reached my destination by one o’clock.” (Dewey 1910: 68–69; 1933: 91–92)

Ferryboat : “Projecting nearly horizontally from the upper deck of the ferryboat on which I daily cross the river is a long white pole, having a gilded ball at its tip. It suggested a flagpole when I first saw it; its color, shape, and gilded ball agreed with this idea, and these reasons seemed to justify me in this belief. But soon difficulties presented themselves. The pole was nearly horizontal, an unusual position for a flagpole; in the next place, there was no pulley, ring, or cord by which to attach a flag; finally, there were elsewhere on the boat two vertical staffs from which flags were occasionally flown. It seemed probable that the pole was not there for flag-flying.

“I then tried to imagine all possible purposes of the pole, and to consider for which of these it was best suited: (a) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried poles, this hypothesis was rejected. (b) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house. (c) Its purpose might be to point out the direction in which the boat is moving.

“In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it. Moreover, the tip was enough higher than the base, so that, from the pilot’s position, it must appear to project far out in front of the boat. Moreover, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly.” (Dewey 1910: 69–70; 1933: 92–93)

Bubbles : “In washing tumblers in hot soapsuds and placing them mouth downward on a plate, bubbles appeared on the outside of the mouth of the tumblers and then went inside. Why? The presence of bubbles suggests air, which I note must come from inside the tumbler. I see that the soapy water on the plate prevents escape of the air save as it may be caught in bubbles. But why should air leave the tumbler? There was no substance entering to force it out. It must have expanded. It expands by increase of heat, or by decrease of pressure, or both. Could the air have become heated after the tumbler was taken from the hot suds? Clearly not the air that was already entangled in the water. If heated air was the cause, cold air must have entered in transferring the tumblers from the suds to the plate. I test to see if this supposition is true by taking several more tumblers out. Some I shake so as to make sure of entrapping cold air in them. Some I take out holding mouth downward in order to prevent cold air from entering. Bubbles appear on the outside of every one of the former and on none of the latter. I must be right in my inference. Air from the outside must have been expanded by the heat of the tumbler, which explains the appearance of the bubbles on the outside. But why do they then go inside? Cold contracts. The tumbler cooled and also the air inside it. Tension was removed, and hence bubbles appeared inside. To be sure of this, I test by placing a cup of ice on the tumbler while the bubbles are still forming outside. They soon reverse” (Dewey 1910: 70–71; 1933: 93–94).

Dewey (1910, 1933) sprinkles his book with other examples of critical thinking. We will refer to the following.

Weather : A man on a walk notices that it has suddenly become cool, thinks that it is probably going to rain, looks up and sees a dark cloud obscuring the sun, and quickens his steps (1910: 6–10; 1933: 9–13).

Disorder : A man finds his rooms on his return to them in disorder with his belongings thrown about, thinks at first of burglary as an explanation, then thinks of mischievous children as being an alternative explanation, then looks to see whether valuables are missing, and discovers that they are (1910: 82–83; 1933: 166–168).

Typhoid : A physician diagnosing a patient whose conspicuous symptoms suggest typhoid avoids drawing a conclusion until more data are gathered by questioning the patient and by making tests (1910: 85–86; 1933: 170).

Blur : A moving blur catches our eye in the distance, we ask ourselves whether it is a cloud of whirling dust or a tree moving its branches or a man signaling to us, we think of other traits that should be found on each of those possibilities, and we look and see if those traits are found (1910: 102, 108; 1933: 121, 133).

Suction pump : In thinking about the suction pump, the scientist first notes that it will draw water only to a maximum height of 33 feet at sea level and to a lesser maximum height at higher elevations, selects for attention the differing atmospheric pressure at these elevations, sets up experiments in which the air is removed from a vessel containing water (when suction no longer works) and in which the weight of air at various levels is calculated, compares the results of reasoning about the height to which a given weight of air will allow a suction pump to raise water with the observed maximum height at different elevations, and finally assimilates the suction pump to such apparently different phenomena as the siphon and the rising of a balloon (1910: 150–153; 1933: 195–198).

Diamond : A passenger in a car driving in a diamond lane reserved for vehicles with at least one passenger notices that the diamond marks on the pavement are far apart in some places and close together in others. Why? The driver suggests that the reason may be that the diamond marks are not needed where there is a solid double line separating the diamond lane from the adjoining lane, but are needed when there is a dotted single line permitting crossing into the diamond lane. Further observation confirms that the diamonds are close together when a dotted line separates the diamond lane from its neighbour, but otherwise far apart.

Rash : A woman suddenly develops a very itchy red rash on her throat and upper chest. She recently noticed a mark on the back of her right hand, but was not sure whether the mark was a rash or a scrape. She lies down in bed and thinks about what might be causing the rash and what to do about it. About two weeks before, she began taking blood pressure medication that contained a sulfa drug, and the pharmacist had warned her, in view of a previous allergic reaction to a medication containing a sulfa drug, to be on the alert for an allergic reaction; however, she had been taking the medication for two weeks with no such effect. The day before, she began using a new cream on her neck and upper chest; against the new cream as the cause was mark on the back of her hand, which had not been exposed to the cream. She began taking probiotics about a month before. She also recently started new eye drops, but she supposed that manufacturers of eye drops would be careful not to include allergy-causing components in the medication. The rash might be a heat rash, since she recently was sweating profusely from her upper body. Since she is about to go away on a short vacation, where she would not have access to her usual physician, she decides to keep taking the probiotics and using the new eye drops but to discontinue the blood pressure medication and to switch back to the old cream for her neck and upper chest. She forms a plan to consult her regular physician on her return about the blood pressure medication.

Candidate : Although Dewey included no examples of thinking directed at appraising the arguments of others, such thinking has come to be considered a kind of critical thinking. We find an example of such thinking in the performance task on the Collegiate Learning Assessment (CLA+), which its sponsoring organization describes as

a performance-based assessment that provides a measure of an institution’s contribution to the development of critical-thinking and written communication skills of its students. (Council for Aid to Education 2017)

A sample task posted on its website requires the test-taker to write a report for public distribution evaluating a fictional candidate’s policy proposals and their supporting arguments, using supplied background documents, with a recommendation on whether to endorse the candidate.

Immediate acceptance of an idea that suggests itself as a solution to a problem (e.g., a possible explanation of an event or phenomenon, an action that seems likely to produce a desired result) is “uncritical thinking, the minimum of reflection” (Dewey 1910: 13). On-going suspension of judgment in the light of doubt about a possible solution is not critical thinking (Dewey 1910: 108). Critique driven by a dogmatically held political or religious ideology is not critical thinking; thus Paulo Freire (1968 [1970]) is using the term (e.g., at 1970: 71, 81, 100, 146) in a more politically freighted sense that includes not only reflection but also revolutionary action against oppression. Derivation of a conclusion from given data using an algorithm is not critical thinking.

What is critical thinking? There are many definitions. Ennis (2016) lists 14 philosophically oriented scholarly definitions and three dictionary definitions. Following Rawls (1971), who distinguished his conception of justice from a utilitarian conception but regarded them as rival conceptions of the same concept, Ennis maintains that the 17 definitions are different conceptions of the same concept. Rawls articulated the shared concept of justice as

a characteristic set of principles for assigning basic rights and duties and for determining… the proper distribution of the benefits and burdens of social cooperation. (Rawls 1971: 5)

Bailin et al. (1999b) claim that, if one considers what sorts of thinking an educator would take not to be critical thinking and what sorts to be critical thinking, one can conclude that educators typically understand critical thinking to have at least three features.

• It is done for the purpose of making up one’s mind about what to believe or do.
• The person engaging in the thinking is trying to fulfill standards of adequacy and accuracy appropriate to the thinking.
• The thinking fulfills the relevant standards to some threshold level.

One could sum up the core concept that involves these three features by saying that critical thinking is careful goal-directed thinking. This core concept seems to apply to all the examples of critical thinking described in the previous section. As for the non-examples, their exclusion depends on construing careful thinking as excluding jumping immediately to conclusions, suspending judgment no matter how strong the evidence, reasoning from an unquestioned ideological or religious perspective, and routinely using an algorithm to answer a question.

If the core of critical thinking is careful goal-directed thinking, conceptions of it can vary according to its presumed scope, its presumed goal, one’s criteria and threshold for being careful, and the thinking component on which one focuses. As to its scope, some conceptions (e.g., Dewey 1910, 1933) restrict it to constructive thinking on the basis of one’s own observations and experiments, others (e.g., Ennis 1962; Fisher & Scriven 1997; Johnson 1992) to appraisal of the products of such thinking. Ennis (1991) and Bailin et al. (1999b) take it to cover both construction and appraisal. As to its goal, some conceptions restrict it to forming a judgment (Dewey 1910, 1933; Lipman 1987; Facione 1990a). Others allow for actions as well as beliefs as the end point of a process of critical thinking (Ennis 1991; Bailin et al. 1999b). As to the criteria and threshold for being careful, definitions vary in the term used to indicate that critical thinking satisfies certain norms: “intellectually disciplined” (Scriven & Paul 1987), “reasonable” (Ennis 1991), “skillful” (Lipman 1987), “skilled” (Fisher & Scriven 1997), “careful” (Bailin & Battersby 2009). Some definitions specify these norms, referring variously to “consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends” (Dewey 1910, 1933); “the methods of logical inquiry and reasoning” (Glaser 1941); “conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication” (Scriven & Paul 1987); the requirement that “it is sensitive to context, relies on criteria, and is self-correcting” (Lipman 1987); “evidential, conceptual, methodological, criteriological, or contextual considerations” (Facione 1990a); and “plus-minus considerations of the product in terms of appropriate standards (or criteria)” (Johnson 1992). Stanovich and Stanovich (2010) propose to ground the concept of critical thinking in the concept of rationality, which they understand as combining epistemic rationality (fitting one’s beliefs to the world) and instrumental rationality (optimizing goal fulfillment); a critical thinker, in their view, is someone with “a propensity to override suboptimal responses from the autonomous mind” (2010: 227). These variant specifications of norms for critical thinking are not necessarily incompatible with one another, and in any case presuppose the core notion of thinking carefully. As to the thinking component singled out, some definitions focus on suspension of judgment during the thinking (Dewey 1910; McPeck 1981), others on inquiry while judgment is suspended (Bailin & Battersby 2009, 2021), others on the resulting judgment (Facione 1990a), and still others on responsiveness to reasons (Siegel 1988). Kuhn (2019) takes critical thinking to be more a dialogic practice of advancing and responding to arguments than an individual ability.

In educational contexts, a definition of critical thinking is a “programmatic definition” (Scheffler 1960: 19). It expresses a practical program for achieving an educational goal. For this purpose, a one-sentence formulaic definition is much less useful than articulation of a critical thinking process, with criteria and standards for the kinds of thinking that the process may involve. The real educational goal is recognition, adoption and implementation by students of those criteria and standards. That adoption and implementation in turn consists in acquiring the knowledge, abilities and dispositions of a critical thinker.

Conceptions of critical thinking generally do not include moral integrity as part of the concept. Dewey, for example, took critical thinking to be the ultimate intellectual goal of education, but distinguished it from the development of social cooperation among school children, which he took to be the central moral goal. Ennis (1996, 2011) added to his previous list of critical thinking dispositions a group of dispositions to care about the dignity and worth of every person, which he described as a “correlative” (1996) disposition without which critical thinking would be less valuable and perhaps harmful. An educational program that aimed at developing critical thinking but not the correlative disposition to care about the dignity and worth of every person, he asserted, “would be deficient and perhaps dangerous” (Ennis 1996: 172).

Dewey thought that education for reflective thinking would be of value to both the individual and society; recognition in educational practice of the kinship to the scientific attitude of children’s native curiosity, fertile imagination and love of experimental inquiry “would make for individual happiness and the reduction of social waste” (Dewey 1910: iii). Schools participating in the Eight-Year Study took development of the habit of reflective thinking and skill in solving problems as a means to leading young people to understand, appreciate and live the democratic way of life characteristic of the United States (Aikin 1942: 17–18, 81). Harvey Siegel (1988: 55–61) has offered four considerations in support of adopting critical thinking as an educational ideal. (1) Respect for persons requires that schools and teachers honour students’ demands for reasons and explanations, deal with students honestly, and recognize the need to confront students’ independent judgment; these requirements concern the manner in which teachers treat students. (2) Education has the task of preparing children to be successful adults, a task that requires development of their self-sufficiency. (3) Education should initiate children into the rational traditions in such fields as history, science and mathematics. (4) Education should prepare children to become democratic citizens, which requires reasoned procedures and critical talents and attitudes. To supplement these considerations, Siegel (1988: 62–90) responds to two objections: the ideology objection that adoption of any educational ideal requires a prior ideological commitment and the indoctrination objection that cultivation of critical thinking cannot escape being a form of indoctrination.

Despite the diversity of our 11 examples, one can recognize a common pattern. Dewey analyzed it as consisting of five phases:

• suggestions , in which the mind leaps forward to a possible solution;
• an intellectualization of the difficulty or perplexity into a problem to be solved, a question for which the answer must be sought;
• the use of one suggestion after another as a leading idea, or hypothesis , to initiate and guide observation and other operations in collection of factual material;
• the mental elaboration of the idea or supposition as an idea or supposition ( reasoning , in the sense on which reasoning is a part, not the whole, of inference); and
• testing the hypothesis by overt or imaginative action. (Dewey 1933: 106–107; italics in original)

The process of reflective thinking consisting of these phases would be preceded by a perplexed, troubled or confused situation and followed by a cleared-up, unified, resolved situation (Dewey 1933: 106). The term ‘phases’ replaced the term ‘steps’ (Dewey 1910: 72), thus removing the earlier suggestion of an invariant sequence. Variants of the above analysis appeared in (Dewey 1916: 177) and (Dewey 1938: 101–119).

The variant formulations indicate the difficulty of giving a single logical analysis of such a varied process. The process of critical thinking may have a spiral pattern, with the problem being redefined in the light of obstacles to solving it as originally formulated. For example, the person in Transit might have concluded that getting to the appointment at the scheduled time was impossible and have reformulated the problem as that of rescheduling the appointment for a mutually convenient time. Further, defining a problem does not always follow after or lead immediately to an idea of a suggested solution. Nor should it do so, as Dewey himself recognized in describing the physician in Typhoid as avoiding any strong preference for this or that conclusion before getting further information (Dewey 1910: 85; 1933: 170). People with a hypothesis in mind, even one to which they have a very weak commitment, have a so-called “confirmation bias” (Nickerson 1998): they are likely to pay attention to evidence that confirms the hypothesis and to ignore evidence that counts against it or for some competing hypothesis. Detectives, intelligence agencies, and investigators of airplane accidents are well advised to gather relevant evidence systematically and to postpone even tentative adoption of an explanatory hypothesis until the collected evidence rules out with the appropriate degree of certainty all but one explanation. Dewey’s analysis of the critical thinking process can be faulted as well for requiring acceptance or rejection of a possible solution to a defined problem, with no allowance for deciding in the light of the available evidence to suspend judgment. Further, given the great variety of kinds of problems for which reflection is appropriate, there is likely to be variation in its component events. Perhaps the best way to conceptualize the critical thinking process is as a checklist whose component events can occur in a variety of orders, selectively, and more than once. These component events might include (1) noticing a difficulty, (2) defining the problem, (3) dividing the problem into manageable sub-problems, (4) formulating a variety of possible solutions to the problem or sub-problem, (5) determining what evidence is relevant to deciding among possible solutions to the problem or sub-problem, (6) devising a plan of systematic observation or experiment that will uncover the relevant evidence, (7) carrying out the plan of systematic observation or experimentation, (8) noting the results of the systematic observation or experiment, (9) gathering relevant testimony and information from others, (10) judging the credibility of testimony and information gathered from others, (11) drawing conclusions from gathered evidence and accepted testimony, and (12) accepting a solution that the evidence adequately supports (cf. Hitchcock 2017: 485).

Checklist conceptions of the process of critical thinking are open to the objection that they are too mechanical and procedural to fit the multi-dimensional and emotionally charged issues for which critical thinking is urgently needed (Paul 1984). For such issues, a more dialectical process is advocated, in which competing relevant world views are identified, their implications explored, and some sort of creative synthesis attempted.

If one considers the critical thinking process illustrated by the 11 examples, one can identify distinct kinds of mental acts and mental states that form part of it. To distinguish, label and briefly characterize these components is a useful preliminary to identifying abilities, skills, dispositions, attitudes, habits and the like that contribute causally to thinking critically. Identifying such abilities and habits is in turn a useful preliminary to setting educational goals. Setting the goals is in its turn a useful preliminary to designing strategies for helping learners to achieve the goals and to designing ways of measuring the extent to which learners have done so. Such measures provide both feedback to learners on their achievement and a basis for experimental research on the effectiveness of various strategies for educating people to think critically. Let us begin, then, by distinguishing the kinds of mental acts and mental events that can occur in a critical thinking process.

• Observing : One notices something in one’s immediate environment (sudden cooling of temperature in Weather , bubbles forming outside a glass and then going inside in Bubbles , a moving blur in the distance in Blur , a rash in Rash ). Or one notes the results of an experiment or systematic observation (valuables missing in Disorder , no suction without air pressure in Suction pump )
• Feeling : One feels puzzled or uncertain about something (how to get to an appointment on time in Transit , why the diamonds vary in spacing in Diamond ). One wants to resolve this perplexity. One feels satisfaction once one has worked out an answer (to take the subway express in Transit , diamonds closer when needed as a warning in Diamond ).
• Wondering : One formulates a question to be addressed (why bubbles form outside a tumbler taken from hot water in Bubbles , how suction pumps work in Suction pump , what caused the rash in Rash ).
• Imagining : One thinks of possible answers (bus or subway or elevated in Transit , flagpole or ornament or wireless communication aid or direction indicator in Ferryboat , allergic reaction or heat rash in Rash ).
• Inferring : One works out what would be the case if a possible answer were assumed (valuables missing if there has been a burglary in Disorder , earlier start to the rash if it is an allergic reaction to a sulfa drug in Rash ). Or one draws a conclusion once sufficient relevant evidence is gathered (take the subway in Transit , burglary in Disorder , discontinue blood pressure medication and new cream in Rash ).
• Knowledge : One uses stored knowledge of the subject-matter to generate possible answers or to infer what would be expected on the assumption of a particular answer (knowledge of a city’s public transit system in Transit , of the requirements for a flagpole in Ferryboat , of Boyle’s law in Bubbles , of allergic reactions in Rash ).
• Experimenting : One designs and carries out an experiment or a systematic observation to find out whether the results deduced from a possible answer will occur (looking at the location of the flagpole in relation to the pilot’s position in Ferryboat , putting an ice cube on top of a tumbler taken from hot water in Bubbles , measuring the height to which a suction pump will draw water at different elevations in Suction pump , noticing the spacing of diamonds when movement to or from a diamond lane is allowed in Diamond ).
• Consulting : One finds a source of information, gets the information from the source, and makes a judgment on whether to accept it. None of our 11 examples include searching for sources of information. In this respect they are unrepresentative, since most people nowadays have almost instant access to information relevant to answering any question, including many of those illustrated by the examples. However, Candidate includes the activities of extracting information from sources and evaluating its credibility.
• Identifying and analyzing arguments : One notices an argument and works out its structure and content as a preliminary to evaluating its strength. This activity is central to Candidate . It is an important part of a critical thinking process in which one surveys arguments for various positions on an issue.
• Judging : One makes a judgment on the basis of accumulated evidence and reasoning, such as the judgment in Ferryboat that the purpose of the pole is to provide direction to the pilot.
• Deciding : One makes a decision on what to do or on what policy to adopt, as in the decision in Transit to take the subway.

By definition, a person who does something voluntarily is both willing and able to do that thing at that time. Both the willingness and the ability contribute causally to the person’s action, in the sense that the voluntary action would not occur if either (or both) of these were lacking. For example, suppose that one is standing with one’s arms at one’s sides and one voluntarily lifts one’s right arm to an extended horizontal position. One would not do so if one were unable to lift one’s arm, if for example one’s right side was paralyzed as the result of a stroke. Nor would one do so if one were unwilling to lift one’s arm, if for example one were participating in a street demonstration at which a white supremacist was urging the crowd to lift their right arm in a Nazi salute and one were unwilling to express support in this way for the racist Nazi ideology. The same analysis applies to a voluntary mental process of thinking critically. It requires both willingness and ability to think critically, including willingness and ability to perform each of the mental acts that compose the process and to coordinate those acts in a sequence that is directed at resolving the initiating perplexity.

Consider willingness first. We can identify causal contributors to willingness to think critically by considering factors that would cause a person who was able to think critically about an issue nevertheless not to do so (Hamby 2014). For each factor, the opposite condition thus contributes causally to willingness to think critically on a particular occasion. For example, people who habitually jump to conclusions without considering alternatives will not think critically about issues that arise, even if they have the required abilities. The contrary condition of willingness to suspend judgment is thus a causal contributor to thinking critically.

Now consider ability. In contrast to the ability to move one’s arm, which can be completely absent because a stroke has left the arm paralyzed, the ability to think critically is a developed ability, whose absence is not a complete absence of ability to think but absence of ability to think well. We can identify the ability to think well directly, in terms of the norms and standards for good thinking. In general, to be able do well the thinking activities that can be components of a critical thinking process, one needs to know the concepts and principles that characterize their good performance, to recognize in particular cases that the concepts and principles apply, and to apply them. The knowledge, recognition and application may be procedural rather than declarative. It may be domain-specific rather than widely applicable, and in either case may need subject-matter knowledge, sometimes of a deep kind.

Reflections of the sort illustrated by the previous two paragraphs have led scholars to identify the knowledge, abilities and dispositions of a “critical thinker”, i.e., someone who thinks critically whenever it is appropriate to do so. We turn now to these three types of causal contributors to thinking critically. We start with dispositions, since arguably these are the most powerful contributors to being a critical thinker, can be fostered at an early stage of a child’s development, and are susceptible to general improvement (Glaser 1941: 175)

8. Critical Thinking Dispositions

Educational researchers use the term ‘dispositions’ broadly for the habits of mind and attitudes that contribute causally to being a critical thinker. Some writers (e.g., Paul & Elder 2006; Hamby 2014; Bailin & Battersby 2016a) propose to use the term ‘virtues’ for this dimension of a critical thinker. The virtues in question, although they are virtues of character, concern the person’s ways of thinking rather than the person’s ways of behaving towards others. They are not moral virtues but intellectual virtues, of the sort articulated by Zagzebski (1996) and discussed by Turri, Alfano, and Greco (2017).

On a realistic conception, thinking dispositions or intellectual virtues are real properties of thinkers. They are general tendencies, propensities, or inclinations to think in particular ways in particular circumstances, and can be genuinely explanatory (Siegel 1999). Sceptics argue that there is no evidence for a specific mental basis for the habits of mind that contribute to thinking critically, and that it is pedagogically misleading to posit such a basis (Bailin et al. 1999a). Whatever their status, critical thinking dispositions need motivation for their initial formation in a child—motivation that may be external or internal. As children develop, the force of habit will gradually become important in sustaining the disposition (Nieto & Valenzuela 2012). Mere force of habit, however, is unlikely to sustain critical thinking dispositions. Critical thinkers must value and enjoy using their knowledge and abilities to think things through for themselves. They must be committed to, and lovers of, inquiry.

A person may have a critical thinking disposition with respect to only some kinds of issues. For example, one could be open-minded about scientific issues but not about religious issues. Similarly, one could be confident in one’s ability to reason about the theological implications of the existence of evil in the world but not in one’s ability to reason about the best design for a guided ballistic missile.

Facione (1990a: 25) divides “affective dispositions” of critical thinking into approaches to life and living in general and approaches to specific issues, questions or problems. Adapting this distinction, one can usefully divide critical thinking dispositions into initiating dispositions (those that contribute causally to starting to think critically about an issue) and internal dispositions (those that contribute causally to doing a good job of thinking critically once one has started). The two categories are not mutually exclusive. For example, open-mindedness, in the sense of willingness to consider alternative points of view to one’s own, is both an initiating and an internal disposition.

Using the strategy of considering factors that would block people with the ability to think critically from doing so, we can identify as initiating dispositions for thinking critically attentiveness, a habit of inquiry, self-confidence, courage, open-mindedness, willingness to suspend judgment, trust in reason, wanting evidence for one’s beliefs, and seeking the truth. We consider briefly what each of these dispositions amounts to, in each case citing sources that acknowledge them.

• Attentiveness : One will not think critically if one fails to recognize an issue that needs to be thought through. For example, the pedestrian in Weather would not have looked up if he had not noticed that the air was suddenly cooler. To be a critical thinker, then, one needs to be habitually attentive to one’s surroundings, noticing not only what one senses but also sources of perplexity in messages received and in one’s own beliefs and attitudes (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
• Habit of inquiry : Inquiry is effortful, and one needs an internal push to engage in it. For example, the student in Bubbles could easily have stopped at idle wondering about the cause of the bubbles rather than reasoning to a hypothesis, then designing and executing an experiment to test it. Thus willingness to think critically needs mental energy and initiative. What can supply that energy? Love of inquiry, or perhaps just a habit of inquiry. Hamby (2015) has argued that willingness to inquire is the central critical thinking virtue, one that encompasses all the others. It is recognized as a critical thinking disposition by Dewey (1910: 29; 1933: 35), Glaser (1941: 5), Ennis (1987: 12; 1991: 8), Facione (1990a: 25), Bailin et al. (1999b: 294), Halpern (1998: 452), and Facione, Facione, & Giancarlo (2001).
• Self-confidence : Lack of confidence in one’s abilities can block critical thinking. For example, if the woman in Rash lacked confidence in her ability to figure things out for herself, she might just have assumed that the rash on her chest was the allergic reaction to her medication against which the pharmacist had warned her. Thus willingness to think critically requires confidence in one’s ability to inquire (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
• Courage : Fear of thinking for oneself can stop one from doing it. Thus willingness to think critically requires intellectual courage (Paul & Elder 2006: 16).
• Open-mindedness : A dogmatic attitude will impede thinking critically. For example, a person who adheres rigidly to a “pro-choice” position on the issue of the legal status of induced abortion is likely to be unwilling to consider seriously the issue of when in its development an unborn child acquires a moral right to life. Thus willingness to think critically requires open-mindedness, in the sense of a willingness to examine questions to which one already accepts an answer but which further evidence or reasoning might cause one to answer differently (Dewey 1933; Facione 1990a; Ennis 1991; Bailin et al. 1999b; Halpern 1998, Facione, Facione, & Giancarlo 2001). Paul (1981) emphasizes open-mindedness about alternative world-views, and recommends a dialectical approach to integrating such views as central to what he calls “strong sense” critical thinking. In three studies, Haran, Ritov, & Mellers (2013) found that actively open-minded thinking, including “the tendency to weigh new evidence against a favored belief, to spend sufficient time on a problem before giving up, and to consider carefully the opinions of others in forming one’s own”, led study participants to acquire information and thus to make accurate estimations.
• Willingness to suspend judgment : Premature closure on an initial solution will block critical thinking. Thus willingness to think critically requires a willingness to suspend judgment while alternatives are explored (Facione 1990a; Ennis 1991; Halpern 1998).
• Trust in reason : Since distrust in the processes of reasoned inquiry will dissuade one from engaging in it, trust in them is an initiating critical thinking disposition (Facione 1990a, 25; Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001; Paul & Elder 2006). In reaction to an allegedly exclusive emphasis on reason in critical thinking theory and pedagogy, Thayer-Bacon (2000) argues that intuition, imagination, and emotion have important roles to play in an adequate conception of critical thinking that she calls “constructive thinking”. From her point of view, critical thinking requires trust not only in reason but also in intuition, imagination, and emotion.
• Seeking the truth : If one does not care about the truth but is content to stick with one’s initial bias on an issue, then one will not think critically about it. Seeking the truth is thus an initiating critical thinking disposition (Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001). A disposition to seek the truth is implicit in more specific critical thinking dispositions, such as trying to be well-informed, considering seriously points of view other than one’s own, looking for alternatives, suspending judgment when the evidence is insufficient, and adopting a position when the evidence supporting it is sufficient.

Some of the initiating dispositions, such as open-mindedness and willingness to suspend judgment, are also internal critical thinking dispositions, in the sense of mental habits or attitudes that contribute causally to doing a good job of critical thinking once one starts the process. But there are many other internal critical thinking dispositions. Some of them are parasitic on one’s conception of good thinking. For example, it is constitutive of good thinking about an issue to formulate the issue clearly and to maintain focus on it. For this purpose, one needs not only the corresponding ability but also the corresponding disposition. Ennis (1991: 8) describes it as the disposition “to determine and maintain focus on the conclusion or question”, Facione (1990a: 25) as “clarity in stating the question or concern”. Other internal dispositions are motivators to continue or adjust the critical thinking process, such as willingness to persist in a complex task and willingness to abandon nonproductive strategies in an attempt to self-correct (Halpern 1998: 452). For a list of identified internal critical thinking dispositions, see the Supplement on Internal Critical Thinking Dispositions .

Some theorists postulate skills, i.e., acquired abilities, as operative in critical thinking. It is not obvious, however, that a good mental act is the exercise of a generic acquired skill. Inferring an expected time of arrival, as in Transit , has some generic components but also uses non-generic subject-matter knowledge. Bailin et al. (1999a) argue against viewing critical thinking skills as generic and discrete, on the ground that skilled performance at a critical thinking task cannot be separated from knowledge of concepts and from domain-specific principles of good thinking. Talk of skills, they concede, is unproblematic if it means merely that a person with critical thinking skills is capable of intelligent performance.

Despite such scepticism, theorists of critical thinking have listed as general contributors to critical thinking what they variously call abilities (Glaser 1941; Ennis 1962, 1991), skills (Facione 1990a; Halpern 1998) or competencies (Fisher & Scriven 1997). Amalgamating these lists would produce a confusing and chaotic cornucopia of more than 50 possible educational objectives, with only partial overlap among them. It makes sense instead to try to understand the reasons for the multiplicity and diversity, and to make a selection according to one’s own reasons for singling out abilities to be developed in a critical thinking curriculum. Two reasons for diversity among lists of critical thinking abilities are the underlying conception of critical thinking and the envisaged educational level. Appraisal-only conceptions, for example, involve a different suite of abilities than constructive-only conceptions. Some lists, such as those in (Glaser 1941), are put forward as educational objectives for secondary school students, whereas others are proposed as objectives for college students (e.g., Facione 1990a).

The abilities described in the remaining paragraphs of this section emerge from reflection on the general abilities needed to do well the thinking activities identified in section 6 as components of the critical thinking process described in section 5 . The derivation of each collection of abilities is accompanied by citation of sources that list such abilities and of standardized tests that claim to test them.

Observational abilities : Careful and accurate observation sometimes requires specialist expertise and practice, as in the case of observing birds and observing accident scenes. However, there are general abilities of noticing what one’s senses are picking up from one’s environment and of being able to articulate clearly and accurately to oneself and others what one has observed. It helps in exercising them to be able to recognize and take into account factors that make one’s observation less trustworthy, such as prior framing of the situation, inadequate time, deficient senses, poor observation conditions, and the like. It helps as well to be skilled at taking steps to make one’s observation more trustworthy, such as moving closer to get a better look, measuring something three times and taking the average, and checking what one thinks one is observing with someone else who is in a good position to observe it. It also helps to be skilled at recognizing respects in which one’s report of one’s observation involves inference rather than direct observation, so that one can then consider whether the inference is justified. These abilities come into play as well when one thinks about whether and with what degree of confidence to accept an observation report, for example in the study of history or in a criminal investigation or in assessing news reports. Observational abilities show up in some lists of critical thinking abilities (Ennis 1962: 90; Facione 1990a: 16; Ennis 1991: 9). There are items testing a person’s ability to judge the credibility of observation reports in the Cornell Critical Thinking Tests, Levels X and Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). Norris and King (1983, 1985, 1990a, 1990b) is a test of ability to appraise observation reports.

Emotional abilities : The emotions that drive a critical thinking process are perplexity or puzzlement, a wish to resolve it, and satisfaction at achieving the desired resolution. Children experience these emotions at an early age, without being trained to do so. Education that takes critical thinking as a goal needs only to channel these emotions and to make sure not to stifle them. Collaborative critical thinking benefits from ability to recognize one’s own and others’ emotional commitments and reactions.

Questioning abilities : A critical thinking process needs transformation of an inchoate sense of perplexity into a clear question. Formulating a question well requires not building in questionable assumptions, not prejudging the issue, and using language that in context is unambiguous and precise enough (Ennis 1962: 97; 1991: 9).

Imaginative abilities : Thinking directed at finding the correct causal explanation of a general phenomenon or particular event requires an ability to imagine possible explanations. Thinking about what policy or plan of action to adopt requires generation of options and consideration of possible consequences of each option. Domain knowledge is required for such creative activity, but a general ability to imagine alternatives is helpful and can be nurtured so as to become easier, quicker, more extensive, and deeper (Dewey 1910: 34–39; 1933: 40–47). Facione (1990a) and Halpern (1998) include the ability to imagine alternatives as a critical thinking ability.

Inferential abilities : The ability to draw conclusions from given information, and to recognize with what degree of certainty one’s own or others’ conclusions follow, is universally recognized as a general critical thinking ability. All 11 examples in section 2 of this article include inferences, some from hypotheses or options (as in Transit , Ferryboat and Disorder ), others from something observed (as in Weather and Rash ). None of these inferences is formally valid. Rather, they are licensed by general, sometimes qualified substantive rules of inference (Toulmin 1958) that rest on domain knowledge—that a bus trip takes about the same time in each direction, that the terminal of a wireless telegraph would be located on the highest possible place, that sudden cooling is often followed by rain, that an allergic reaction to a sulfa drug generally shows up soon after one starts taking it. It is a matter of controversy to what extent the specialized ability to deduce conclusions from premisses using formal rules of inference is needed for critical thinking. Dewey (1933) locates logical forms in setting out the products of reflection rather than in the process of reflection. Ennis (1981a), on the other hand, maintains that a liberally-educated person should have the following abilities: to translate natural-language statements into statements using the standard logical operators, to use appropriately the language of necessary and sufficient conditions, to deal with argument forms and arguments containing symbols, to determine whether in virtue of an argument’s form its conclusion follows necessarily from its premisses, to reason with logically complex propositions, and to apply the rules and procedures of deductive logic. Inferential abilities are recognized as critical thinking abilities by Glaser (1941: 6), Facione (1990a: 9), Ennis (1991: 9), Fisher & Scriven (1997: 99, 111), and Halpern (1998: 452). Items testing inferential abilities constitute two of the five subtests of the Watson Glaser Critical Thinking Appraisal (Watson & Glaser 1980a, 1980b, 1994), two of the four sections in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), three of the seven sections in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), 11 of the 34 items on Forms A and B of the California Critical Thinking Skills Test (Facione 1990b, 1992), and a high but variable proportion of the 25 selected-response questions in the Collegiate Learning Assessment (Council for Aid to Education 2017).

Experimenting abilities : Knowing how to design and execute an experiment is important not just in scientific research but also in everyday life, as in Rash . Dewey devoted a whole chapter of his How We Think (1910: 145–156; 1933: 190–202) to the superiority of experimentation over observation in advancing knowledge. Experimenting abilities come into play at one remove in appraising reports of scientific studies. Skill in designing and executing experiments includes the acknowledged abilities to appraise evidence (Glaser 1941: 6), to carry out experiments and to apply appropriate statistical inference techniques (Facione 1990a: 9), to judge inductions to an explanatory hypothesis (Ennis 1991: 9), and to recognize the need for an adequately large sample size (Halpern 1998). The Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) includes four items (out of 52) on experimental design. The Collegiate Learning Assessment (Council for Aid to Education 2017) makes room for appraisal of study design in both its performance task and its selected-response questions.

Consulting abilities : Skill at consulting sources of information comes into play when one seeks information to help resolve a problem, as in Candidate . Ability to find and appraise information includes ability to gather and marshal pertinent information (Glaser 1941: 6), to judge whether a statement made by an alleged authority is acceptable (Ennis 1962: 84), to plan a search for desired information (Facione 1990a: 9), and to judge the credibility of a source (Ennis 1991: 9). Ability to judge the credibility of statements is tested by 24 items (out of 76) in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) and by four items (out of 52) in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). The College Learning Assessment’s performance task requires evaluation of whether information in documents is credible or unreliable (Council for Aid to Education 2017).

Argument analysis abilities : The ability to identify and analyze arguments contributes to the process of surveying arguments on an issue in order to form one’s own reasoned judgment, as in Candidate . The ability to detect and analyze arguments is recognized as a critical thinking skill by Facione (1990a: 7–8), Ennis (1991: 9) and Halpern (1998). Five items (out of 34) on the California Critical Thinking Skills Test (Facione 1990b, 1992) test skill at argument analysis. The College Learning Assessment (Council for Aid to Education 2017) incorporates argument analysis in its selected-response tests of critical reading and evaluation and of critiquing an argument.

Judging skills and deciding skills : Skill at judging and deciding is skill at recognizing what judgment or decision the available evidence and argument supports, and with what degree of confidence. It is thus a component of the inferential skills already discussed.

Lists and tests of critical thinking abilities often include two more abilities: identifying assumptions and constructing and evaluating definitions.

In addition to dispositions and abilities, critical thinking needs knowledge: of critical thinking concepts, of critical thinking principles, and of the subject-matter of the thinking.

We can derive a short list of concepts whose understanding contributes to critical thinking from the critical thinking abilities described in the preceding section. Observational abilities require an understanding of the difference between observation and inference. Questioning abilities require an understanding of the concepts of ambiguity and vagueness. Inferential abilities require an understanding of the difference between conclusive and defeasible inference (traditionally, between deduction and induction), as well as of the difference between necessary and sufficient conditions. Experimenting abilities require an understanding of the concepts of hypothesis, null hypothesis, assumption and prediction, as well as of the concept of statistical significance and of its difference from importance. They also require an understanding of the difference between an experiment and an observational study, and in particular of the difference between a randomized controlled trial, a prospective correlational study and a retrospective (case-control) study. Argument analysis abilities require an understanding of the concepts of argument, premiss, assumption, conclusion and counter-consideration. Additional critical thinking concepts are proposed by Bailin et al. (1999b: 293), Fisher & Scriven (1997: 105–106), Black (2012), and Blair (2021).

According to Glaser (1941: 25), ability to think critically requires knowledge of the methods of logical inquiry and reasoning. If we review the list of abilities in the preceding section, however, we can see that some of them can be acquired and exercised merely through practice, possibly guided in an educational setting, followed by feedback. Searching intelligently for a causal explanation of some phenomenon or event requires that one consider a full range of possible causal contributors, but it seems more important that one implements this principle in one’s practice than that one is able to articulate it. What is important is “operational knowledge” of the standards and principles of good thinking (Bailin et al. 1999b: 291–293). But the development of such critical thinking abilities as designing an experiment or constructing an operational definition can benefit from learning their underlying theory. Further, explicit knowledge of quirks of human thinking seems useful as a cautionary guide. Human memory is not just fallible about details, as people learn from their own experiences of misremembering, but is so malleable that a detailed, clear and vivid recollection of an event can be a total fabrication (Loftus 2017). People seek or interpret evidence in ways that are partial to their existing beliefs and expectations, often unconscious of their “confirmation bias” (Nickerson 1998). Not only are people subject to this and other cognitive biases (Kahneman 2011), of which they are typically unaware, but it may be counter-productive for one to make oneself aware of them and try consciously to counteract them or to counteract social biases such as racial or sexual stereotypes (Kenyon & Beaulac 2014). It is helpful to be aware of these facts and of the superior effectiveness of blocking the operation of biases—for example, by making an immediate record of one’s observations, refraining from forming a preliminary explanatory hypothesis, blind refereeing, double-blind randomized trials, and blind grading of students’ work. It is also helpful to be aware of the prevalence of “noise” (unwanted unsystematic variability of judgments), of how to detect noise (through a noise audit), and of how to reduce noise: make accuracy the goal, think statistically, break a process of arriving at a judgment into independent tasks, resist premature intuitions, in a group get independent judgments first, favour comparative judgments and scales (Kahneman, Sibony, & Sunstein 2021). It is helpful as well to be aware of the concept of “bounded rationality” in decision-making and of the related distinction between “satisficing” and optimizing (Simon 1956; Gigerenzer 2001).

Critical thinking about an issue requires substantive knowledge of the domain to which the issue belongs. Critical thinking abilities are not a magic elixir that can be applied to any issue whatever by somebody who has no knowledge of the facts relevant to exploring that issue. For example, the student in Bubbles needed to know that gases do not penetrate solid objects like a glass, that air expands when heated, that the volume of an enclosed gas varies directly with its temperature and inversely with its pressure, and that hot objects will spontaneously cool down to the ambient temperature of their surroundings unless kept hot by insulation or a source of heat. Critical thinkers thus need a rich fund of subject-matter knowledge relevant to the variety of situations they encounter. This fact is recognized in the inclusion among critical thinking dispositions of a concern to become and remain generally well informed.

Experimental educational interventions, with control groups, have shown that education can improve critical thinking skills and dispositions, as measured by standardized tests. For information about these tests, see the Supplement on Assessment .

What educational methods are most effective at developing the dispositions, abilities and knowledge of a critical thinker? In a comprehensive meta-analysis of experimental and quasi-experimental studies of strategies for teaching students to think critically, Abrami et al. (2015) found that dialogue, anchored instruction, and mentoring each increased the effectiveness of the educational intervention, and that they were most effective when combined. They also found that in these studies a combination of separate instruction in critical thinking with subject-matter instruction in which students are encouraged to think critically was more effective than either by itself. However, the difference was not statistically significant; that is, it might have arisen by chance.

Most of these studies lack the longitudinal follow-up required to determine whether the observed differential improvements in critical thinking abilities or dispositions continue over time, for example until high school or college graduation. For details on studies of methods of developing critical thinking skills and dispositions, see the Supplement on Educational Methods .

12. Controversies

Scholars have denied the generalizability of critical thinking abilities across subject domains, have alleged bias in critical thinking theory and pedagogy, and have investigated the relationship of critical thinking to other kinds of thinking.

McPeck (1981) attacked the thinking skills movement of the 1970s, including the critical thinking movement. He argued that there are no general thinking skills, since thinking is always thinking about some subject-matter. It is futile, he claimed, for schools and colleges to teach thinking as if it were a separate subject. Rather, teachers should lead their pupils to become autonomous thinkers by teaching school subjects in a way that brings out their cognitive structure and that encourages and rewards discussion and argument. As some of his critics (e.g., Paul 1985; Siegel 1985) pointed out, McPeck’s central argument needs elaboration, since it has obvious counter-examples in writing and speaking, for which (up to a certain level of complexity) there are teachable general abilities even though they are always about some subject-matter. To make his argument convincing, McPeck needs to explain how thinking differs from writing and speaking in a way that does not permit useful abstraction of its components from the subject-matters with which it deals. He has not done so. Nevertheless, his position that the dispositions and abilities of a critical thinker are best developed in the context of subject-matter instruction is shared by many theorists of critical thinking, including Dewey (1910, 1933), Glaser (1941), Passmore (1980), Weinstein (1990), Bailin et al. (1999b), and Willingham (2019).

McPeck’s challenge prompted reflection on the extent to which critical thinking is subject-specific. McPeck argued for a strong subject-specificity thesis, according to which it is a conceptual truth that all critical thinking abilities are specific to a subject. (He did not however extend his subject-specificity thesis to critical thinking dispositions. In particular, he took the disposition to suspend judgment in situations of cognitive dissonance to be a general disposition.) Conceptual subject-specificity is subject to obvious counter-examples, such as the general ability to recognize confusion of necessary and sufficient conditions. A more modest thesis, also endorsed by McPeck, is epistemological subject-specificity, according to which the norms of good thinking vary from one field to another. Epistemological subject-specificity clearly holds to a certain extent; for example, the principles in accordance with which one solves a differential equation are quite different from the principles in accordance with which one determines whether a painting is a genuine Picasso. But the thesis suffers, as Ennis (1989) points out, from vagueness of the concept of a field or subject and from the obvious existence of inter-field principles, however broadly the concept of a field is construed. For example, the principles of hypothetico-deductive reasoning hold for all the varied fields in which such reasoning occurs. A third kind of subject-specificity is empirical subject-specificity, according to which as a matter of empirically observable fact a person with the abilities and dispositions of a critical thinker in one area of investigation will not necessarily have them in another area of investigation.

The thesis of empirical subject-specificity raises the general problem of transfer. If critical thinking abilities and dispositions have to be developed independently in each school subject, how are they of any use in dealing with the problems of everyday life and the political and social issues of contemporary society, most of which do not fit into the framework of a traditional school subject? Proponents of empirical subject-specificity tend to argue that transfer is more likely to occur if there is critical thinking instruction in a variety of domains, with explicit attention to dispositions and abilities that cut across domains. But evidence for this claim is scanty. There is a need for well-designed empirical studies that investigate the conditions that make transfer more likely.

It is common ground in debates about the generality or subject-specificity of critical thinking dispositions and abilities that critical thinking about any topic requires background knowledge about the topic. For example, the most sophisticated understanding of the principles of hypothetico-deductive reasoning is of no help unless accompanied by some knowledge of what might be plausible explanations of some phenomenon under investigation.

Critics have objected to bias in the theory, pedagogy and practice of critical thinking. Commentators (e.g., Alston 1995; Ennis 1998) have noted that anyone who takes a position has a bias in the neutral sense of being inclined in one direction rather than others. The critics, however, are objecting to bias in the pejorative sense of an unjustified favoring of certain ways of knowing over others, frequently alleging that the unjustly favoured ways are those of a dominant sex or culture (Bailin 1995). These ways favour:

• reinforcement of egocentric and sociocentric biases over dialectical engagement with opposing world-views (Paul 1981, 1984; Warren 1998)
• distancing from the object of inquiry over closeness to it (Martin 1992; Thayer-Bacon 1992)
• indifference to the situation of others over care for them (Martin 1992)
• orientation to thought over orientation to action (Martin 1992)
• being reasonable over caring to understand people’s ideas (Thayer-Bacon 1993)
• being neutral and objective over being embodied and situated (Thayer-Bacon 1995a)
• doubting over believing (Thayer-Bacon 1995b)
• reason over emotion, imagination and intuition (Thayer-Bacon 2000)
• solitary thinking over collaborative thinking (Thayer-Bacon 2000)
• written and spoken assignments over other forms of expression (Alston 2001)
• attention to written and spoken communications over attention to human problems (Alston 2001)
• winning debates in the public sphere over making and understanding meaning (Alston 2001)

A common thread in this smorgasbord of accusations is dissatisfaction with focusing on the logical analysis and evaluation of reasoning and arguments. While these authors acknowledge that such analysis and evaluation is part of critical thinking and should be part of its conceptualization and pedagogy, they insist that it is only a part. Paul (1981), for example, bemoans the tendency of atomistic teaching of methods of analyzing and evaluating arguments to turn students into more able sophists, adept at finding fault with positions and arguments with which they disagree but even more entrenched in the egocentric and sociocentric biases with which they began. Martin (1992) and Thayer-Bacon (1992) cite with approval the self-reported intimacy with their subject-matter of leading researchers in biology and medicine, an intimacy that conflicts with the distancing allegedly recommended in standard conceptions and pedagogy of critical thinking. Thayer-Bacon (2000) contrasts the embodied and socially embedded learning of her elementary school students in a Montessori school, who used their imagination, intuition and emotions as well as their reason, with conceptions of critical thinking as

thinking that is used to critique arguments, offer justifications, and make judgments about what are the good reasons, or the right answers. (Thayer-Bacon 2000: 127–128)

Alston (2001) reports that her students in a women’s studies class were able to see the flaws in the Cinderella myth that pervades much romantic fiction but in their own romantic relationships still acted as if all failures were the woman’s fault and still accepted the notions of love at first sight and living happily ever after. Students, she writes, should

be able to connect their intellectual critique to a more affective, somatic, and ethical account of making risky choices that have sexist, racist, classist, familial, sexual, or other consequences for themselves and those both near and far… critical thinking that reads arguments, texts, or practices merely on the surface without connections to feeling/desiring/doing or action lacks an ethical depth that should infuse the difference between mere cognitive activity and something we want to call critical thinking. (Alston 2001: 34)

Some critics portray such biases as unfair to women. Thayer-Bacon (1992), for example, has charged modern critical thinking theory with being sexist, on the ground that it separates the self from the object and causes one to lose touch with one’s inner voice, and thus stigmatizes women, who (she asserts) link self to object and listen to their inner voice. Her charge does not imply that women as a group are on average less able than men to analyze and evaluate arguments. Facione (1990c) found no difference by sex in performance on his California Critical Thinking Skills Test. Kuhn (1991: 280–281) found no difference by sex in either the disposition or the competence to engage in argumentative thinking.

The critics propose a variety of remedies for the biases that they allege. In general, they do not propose to eliminate or downplay critical thinking as an educational goal. Rather, they propose to conceptualize critical thinking differently and to change its pedagogy accordingly. Their pedagogical proposals arise logically from their objections. They can be summarized as follows:

• Focus on argument networks with dialectical exchanges reflecting contesting points of view rather than on atomic arguments, so as to develop “strong sense” critical thinking that transcends egocentric and sociocentric biases (Paul 1981, 1984).
• Foster closeness to the subject-matter and feeling connected to others in order to inform a humane democracy (Martin 1992).
• Develop “constructive thinking” as a social activity in a community of physically embodied and socially embedded inquirers with personal voices who value not only reason but also imagination, intuition and emotion (Thayer-Bacon 2000).
• In developing critical thinking in school subjects, treat as important neither skills nor dispositions but opening worlds of meaning (Alston 2001).
• Attend to the development of critical thinking dispositions as well as skills, and adopt the “critical pedagogy” practised and advocated by Freire (1968 [1970]) and hooks (1994) (Dalgleish, Girard, & Davies 2017).

A common thread in these proposals is treatment of critical thinking as a social, interactive, personally engaged activity like that of a quilting bee or a barn-raising (Thayer-Bacon 2000) rather than as an individual, solitary, distanced activity symbolized by Rodin’s The Thinker . One can get a vivid description of education with the former type of goal from the writings of bell hooks (1994, 2010). Critical thinking for her is open-minded dialectical exchange across opposing standpoints and from multiple perspectives, a conception similar to Paul’s “strong sense” critical thinking (Paul 1981). She abandons the structure of domination in the traditional classroom. In an introductory course on black women writers, for example, she assigns students to write an autobiographical paragraph about an early racial memory, then to read it aloud as the others listen, thus affirming the uniqueness and value of each voice and creating a communal awareness of the diversity of the group’s experiences (hooks 1994: 84). Her “engaged pedagogy” is thus similar to the “freedom under guidance” implemented in John Dewey’s Laboratory School of Chicago in the late 1890s and early 1900s. It incorporates the dialogue, anchored instruction, and mentoring that Abrami (2015) found to be most effective in improving critical thinking skills and dispositions.

What is the relationship of critical thinking to problem solving, decision-making, higher-order thinking, creative thinking, and other recognized types of thinking? One’s answer to this question obviously depends on how one defines the terms used in the question. If critical thinking is conceived broadly to cover any careful thinking about any topic for any purpose, then problem solving and decision making will be kinds of critical thinking, if they are done carefully. Historically, ‘critical thinking’ and ‘problem solving’ were two names for the same thing. If critical thinking is conceived more narrowly as consisting solely of appraisal of intellectual products, then it will be disjoint with problem solving and decision making, which are constructive.

Bloom’s taxonomy of educational objectives used the phrase “intellectual abilities and skills” for what had been labeled “critical thinking” by some, “reflective thinking” by Dewey and others, and “problem solving” by still others (Bloom et al. 1956: 38). Thus, the so-called “higher-order thinking skills” at the taxonomy’s top levels of analysis, synthesis and evaluation are just critical thinking skills, although they do not come with general criteria for their assessment (Ennis 1981b). The revised version of Bloom’s taxonomy (Anderson et al. 2001) likewise treats critical thinking as cutting across those types of cognitive process that involve more than remembering (Anderson et al. 2001: 269–270). For details, see the Supplement on History .

As to creative thinking, it overlaps with critical thinking (Bailin 1987, 1988). Thinking about the explanation of some phenomenon or event, as in Ferryboat , requires creative imagination in constructing plausible explanatory hypotheses. Likewise, thinking about a policy question, as in Candidate , requires creativity in coming up with options. Conversely, creativity in any field needs to be balanced by critical appraisal of the draft painting or novel or mathematical theory.

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• v.17(1); Spring 2018

Understanding the Complex Relationship between Critical Thinking and Science Reasoning among Undergraduate Thesis Writers

Jason e. dowd.

† Department of Biology, Duke University, Durham, NC 27708

Robert J. Thompson, Jr.

‡ Department of Psychology and Neuroscience, Duke University, Durham, NC 27708

Leslie A. Schiff

§ Department of Microbiology and Immunology, University of Minnesota, Minneapolis, MN 55455

Julie A. Reynolds

Associated data.

This study empirically examines the relationship between students’ critical-thinking skills and scientific reasoning as reflected in undergraduate thesis writing in biology. Writing offers a unique window into studying this relationship, and the findings raise potential implications for instruction.

Developing critical-thinking and scientific reasoning skills are core learning objectives of science education, but little empirical evidence exists regarding the interrelationships between these constructs. Writing effectively fosters students’ development of these constructs, and it offers a unique window into studying how they relate. In this study of undergraduate thesis writing in biology at two universities, we examine how scientific reasoning exhibited in writing (assessed using the Biology Thesis Assessment Protocol) relates to general and specific critical-thinking skills (assessed using the California Critical Thinking Skills Test), and we consider implications for instruction. We find that scientific reasoning in writing is strongly related to inference , while other aspects of science reasoning that emerge in writing (epistemological considerations, writing conventions, etc.) are not significantly related to critical-thinking skills. Science reasoning in writing is not merely a proxy for critical thinking. In linking features of students’ writing to their critical-thinking skills, this study 1) provides a bridge to prior work suggesting that engagement in science writing enhances critical thinking and 2) serves as a foundational step for subsequently determining whether instruction focused explicitly on developing critical-thinking skills (particularly inference ) can actually improve students’ scientific reasoning in their writing.

INTRODUCTION

Critical-thinking and scientific reasoning skills are core learning objectives of science education for all students, regardless of whether or not they intend to pursue a career in science or engineering. Consistent with the view of learning as construction of understanding and meaning ( National Research Council, 2000 ), the pedagogical practice of writing has been found to be effective not only in fostering the development of students’ conceptual and procedural knowledge ( Gerdeman et al. , 2007 ) and communication skills ( Clase et al. , 2010 ), but also scientific reasoning ( Reynolds et al. , 2012 ) and critical-thinking skills ( Quitadamo and Kurtz, 2007 ).

Critical thinking and scientific reasoning are similar but different constructs that include various types of higher-order cognitive processes, metacognitive strategies, and dispositions involved in making meaning of information. Critical thinking is generally understood as the broader construct ( Holyoak and Morrison, 2005 ), comprising an array of cognitive processes and dispostions that are drawn upon differentially in everyday life and across domains of inquiry such as the natural sciences, social sciences, and humanities. Scientific reasoning, then, may be interpreted as the subset of critical-thinking skills (cognitive and metacognitive processes and dispositions) that 1) are involved in making meaning of information in scientific domains and 2) support the epistemological commitment to scientific methodology and paradigm(s).

Although there has been an enduring focus in higher education on promoting critical thinking and reasoning as general or “transferable” skills, research evidence provides increasing support for the view that reasoning and critical thinking are also situational or domain specific ( Beyer et al. , 2013 ). Some researchers, such as Lawson (2010) , present frameworks in which science reasoning is characterized explicitly in terms of critical-thinking skills. There are, however, limited coherent frameworks and empirical evidence regarding either the general or domain-specific interrelationships of scientific reasoning, as it is most broadly defined, and critical-thinking skills.

The Vision and Change in Undergraduate Biology Education Initiative provides a framework for thinking about these constructs and their interrelationship in the context of the core competencies and disciplinary practice they describe ( American Association for the Advancement of Science, 2011 ). These learning objectives aim for undergraduates to “understand the process of science, the interdisciplinary nature of the new biology and how science is closely integrated within society; be competent in communication and collaboration; have quantitative competency and a basic ability to interpret data; and have some experience with modeling, simulation and computational and systems level approaches as well as with using large databases” ( Woodin et al. , 2010 , pp. 71–72). This framework makes clear that science reasoning and critical-thinking skills play key roles in major learning outcomes; for example, “understanding the process of science” requires students to engage in (and be metacognitive about) scientific reasoning, and having the “ability to interpret data” requires critical-thinking skills. To help students better achieve these core competencies, we must better understand the interrelationships of their composite parts. Thus, the next step is to determine which specific critical-thinking skills are drawn upon when students engage in science reasoning in general and with regard to the particular scientific domain being studied. Such a determination could be applied to improve science education for both majors and nonmajors through pedagogical approaches that foster critical-thinking skills that are most relevant to science reasoning.

Writing affords one of the most effective means for making thinking visible ( Reynolds et al. , 2012 ) and learning how to “think like” and “write like” disciplinary experts ( Meizlish et al. , 2013 ). As a result, student writing affords the opportunities to both foster and examine the interrelationship of scientific reasoning and critical-thinking skills within and across disciplinary contexts. The purpose of this study was to better understand the relationship between students’ critical-thinking skills and scientific reasoning skills as reflected in the genre of undergraduate thesis writing in biology departments at two research universities, the University of Minnesota and Duke University.

In the following subsections, we discuss in greater detail the constructs of scientific reasoning and critical thinking, as well as the assessment of scientific reasoning in students’ thesis writing. In subsequent sections, we discuss our study design, findings, and the implications for enhancing educational practices.

Critical Thinking

The advances in cognitive science in the 21st century have increased our understanding of the mental processes involved in thinking and reasoning, as well as memory, learning, and problem solving. Critical thinking is understood to include both a cognitive dimension and a disposition dimension (e.g., reflective thinking) and is defined as “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” ( Facione, 1990, p. 3 ). Although various other definitions of critical thinking have been proposed, researchers have generally coalesced on this consensus: expert view ( Blattner and Frazier, 2002 ; Condon and Kelly-Riley, 2004 ; Bissell and Lemons, 2006 ; Quitadamo and Kurtz, 2007 ) and the corresponding measures of critical-­thinking skills ( August, 2016 ; Stephenson and Sadler-McKnight, 2016 ).

Both the cognitive skills and dispositional components of critical thinking have been recognized as important to science education ( Quitadamo and Kurtz, 2007 ). Empirical research demonstrates that specific pedagogical practices in science courses are effective in fostering students’ critical-thinking skills. Quitadamo and Kurtz (2007) found that students who engaged in a laboratory writing component in the context of a general education biology course significantly improved their overall critical-thinking skills (and their analytical and inference skills, in particular), whereas students engaged in a traditional quiz-based laboratory did not improve their critical-thinking skills. In related work, Quitadamo et al. (2008) found that a community-based inquiry experience, involving inquiry, writing, research, and analysis, was associated with improved critical thinking in a biology course for nonmajors, compared with traditionally taught sections. In both studies, students who exhibited stronger presemester critical-thinking skills exhibited stronger gains, suggesting that “students who have not been explicitly taught how to think critically may not reach the same potential as peers who have been taught these skills” ( Quitadamo and Kurtz, 2007 , p. 151).

Recently, Stephenson and Sadler-McKnight (2016) found that first-year general chemistry students who engaged in a science writing heuristic laboratory, which is an inquiry-based, writing-to-learn approach to instruction ( Hand and Keys, 1999 ), had significantly greater gains in total critical-thinking scores than students who received traditional laboratory instruction. Each of the four components—inquiry, writing, collaboration, and reflection—have been linked to critical thinking ( Stephenson and Sadler-McKnight, 2016 ). Like the other studies, this work highlights the value of targeting critical-thinking skills and the effectiveness of an inquiry-based, writing-to-learn approach to enhance critical thinking. Across studies, authors advocate adopting critical thinking as the course framework ( Pukkila, 2004 ) and developing explicit examples of how critical thinking relates to the scientific method ( Miri et al. , 2007 ).

In these examples, the important connection between writing and critical thinking is highlighted by the fact that each intervention involves the incorporation of writing into science, technology, engineering, and mathematics education (either alone or in combination with other pedagogical practices). However, critical-thinking skills are not always the primary learning outcome; in some contexts, scientific reasoning is the primary outcome that is assessed.

Scientific Reasoning

Scientific reasoning is a complex process that is broadly defined as “the skills involved in inquiry, experimentation, evidence evaluation, and inference that are done in the service of conceptual change or scientific understanding” ( Zimmerman, 2007 , p. 172). Scientific reasoning is understood to include both conceptual knowledge and the cognitive processes involved with generation of hypotheses (i.e., inductive processes involved in the generation of hypotheses and the deductive processes used in the testing of hypotheses), experimentation strategies, and evidence evaluation strategies. These dimensions are interrelated, in that “experimentation and inference strategies are selected based on prior conceptual knowledge of the domain” ( Zimmerman, 2000 , p. 139). Furthermore, conceptual and procedural knowledge and cognitive process dimensions can be general and domain specific (or discipline specific).

With regard to conceptual knowledge, attention has been focused on the acquisition of core methodological concepts fundamental to scientists’ causal reasoning and metacognitive distancing (or decontextualized thinking), which is the ability to reason independently of prior knowledge or beliefs ( Greenhoot et al. , 2004 ). The latter involves what Kuhn and Dean (2004) refer to as the coordination of theory and evidence, which requires that one question existing theories (i.e., prior knowledge and beliefs), seek contradictory evidence, eliminate alternative explanations, and revise one’s prior beliefs in the face of contradictory evidence. Kuhn and colleagues (2008) further elaborate that scientific thinking requires “a mature understanding of the epistemological foundations of science, recognizing scientific knowledge as constructed by humans rather than simply discovered in the world,” and “the ability to engage in skilled argumentation in the scientific domain, with an appreciation of argumentation as entailing the coordination of theory and evidence” ( Kuhn et al. , 2008 , p. 435). “This approach to scientific reasoning not only highlights the skills of generating and evaluating evidence-based inferences, but also encompasses epistemological appreciation of the functions of evidence and theory” ( Ding et al. , 2016 , p. 616). Evaluating evidence-based inferences involves epistemic cognition, which Moshman (2015) defines as the subset of metacognition that is concerned with justification, truth, and associated forms of reasoning. Epistemic cognition is both general and domain specific (or discipline specific; Moshman, 2015 ).

There is empirical support for the contributions of both prior knowledge and an understanding of the epistemological foundations of science to scientific reasoning. In a study of undergraduate science students, advanced scientific reasoning was most often accompanied by accurate prior knowledge as well as sophisticated epistemological commitments; additionally, for students who had comparable levels of prior knowledge, skillful reasoning was associated with a strong epistemological commitment to the consistency of theory with evidence ( Zeineddin and Abd-El-Khalick, 2010 ). These findings highlight the importance of the need for instructional activities that intentionally help learners develop sophisticated epistemological commitments focused on the nature of knowledge and the role of evidence in supporting knowledge claims ( Zeineddin and Abd-El-Khalick, 2010 ).

Scientific Reasoning in Students’ Thesis Writing

Pedagogical approaches that incorporate writing have also focused on enhancing scientific reasoning. Many rubrics have been developed to assess aspects of scientific reasoning in written artifacts. For example, Timmerman and colleagues (2011) , in the course of describing their own rubric for assessing scientific reasoning, highlight several examples of scientific reasoning assessment criteria ( Haaga, 1993 ; Tariq et al. , 1998 ; Topping et al. , 2000 ; Kelly and Takao, 2002 ; Halonen et al. , 2003 ; Willison and O’Regan, 2007 ).

At both the University of Minnesota and Duke University, we have focused on the genre of the undergraduate honors thesis as the rhetorical context in which to study and improve students’ scientific reasoning and writing. We view the process of writing an undergraduate honors thesis as a form of professional development in the sciences (i.e., a way of engaging students in the practices of a community of discourse). We have found that structured courses designed to scaffold the thesis-­writing process and promote metacognition can improve writing and reasoning skills in biology, chemistry, and economics ( Reynolds and Thompson, 2011 ; Dowd et al. , 2015a , b ). In the context of this prior work, we have defined scientific reasoning in writing as the emergent, underlying construct measured across distinct aspects of students’ written discussion of independent research in their undergraduate theses.

The Biology Thesis Assessment Protocol (BioTAP) was developed at Duke University as a tool for systematically guiding students and faculty through a “draft–feedback–revision” writing process, modeled after professional scientific peer-review processes ( Reynolds et al. , 2009 ). BioTAP includes activities and worksheets that allow students to engage in critical peer review and provides detailed descriptions, presented as rubrics, of the questions (i.e., dimensions, shown in Table 1 ) upon which such review should focus. Nine rubric dimensions focus on communication to the broader scientific community, and four rubric dimensions focus on the accuracy and appropriateness of the research. These rubric dimensions provide criteria by which the thesis is assessed, and therefore allow BioTAP to be used as an assessment tool as well as a teaching resource ( Reynolds et al. , 2009 ). Full details are available at www.science-writing.org/biotap.html .

Theses assessment protocol dimensions

In previous work, we have used BioTAP to quantitatively assess students’ undergraduate honors theses and explore the relationship between thesis-writing courses (or specific interventions within the courses) and the strength of students’ science reasoning in writing across different science disciplines: biology ( Reynolds and Thompson, 2011 ); chemistry ( Dowd et al. , 2015b ); and economics ( Dowd et al. , 2015a ). We have focused exclusively on the nine dimensions related to reasoning and writing (questions 1–9), as the other four dimensions (questions 10–13) require topic-specific expertise and are intended to be used by the student’s thesis supervisor.

Beyond considering individual dimensions, we have investigated whether meaningful constructs underlie students’ thesis scores. We conducted exploratory factor analysis of students’ theses in biology, economics, and chemistry and found one dominant underlying factor in each discipline; we termed the factor “scientific reasoning in writing” ( Dowd et al. , 2015a , b , 2016 ). That is, each of the nine dimensions could be understood as reflecting, in different ways and to different degrees, the construct of scientific reasoning in writing. The findings indicated evidence of both general and discipline-specific components to scientific reasoning in writing that relate to epistemic beliefs and paradigms, in keeping with broader ideas about science reasoning discussed earlier. Specifically, scientific reasoning in writing is more strongly associated with formulating a compelling argument for the significance of the research in the context of current literature in biology, making meaning regarding the implications of the findings in chemistry, and providing an organizational framework for interpreting the thesis in economics. We suggested that instruction, whether occurring in writing studios or in writing courses to facilitate thesis preparation, should attend to both components.

Research Question and Study Design

The genre of thesis writing combines the pedagogies of writing and inquiry found to foster scientific reasoning ( Reynolds et al. , 2012 ) and critical thinking ( Quitadamo and Kurtz, 2007 ; Quitadamo et al. , 2008 ; Stephenson and Sadler-­McKnight, 2016 ). However, there is no empirical evidence regarding the general or domain-specific interrelationships of scientific reasoning and critical-thinking skills, particularly in the rhetorical context of the undergraduate thesis. The BioTAP studies discussed earlier indicate that the rubric-based assessment produces evidence of scientific reasoning in the undergraduate thesis, but it was not designed to foster or measure critical thinking. The current study was undertaken to address the research question: How are students’ critical-thinking skills related to scientific reasoning as reflected in the genre of undergraduate thesis writing in biology? Determining these interrelationships could guide efforts to enhance students’ scientific reasoning and writing skills through focusing instruction on specific critical-thinking skills as well as disciplinary conventions.

To address this research question, we focused on undergraduate thesis writers in biology courses at two institutions, Duke University and the University of Minnesota, and examined the extent to which students’ scientific reasoning in writing, assessed in the undergraduate thesis using BioTAP, corresponds to students’ critical-thinking skills, assessed using the California Critical Thinking Skills Test (CCTST; August, 2016 ).

Study Sample

The study sample was composed of students enrolled in courses designed to scaffold the thesis-writing process in the Department of Biology at Duke University and the College of Biological Sciences at the University of Minnesota. Both courses complement students’ individual work with research advisors. The course is required for thesis writers at the University of Minnesota and optional for writers at Duke University. Not all students are required to complete a thesis, though it is required for students to graduate with honors; at the University of Minnesota, such students are enrolled in an honors program within the college. In total, 28 students were enrolled in the course at Duke University and 44 students were enrolled in the course at the University of Minnesota. Of those students, two students did not consent to participate in the study; additionally, five students did not validly complete the CCTST (i.e., attempted fewer than 60% of items or completed the test in less than 15 minutes). Thus, our overall rate of valid participation is 90%, with 27 students from Duke University and 38 students from the University of Minnesota. We found no statistically significant differences in thesis assessment between students with valid CCTST scores and invalid CCTST scores. Therefore, we focus on the 65 students who consented to participate and for whom we have complete and valid data in most of this study. Additionally, in asking students for their consent to participate, we allowed them to choose whether to provide or decline access to academic and demographic background data. Of the 65 students who consented to participate, 52 students granted access to such data. Therefore, for additional analyses involving academic and background data, we focus on the 52 students who consented. We note that the 13 students who participated but declined to share additional data performed slightly lower on the CCTST than the 52 others (perhaps suggesting that they differ by other measures, but we cannot determine this with certainty). Among the 52 students, 60% identified as female and 10% identified as being from underrepresented ethnicities.

In both courses, students completed the CCTST online, either in class or on their own, late in the Spring 2016 semester. This is the same assessment that was used in prior studies of critical thinking ( Quitadamo and Kurtz, 2007 ; Quitadamo et al. , 2008 ; Stephenson and Sadler-McKnight, 2016 ). It is “an objective measure of the core reasoning skills needed for reflective decision making concerning what to believe or what to do” ( Insight Assessment, 2016a ). In the test, students are asked to read and consider information as they answer multiple-choice questions. The questions are intended to be appropriate for all users, so there is no expectation of prior disciplinary knowledge in biology (or any other subject). Although actual test items are protected, sample items are available on the Insight Assessment website ( Insight Assessment, 2016b ). We have included one sample item in the Supplemental Material.

The CCTST is based on a consensus definition of critical thinking, measures cognitive and metacognitive skills associated with critical thinking, and has been evaluated for validity and reliability at the college level ( August, 2016 ; Stephenson and Sadler-McKnight, 2016 ). In addition to providing overall critical-thinking score, the CCTST assesses seven dimensions of critical thinking: analysis, interpretation, inference, evaluation, explanation, induction, and deduction. Scores on each dimension are calculated based on students’ performance on items related to that dimension. Analysis focuses on identifying assumptions, reasons, and claims and examining how they interact to form arguments. Interpretation, related to analysis, focuses on determining the precise meaning and significance of information. Inference focuses on drawing conclusions from reasons and evidence. Evaluation focuses on assessing the credibility of sources of information and claims they make. Explanation, related to evaluation, focuses on describing the evidence, assumptions, or rationale for beliefs and conclusions. Induction focuses on drawing inferences about what is probably true based on evidence. Deduction focuses on drawing conclusions about what must be true when the context completely determines the outcome. These are not independent dimensions; the fact that they are related supports their collective interpretation as critical thinking. Together, the CCTST dimensions provide a basis for evaluating students’ overall strength in using reasoning to form reflective judgments about what to believe or what to do ( August, 2016 ). Each of the seven dimensions and the overall CCTST score are measured on a scale of 0–100, where higher scores indicate superior performance. Scores correspond to superior (86–100), strong (79–85), moderate (70–78), weak (63–69), or not manifested (62 and below) skills.

Scientific Reasoning in Writing

At the end of the semester, students’ final, submitted undergraduate theses were assessed using BioTAP, which consists of nine rubric dimensions that focus on communication to the broader scientific community and four additional dimensions that focus on the exhibition of topic-specific expertise ( Reynolds et al. , 2009 ). These dimensions, framed as questions, are displayed in Table 1 .

Student theses were assessed on questions 1–9 of BioTAP using the same procedures described in previous studies ( Reynolds and Thompson, 2011 ; Dowd et al. , 2015a , b ). In this study, six raters were trained in the valid, reliable use of BioTAP rubrics. Each dimension was rated on a five-point scale: 1 indicates the dimension is missing, incomplete, or below acceptable standards; 3 indicates that the dimension is adequate but not exhibiting mastery; and 5 indicates that the dimension is excellent and exhibits mastery (intermediate ratings of 2 and 4 are appropriate when different parts of the thesis make a single category challenging). After training, two raters independently assessed each thesis and then discussed their independent ratings with one another to form a consensus rating. The consensus score is not an average score, but rather an agreed-upon, discussion-based score. On a five-point scale, raters independently assessed dimensions to be within 1 point of each other 82.4% of the time before discussion and formed consensus ratings 100% of the time after discussion.

In this study, we consider both categorical (mastery/nonmastery, where a score of 5 corresponds to mastery) and numerical treatments of individual BioTAP scores to better relate the manifestation of critical thinking in BioTAP assessment to all of the prior studies. For comprehensive/cumulative measures of BioTAP, we focus on the partial sum of questions 1–5, as these questions relate to higher-order scientific reasoning (whereas questions 6–9 relate to mid- and lower-order writing mechanics [ Reynolds et al. , 2009 ]), and the factor scores (i.e., numerical representations of the extent to which each student exhibits the underlying factor), which are calculated from the factor loadings published by Dowd et al. (2016) . We do not focus on questions 6–9 individually in statistical analyses, because we do not expect critical-thinking skills to relate to mid- and lower-order writing skills.

The final, submitted thesis reflects the student’s writing, the student’s scientific reasoning, the quality of feedback provided to the student by peers and mentors, and the student’s ability to incorporate that feedback into his or her work. Therefore, our assessment is not the same as an assessment of unpolished, unrevised samples of students’ written work. While one might imagine that such an unpolished sample may be more strongly correlated with critical-thinking skills measured by the CCTST, we argue that the complete, submitted thesis, assessed using BioTAP, is ultimately a more appropriate reflection of how students exhibit science reasoning in the scientific community.

Statistical Analyses

We took several steps to analyze the collected data. First, to provide context for subsequent interpretations, we generated descriptive statistics for the CCTST scores of the participants based on the norms for undergraduate CCTST test takers. To determine the strength of relationships among CCTST dimensions (including overall score) and the BioTAP dimensions, partial-sum score (questions 1–5), and factor score, we calculated Pearson’s correlations for each pair of measures. To examine whether falling on one side of the nonmastery/mastery threshold (as opposed to a linear scale of performance) was related to critical thinking, we grouped BioTAP dimensions into categories (mastery/nonmastery) and conducted Student’s t tests to compare the means scores of the two groups on each of the seven dimensions and overall score of the CCTST. Finally, for the strongest relationship that emerged, we included additional academic and background variables as covariates in multiple linear-regression analysis to explore questions about how much observed relationships between critical-thinking skills and science reasoning in writing might be explained by variation in these other factors.

Although BioTAP scores represent discreet, ordinal bins, the five-point scale is intended to capture an underlying continuous construct (from inadequate to exhibiting mastery). It has been argued that five categories is an appropriate cutoff for treating ordinal variables as pseudo-continuous ( Rhemtulla et al. , 2012 )—and therefore using continuous-variable statistical methods (e.g., Pearson’s correlations)—as long as the underlying assumption that ordinal scores are linearly distributed is valid. Although we have no way to statistically test this assumption, we interpret adequate scores to be approximately halfway between inadequate and mastery scores, resulting in a linear scale. In part because this assumption is subject to disagreement, we also consider and interpret a categorical (mastery/nonmastery) treatment of BioTAP variables.

We corrected for multiple comparisons using the Holm-Bonferroni method ( Holm, 1979 ). At the most general level, where we consider the single, comprehensive measures for BioTAP (partial-sum and factor score) and the CCTST (overall score), there is no need to correct for multiple comparisons, because the multiple, individual dimensions are collapsed into single dimensions. When we considered individual CCTST dimensions in relation to comprehensive measures for BioTAP, we accounted for seven comparisons; similarly, when we considered individual dimensions of BioTAP in relation to overall CCTST score, we accounted for five comparisons. When all seven CCTST and five BioTAP dimensions were examined individually and without prior knowledge, we accounted for 35 comparisons; such a rigorous threshold is likely to reject weak and moderate relationships, but it is appropriate if there are no specific pre-existing hypotheses. All p values are presented in tables for complete transparency, and we carefully consider the implications of our interpretation of these data in the Discussion section.

CCTST scores for students in this sample ranged from the 39th to 99th percentile of the general population of undergraduate CCTST test takers (mean percentile = 84.3, median = 85th percentile; Table 2 ); these percentiles reflect overall scores that range from moderate to superior. Scores on individual dimensions and overall scores were sufficiently normal and far enough from the ceiling of the scale to justify subsequent statistical analyses.

Descriptive statistics of CCTST dimensions a

a Scores correspond to superior (86–100), strong (79–85), moderate (70–78), weak (63–69), or not manifested (62 and lower) skills.

The Pearson’s correlations between students’ cumulative scores on BioTAP (the factor score based on loadings published by Dowd et al. , 2016 , and the partial sum of scores on questions 1–5) and students’ overall scores on the CCTST are presented in Table 3 . We found that the partial-sum measure of BioTAP was significantly related to the overall measure of critical thinking ( r = 0.27, p = 0.03), while the BioTAP factor score was marginally related to overall CCTST ( r = 0.24, p = 0.05). When we looked at relationships between comprehensive BioTAP measures and scores for individual dimensions of the CCTST ( Table 3 ), we found significant positive correlations between the both BioTAP partial-sum and factor scores and CCTST inference ( r = 0.45, p < 0.001, and r = 0.41, p < 0.001, respectively). Although some other relationships have p values below 0.05 (e.g., the correlations between BioTAP partial-sum scores and CCTST induction and interpretation scores), they are not significant when we correct for multiple comparisons.

Correlations between dimensions of CCTST and dimensions of BioTAP a

a In each cell, the top number is the correlation, and the bottom, italicized number is the associated p value. Correlations that are statistically significant after correcting for multiple comparisons are shown in bold.

b This is the partial sum of BioTAP scores on questions 1–5.

c This is the factor score calculated from factor loadings published by Dowd et al. (2016) .

When we expanded comparisons to include all 35 potential correlations among individual BioTAP and CCTST dimensions—and, accordingly, corrected for 35 comparisons—we did not find any additional statistically significant relationships. The Pearson’s correlations between students’ scores on each dimension of BioTAP and students’ scores on each dimension of the CCTST range from −0.11 to 0.35 ( Table 3 ); although the relationship between discussion of implications (BioTAP question 5) and inference appears to be relatively large ( r = 0.35), it is not significant ( p = 0.005; the Holm-Bonferroni cutoff is 0.00143). We found no statistically significant relationships between BioTAP questions 6–9 and CCTST dimensions (unpublished data), regardless of whether we correct for multiple comparisons.

The results of Student’s t tests comparing scores on each dimension of the CCTST of students who exhibit mastery with those of students who do not exhibit mastery on each dimension of BioTAP are presented in Table 4 . Focusing first on the overall CCTST scores, we found that the difference between those who exhibit mastery and those who do not in discussing implications of results (BioTAP question 5) is statistically significant ( t = 2.73, p = 0.008, d = 0.71). When we expanded t tests to include all 35 comparisons—and, like above, corrected for 35 comparisons—we found a significant difference in inference scores between students who exhibit mastery on question 5 and students who do not ( t = 3.41, p = 0.0012, d = 0.88), as well as a marginally significant difference in these students’ induction scores ( t = 3.26, p = 0.0018, d = 0.84; the Holm-Bonferroni cutoff is p = 0.00147). Cohen’s d effect sizes, which reveal the strength of the differences for statistically significant relationships, range from 0.71 to 0.88.

The t statistics and effect sizes of differences in ­dimensions of CCTST across dimensions of BioTAP a

a In each cell, the top number is the t statistic for each comparison, and the middle, italicized number is the associated p value. The bottom number is the effect size. Correlations that are statistically significant after correcting for multiple comparisons are shown in bold.

Finally, we more closely examined the strongest relationship that we observed, which was between the CCTST dimension of inference and the BioTAP partial-sum composite score (shown in Table 3 ), using multiple regression analysis ( Table 5 ). Focusing on the 52 students for whom we have background information, we looked at the simple relationship between BioTAP and inference (model 1), a robust background model including multiple covariates that one might expect to explain some part of the variation in BioTAP (model 2), and a combined model including all variables (model 3). As model 3 shows, the covariates explain very little variation in BioTAP scores, and the relationship between inference and BioTAP persists even in the presence of all of the covariates.

Partial sum (questions 1–5) of BioTAP scores ( n = 52)

** p < 0.01.

*** p < 0.001.

The aim of this study was to examine the extent to which the various components of scientific reasoning—manifested in writing in the genre of undergraduate thesis and assessed using BioTAP—draw on general and specific critical-thinking skills (assessed using CCTST) and to consider the implications for educational practices. Although science reasoning involves critical-thinking skills, it also relates to conceptual knowledge and the epistemological foundations of science disciplines ( Kuhn et al. , 2008 ). Moreover, science reasoning in writing , captured in students’ undergraduate theses, reflects habits, conventions, and the incorporation of feedback that may alter evidence of individuals’ critical-thinking skills. Our findings, however, provide empirical evidence that cumulative measures of science reasoning in writing are nonetheless related to students’ overall critical-thinking skills ( Table 3 ). The particularly significant roles of inference skills ( Table 3 ) and the discussion of implications of results (BioTAP question 5; Table 4 ) provide a basis for more specific ideas about how these constructs relate to one another and what educational interventions may have the most success in fostering these skills.

Our results build on previous findings. The genre of thesis writing combines pedagogies of writing and inquiry found to foster scientific reasoning ( Reynolds et al. , 2012 ) and critical thinking ( Quitadamo and Kurtz, 2007 ; Quitadamo et al. , 2008 ; Stephenson and Sadler-McKnight, 2016 ). Quitadamo and Kurtz (2007) reported that students who engaged in a laboratory writing component in a general education biology course significantly improved their inference and analysis skills, and Quitadamo and colleagues (2008) found that participation in a community-based inquiry biology course (that included a writing component) was associated with significant gains in students’ inference and evaluation skills. The shared focus on inference is noteworthy, because these prior studies actually differ from the current study; the former considered critical-­thinking skills as the primary learning outcome of writing-­focused interventions, whereas the latter focused on emergent links between two learning outcomes (science reasoning in writing and critical thinking). In other words, inference skills are impacted by writing as well as manifested in writing.

Inference focuses on drawing conclusions from argument and evidence. According to the consensus definition of critical thinking, the specific skill of inference includes several processes: querying evidence, conjecturing alternatives, and drawing conclusions. All of these activities are central to the independent research at the core of writing an undergraduate thesis. Indeed, a critical part of what we call “science reasoning in writing” might be characterized as a measure of students’ ability to infer and make meaning of information and findings. Because the cumulative BioTAP measures distill underlying similarities and, to an extent, suppress unique aspects of individual dimensions, we argue that it is appropriate to relate inference to scientific reasoning in writing . Even when we control for other potentially relevant background characteristics, the relationship is strong ( Table 5 ).

In taking the complementary view and focusing on BioTAP, when we compared students who exhibit mastery with those who do not, we found that the specific dimension of “discussing the implications of results” (question 5) differentiates students’ performance on several critical-thinking skills. To achieve mastery on this dimension, students must make connections between their results and other published studies and discuss the future directions of the research; in short, they must demonstrate an understanding of the bigger picture. The specific relationship between question 5 and inference is the strongest observed among all individual comparisons. Altogether, perhaps more than any other BioTAP dimension, this aspect of students’ writing provides a clear view of the role of students’ critical-thinking skills (particularly inference and, marginally, induction) in science reasoning.

While inference and discussion of implications emerge as particularly strongly related dimensions in this work, we note that the strongest contribution to “science reasoning in writing in biology,” as determined through exploratory factor analysis, is “argument for the significance of research” (BioTAP question 2, not question 5; Dowd et al. , 2016 ). Question 2 is not clearly related to critical-thinking skills. These findings are not contradictory, but rather suggest that the epistemological and disciplinary-specific aspects of science reasoning that emerge in writing through BioTAP are not completely aligned with aspects related to critical thinking. In other words, science reasoning in writing is not simply a proxy for those critical-thinking skills that play a role in science reasoning.

In a similar vein, the content-related, epistemological aspects of science reasoning, as well as the conventions associated with writing the undergraduate thesis (including feedback from peers and revision), may explain the lack of significant relationships between some science reasoning dimensions and some critical-thinking skills that might otherwise seem counterintuitive (e.g., BioTAP question 2, which relates to making an argument, and the critical-thinking skill of argument). It is possible that an individual’s critical-thinking skills may explain some variation in a particular BioTAP dimension, but other aspects of science reasoning and practice exert much stronger influence. Although these relationships do not emerge in our analyses, the lack of significant correlation does not mean that there is definitively no correlation. Correcting for multiple comparisons suppresses type 1 error at the expense of exacerbating type 2 error, which, combined with the limited sample size, constrains statistical power and makes weak relationships more difficult to detect. Ultimately, though, the relationships that do emerge highlight places where individuals’ distinct critical-thinking skills emerge most coherently in thesis assessment, which is why we are particularly interested in unpacking those relationships.

We recognize that, because only honors students submit theses at these institutions, this study sample is composed of a selective subset of the larger population of biology majors. Although this is an inherent limitation of focusing on thesis writing, links between our findings and results of other studies (with different populations) suggest that observed relationships may occur more broadly. The goal of improved science reasoning and critical thinking is shared among all biology majors, particularly those engaged in capstone research experiences. So while the implications of this work most directly apply to honors thesis writers, we provisionally suggest that all students could benefit from further study of them.

There are several important implications of this study for science education practices. Students’ inference skills relate to the understanding and effective application of scientific content. The fact that we find no statistically significant relationships between BioTAP questions 6–9 and CCTST dimensions suggests that such mid- to lower-order elements of BioTAP ( Reynolds et al. , 2009 ), which tend to be more structural in nature, do not focus on aspects of the finished thesis that draw strongly on critical thinking. In keeping with prior analyses ( Reynolds and Thompson, 2011 ; Dowd et al. , 2016 ), these findings further reinforce the notion that disciplinary instructors, who are most capable of teaching and assessing scientific reasoning and perhaps least interested in the more mechanical aspects of writing, may nonetheless be best suited to effectively model and assess students’ writing.

The goal of the thesis writing course at both Duke University and the University of Minnesota is not merely to improve thesis scores but to move students’ writing into the category of mastery across BioTAP dimensions. Recognizing that students with differing critical-thinking skills (particularly inference) are more or less likely to achieve mastery in the undergraduate thesis (particularly in discussing implications [question 5]) is important for developing and testing targeted pedagogical interventions to improve learning outcomes for all students.

The competencies characterized by the Vision and Change in Undergraduate Biology Education Initiative provide a general framework for recognizing that science reasoning and critical-thinking skills play key roles in major learning outcomes of science education. Our findings highlight places where science reasoning–related competencies (like “understanding the process of science”) connect to critical-thinking skills and places where critical thinking–related competencies might be manifested in scientific products (such as the ability to discuss implications in scientific writing). We encourage broader efforts to build empirical connections between competencies and pedagogical practices to further improve science education.

One specific implication of this work for science education is to focus on providing opportunities for students to develop their critical-thinking skills (particularly inference). Of course, as this correlational study is not designed to test causality, we do not claim that enhancing students’ inference skills will improve science reasoning in writing. However, as prior work shows that science writing activities influence students’ inference skills ( Quitadamo and Kurtz, 2007 ; Quitadamo et al. , 2008 ), there is reason to test such a hypothesis. Nevertheless, the focus must extend beyond inference as an isolated skill; rather, it is important to relate inference to the foundations of the scientific method ( Miri et al. , 2007 ) in terms of the epistemological appreciation of the functions and coordination of evidence ( Kuhn and Dean, 2004 ; Zeineddin and Abd-El-Khalick, 2010 ; Ding et al. , 2016 ) and disciplinary paradigms of truth and justification ( Moshman, 2015 ).

Although this study is limited to the domain of biology at two institutions with a relatively small number of students, the findings represent a foundational step in the direction of achieving success with more integrated learning outcomes. Hopefully, it will spur greater interest in empirically grounding discussions of the constructs of scientific reasoning and critical-thinking skills.

This study contributes to the efforts to improve science education, for both majors and nonmajors, through an empirically driven analysis of the relationships between scientific reasoning reflected in the genre of thesis writing and critical-thinking skills. This work is rooted in the usefulness of BioTAP as a method 1) to facilitate communication and learning and 2) to assess disciplinary-specific and general dimensions of science reasoning. The findings support the important role of the critical-thinking skill of inference in scientific reasoning in writing, while also highlighting ways in which other aspects of science reasoning (epistemological considerations, writing conventions, etc.) are not significantly related to critical thinking. Future research into the impact of interventions focused on specific critical-thinking skills (i.e., inference) for improved science reasoning in writing will build on this work and its implications for science education.

Supplementary Material

Acknowledgments.

We acknowledge the contributions of Kelaine Haas and Alexander Motten to the implementation and collection of data. We also thank Mine Çetinkaya-­Rundel for her insights regarding our statistical analyses. This research was funded by National Science Foundation award DUE-1525602.

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The Peak Performance Center

The pursuit of performance excellence, critical thinking.

Critical thinking refers to the process of actively analyzing, assessing, synthesizing, evaluating and reflecting on information gathered from observation, experience, or communication. It is thinking in a clear, logical, reasoned, and reflective manner to solve problems or make decisions. Basically, critical thinking is taking a hard look at something to understand what it really means.

Critical Thinkers

Critical thinkers do not simply accept all ideas, theories, and conclusions as facts. They have a mindset of questioning ideas and conclusions. They make reasoned judgments that are logical and well thought out by assessing the evidence that supports a specific theory or conclusion.

When presented with a new piece of new information, critical thinkers may ask questions such as;

“What information supports that?”

“How was this information obtained?”

“Who obtained the information?”

“How do we know the information is valid?”

“Why is it that way?”

“What makes it do that?”

“How do we know that?”

“Are there other possibilities?”

Combination of Analytical and Creative Thinking

Many people perceive critical thinking just as analytical thinking. However, critical thinking incorporates both analytical thinking and creative thinking. Critical thinking does involve breaking down information into parts and analyzing the parts in a logical, step-by-step manner. However, it also involves challenging consensus to formulate new creative ideas and generate innovative solutions. It is critical thinking that helps to evaluate and improve your creative ideas.

Elements of Critical Thinking

Critical thinking involves:

• Gathering relevant information
• Evaluating information
• Asking questions
• Assessing bias or unsubstantiated assumptions
• Making inferences from the information and filling in gaps
• Using abstract ideas to interpret information
• Formulating ideas
• Weighing opinions
• Reaching well-reasoned conclusions
• Considering alternative possibilities
• Testing conclusions
• Verifying if evidence/argument support the conclusions

Developing Critical Thinking Skills

Critical thinking is considered a higher order thinking skills, such as analysis, synthesis, deduction, inference, reason, and evaluation. In order to demonstrate critical thinking, you would need to develop skills in;

Interpreting : understanding the significance or meaning of information

Analyzing : breaking information down into its parts

Connecting : making connections between related items or pieces of information.

Integrating : connecting and combining information to better understand the relationship between the information.

Evaluating : judging the value, credibility, or strength of something

Reasoning : creating an argument through logical steps

Deducing : forming a logical opinion about something based on the information or evidence that is available

Inferring : figuring something out through reasoning based on assumptions and ideas

Generating : producing new information, ideas, products, or ways of viewing things.

Blooms Taxonomy

Bloom’s Taxonomy Revised

Mind Mapping

Chunking Information

Brainstorming

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Search catalog, critical thinking and academic research: assumptions.

• Information
• Point of View
• Assumptions
• Implications

Question Assumptions

An assumption is an unexamined belief: what we think without realizing we think it. Our inferences (also called conclusions) are often based on assumptions that we haven't thought about critically. A critical thinker, however, is attentive to these assumptions because they are sometimes incorrect or misguided. Just because we assume something is true doesn't mean it is.

Think carefully about your assumptions when finding and analyzing information but also think carefully about the assumptions of others. Whether you're looking at a website or a scholarly article, you should always consider the author's assumptions. Are the author's conclusions based on assumptions that she or he hasn't thought about logically?

Critical Questions

• What am I taking for granted?
• Am I assuming something I shouldn't?
• How can I determine whether this assumption is accurate?
• What is this author assuming?
• How can I determine if this author's assumptions are accurate?

Consider the following situations, then respond to these questions:

• Do you agree or disagree with the inference/conclusion? Why or why not?
• What assumption(s) may have led to the inference/conclusion?
• What are some alternative ways of thinking about this situation?

Situation #1

Bill needs six scholarly articles for his paper on the psychological effects of domestic violence. He searches Google for "psychological effects of domestic violence," looks through the first few hits, and finds six sources, including some articles on the websites of legitimate organizations. A few of these articles include bibliographies.

• Bill's Inference/Conclusion: I'm going to stop researching because I have my six sources.

Situation #2

Christie is researching representations of gender in popular music. She decides to search Google and, within a few minutes, locates more sources that she could possibly incorporate into her final paper.

• Christie's Inference/Conclusion: I can just use Google for my research.

Situation #3

Jennifer has decided to write her literary analysis paper on drug use in David Foster Wallace's novel, Infinite Jest (1996). She tries a few Google searches for Infinite Jest, drugs, and drug use, but she has trouble finding scholarly sources. She gives up on Google and moves on to EBSCO Academic Search Premier, one of the databases she heard about in a library instruction class. She runs a search for Infinite Jest and drug use, but she still can't find much.

• Jennifer's Inference/Conclusion: I need to change my topic.
• << Previous: Inferences
• Next: Implications >>
• Last Updated: Jul 10, 2023 11:50 AM
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What Is an Inference? Definition & 10+ Examples

Have you ever predicted the end of a thrilling mystery novel, or gauged a friend’s mood from a text? Believe it or not, you’re exercising a key cognitive process known as inference — a mental process through which people draw conclusions based on evidence, reasoning, and logic.

Inference is invaluable, permeating various fields like science, literature, and communication. It guides us in analyzing situations and making educated guesses, particularly when the full picture isn’t clear, thus facilitating more informed decisions.

The study of inference not only refines one’s cognitive skills but also increases overall awareness and adaptability. With numerous real-world applications and theoretical frameworks, this fascinating topic provides a foundation for understanding human behavior and logical thought processes.

Let’s take a closer look:

Table of Contents

What Is an Inference?

An inference is a mental process by which individuals draw conclusions from available information. It is a fundamental aspect of human reasoning, allowing us to make sense of the world around us.

Inferences are often made through critical thinking or the application of logic, based on evidence and prior knowledge. While inferences can sometimes be incorrect, they are essential for understanding new information within the context of our existing understanding.

Inference differs from assumptions, predictions, and observations in several ways:

• Assumption: Assumptions are pre-existing beliefs or expectations without supporting evidence. While forming the basis for inferences, assumptions are not always grounded in evidence.
• Prediction: A prediction is a future-oriented statement based on current knowledge and trends. While inferences can guide predictions, predictions speculate about future events, unlike inferences that draw conclusions from current information.
• Observation: Observations describe phenomena experienced through our senses, serving as raw material for inferences. They are objective, providing necessary information without offering conclusions, unlike inferences.

The Inference Development Process

Step 1: observation and evidence collection.

The inference development process begins with observation . During this stage, an individual or scientist gathers relevant data and information to identify patterns and variables.

Evidence collection is crucial in this step and can be done through various methods, such as surveys, experiments, or existing data sources. This phase allows individuals to form a strong foundation in their scientific or logical inquiry.

Step 2: Interpreting Patterns and Instances

Once the data and evidence have been collected, the next step is to interpret patterns and instances . This stage involves analyzing the information to recognize relationships among variables, patterns, and instances.

Through critical thinking and analysis, individuals can draw connections between observed events and their potential causes or outcomes. This helps in narrowing down the focus of the inquiry and identifying the most relevant variables to consider.

Step 3: Forming a Conclusion or Educated Guess

The final step of the inference development process is to form a conclusion or educated guess based on the observations and interpretations made in the previous steps.

This is where individuals synthesize their findings into a logical, coherent statement that offers a possible explanation or prediction for the observed phenomena.

In science, this often results in the creation of a hypothesis, which can be further tested and refined through additional research and experimentation.

The inference development process is a fundamental aspect of scientific investigation. Accurate observations, thorough evidence collection, and careful interpretation of patterns and instances contribute to forming informed conclusions or educated guesses.

Inside the Human Mind: The Process of Making Inferences

Inference is the process of drawing conclusions based on available information. It is an essential part of human cognition and plays a crucial role in decision-making, problem-solving, and understanding new concepts.

The cognitive process of making inferences involves several mental activities, such as:

When a person encounters new information, they pay attention to it and process it through their mental filters. This involves comparing the new information with the existing knowledge stored in their long-term memory.

The person then applies reasoning skills to evaluate the various connections formed between the new information and the existing knowledge.

The Role of Prior Knowledge and Information From Our Environment

A crucial factor that impacts the process of making inferences is the individual’s prior knowledge. Prior knowledge serves as a foundation on which new information is organized and interconnected. It also helps in generating hypotheses and predictions while making inferences.

Information from our environment also plays a vital role in the process of making inferences. This information helps us to make connections and develop relevant conclusions based on the given data.

Environmental factors can significantly influence the quality and accuracy of inferences.

Example : If someone has limited exposure to a specific topic, their ability to make inferences may be hindered. In such cases, external resources such as books, experts, or online resources can help improve the process by providing access to the necessary information.

Types of Inference: Mapping the Inference Landscape

In this section, we will explore three main types of inference. Each type has its unique characteristics and is essential in different contexts:

Inductive Reasoning

Inductive reasoning draws general conclusions from specific observations, seeking patterns or trends. However, these conclusions may sometimes be inaccurate due to limited data or observations.

• Deductive Inference

Deductive inference reaches a specific conclusion from general premises or principles, following a logical structure. If the premises are true and the logic is valid, the conclusion must be true.

• Abductive Inference

Abductive inference forms the most plausible explanation based on available evidence, often viewed as educated guesswork. It’s commonly used in investigative fields like medical diagnosis, detective work, and scientific research.

In summary, inductive reasoning, deductive inference, and abductive inference are three critical types of inference. Each serves a distinct purpose and aids in problem-solving, decision-making, and hypothesis-forming.

Deductive Inference: Specific Conclusions from Generals

Deductive inference is a form of logical reasoning where a conclusion is reached based on two or more given premises. The process follows a specific set of rules that determine the validity of an argument.

In the context of deductive inference, a valid argument is one in which the conclusion must be true if the premises are also true.

Deductive inferences are often represented using syllogisms , which are logical statements consisting of a major premise, a minor premise, and a conclusion. For example:

• Major premise : All humans are mammals.
• Minor premise : John is a human.
• Conclusion : John is a mammal.

If the premises in a deductive inference are true, and the logical structure is valid, then the conclusion must also be true. This type of reasoning is, therefore, considered highly reliable and certain.

Deductive Inference in Action

Consider the following real-life application of deductive inference in medical diagnosis:

In this case, the doctor is using deductive reasoning to predict a possible outcome based on the information available.

By comparing Jane’s condition (high blood pressure) to the broader understanding of the effects of high blood pressure, the doctor can make a valid inference about her likelihood of experiencing frequent headaches.

Inductive Inference: Generalizing from Observations

Inductive inference is a method of reasoning used to draw general conclusions based on observations, patterns, or specific instances. It involves looking at specific information and making a broader prediction or hypothesis.

Inductive reasoning is probabilistic , meaning conclusions drawn are based on the probability of an event occurring rather than being absolute.

For example, if a person observes several instances of dogs having fur and concludes that all dogs have fur, they are utilizing inductive reasoning. This type of inference is commonly used in everyday life, scientific research, and various fields of study.

It is important to note that inductive inference is not foolproof . Even when a pattern holds in all observed cases, it may not hold universally. Though often accurate, conclusions drawn from inductive reasoning come with various degrees of uncertainty.

Inductive Inference in Action

Consider a meteorologist who wants to predict the weather for tomorrow using inductive inference. They gather data on several weeks of weather patterns, paying attention to daily temperatures, humidity, and wind patterns.

The meteorologist notices that over the past few weeks, on days when the humidity has been above 70% and the wind is coming from the east, there has been rain 80% of the time. They also note that the current wind direction is from the east and humidity is above 70%.

The meteorologist then concludes, using inductive reasoning, that there is an 80% chance it will rain tomorrow.

In this example, the meteorologist used historical data and observed patterns to make a probability-based prediction about future events. Although the prediction is not guaranteed to be accurate, it is an application of inductive inference in a real-life situation.

Abductive Inference: Educated Guesswork Explanation

Abductive inference, frequently referred to as abduction, is a form of logical reasoning used to arrive at the most plausible explanation for an observed phenomenon. It involves assessing various hypotheses and selecting one that best fits the available evidence.

Unlike deductive reasoning, which ensures a definite conclusion, abductive reasoning only produces a likely explanation as it deals with incomplete information.

Abductive inference is often used in the following situations:

• When the evidence does not conclusively point to a single explanation.
• When some background knowledge is available, but not enough to logically deduce the only possible conclusion.
• When a fast or initial assessment is needed to decide on a course of action.

Abductive Inference in Action

Consider a detective investigating a crime scene. They observe the following:

• Broken window
• Footprints leading away from the scene
• A missing item

The detective comes up with possible explanations to explain the phenomenon:

• A burglar broke into the house, stole something, and left through the window.
• A homeowner accidentally broke the window and went outside to check the damage.
• A visitor entered the house through the broken window, unaware that it was closed.

To determine which explanation is the most probable, the detective assesses each hypothesis using the available evidence and their background knowledge of typical criminal behavior. They may also consider elements such as the time of day , the location of the house , and the financial value of the missing item.

Based on the gathered information, the detective would likely decide that the first hypothesis is the most plausible explanation for the crime scene’s observed state.

Note that while abductive reasoning cannot guarantee the explanation is correct, it serves as a guide for the detective to take the necessary steps in their investigation.

Examples of Inference

In everyday situations.

Making inferences is a part of daily life. People regularly draw conclusions based on observations and information.

• If a person notices their colleague wearing a heavy coat and carrying an umbrella, they may infer it is cold and rainy outside.
• In another case, if a friend seems detached or disinterested during a conversation, one might conclude that the friend is preoccupied or stressed without explicitly knowing the reason.

In Logical Puzzles

Inferences are often utilized in solving logical puzzles. For instance, consider the classic problem:

• Premise 1: All humans are mortal.
• Premise 2: Socrates is human.
• Conclusion: Socrates is mortal.

This is an example of deductive reasoning , where one starts with general premises and reaches a specific conclusion by applying logical rules. Logical puzzles often require a combination of inferences to arrive at the correct solution.

Other Examples of Inference

Deductive Reasoning

• All men are mortal.
• John is a man.
• Therefore, John is mortal.
• The sun has risen every day throughout history.
• Therefore, the sun will rise tomorrow.

Abductive Reasoning

• The lawn is wet.
• It must have rained last night.

The Power of Inference: Its Role Across Different Fields

Inference in literature and fiction.

Inference plays a crucial role in literature and fiction, as it helps readers draw conclusions about a story’s characters, settings, and plot. By providing hints and clues within the context of the narrative, authors invite their audience to interpret and make sense of the story.

These pieces of evidence can be subtle, such as a character’s choice of words or actions, or more explicit, like descriptions of the setting. As readers, we rely on our ability to infer to grasp the underlying themes and messages of a literary work.

Inference in Logic and Philosophy

In the realm of logic and philosophy, inference serves as a fundamental thinking process, helping individuals draw conclusions based on available evidence or premises.

Syllogisms are classic examples of valid inferences in formal logic. They consist of two premises and a conclusion, illustrating the relationships between entities. For example:

• All humans are mortal.
• Socrates is a human.
• Therefore, Socrates is mortal.

This application of inference in logic and philosophy allows for the creation and evaluation of sound arguments and rational opinions.

Inference in Science

Scientific inquiry heavily relies on inference to formulate hypotheses, evaluate data, and make predictions. In this field, observers use available information and prior knowledge to advance our understanding of the natural world:

• They analyze experimental data.
• They develop models.
• They propose explanations for observed phenomena.

These conclusions often lead to further experimentation, demonstrating the iterative process of inference in scientific endeavors.

Inference in Mathematics

In mathematics, inference refers to the process of deducing properties and relationships from given information. Mathematicians use logical reasoning skills to deduce new theorems or statements based on established axioms and previous findings.

This process of inference bridges the gap between discrete pieces of data, helping to develop a coherent and consistent mathematical framework.

Inference in Artificial Intelligence

Artificial intelligence (AI) utilizes inference techniques to process and analyze vast amounts of data, draw conclusions, and make predictions or recommendations.

Machine learning algorithms, a subset of AI, learn to recognize patterns and trends in the data through training, leading to improved performance over time. This ability to infer relationships and structures from data enables AI systems to tackle complex tasks, such as:

• Natural language processing
• Computer vision
• Decision-making in various contexts, such as in schools or businesses

The continuous growth and development of AI systems are a testament to the power and versatility of inference across different fields.

The Art of Inference: A Powerful Tool for Decision Making

Inference plays a significant role in the decision-making process. By analyzing information and deducing conclusions, individuals can make informed decisions based on available evidence and context.

Applying Inference to Personal Decisions

Heuristics in everyday decision-making are often driven by inference. Education and past experiences provide an individual with a foundation to extrapolate information and make informed decisions.

Example : Choosing a school for their child, a parent might infer that a higher-ranking school will offer a better education, considering various factors like reputation and available resources.

Emotions also influence the inference process in personal decisions. When someone feels extremely confident, they might make quicker decisions, relying on their emotional state to infer the needed information.

It is important to be aware of such biases and to ensure that sufficient data is considered before making a decision.

Inference in Legal and Judicial Situations

In legal and judicial situations, inference plays a crucial role in determining outcomes.

Adverse inference , for example, allows a judge or jury to draw a negative conclusion when a party refuses to provide information relevant to a case. This inference can significantly impact the outcome, as it mobilizes specific premises to reach an unfavorable implication for the withholding party.

Inference is also utilized in evaluating evidence presented in cases. TED (Testimony, Exhibits, Depositions) serves as the foundation of evidence, where parties infer the relevance and importance of the presented information. Jurors are tasked with inferring innocents or guilt based on this evidence while considering the context of the case.

In conclusion, inference is a powerful tool in decision-making as it allows individuals to:

• Evaluate available information.
• Deduce conclusions accordingly.

Both in personal situations and legal settings, the importance of inference cannot be overstated. To ensure the best outcomes, it is essential to be aware of the biases and potential pitfalls that might affect the inference process.

Challenges and Limitations of Inference

Inference reasoning can often be influenced by logical fallacies, which are errors in reasoning that weakens the argument. Common fallacies include:

• Ad Hominem : Attacking the person instead of the argument.
• Strawman : Misrepresenting the opponent’s argument to make it easier to attack.
• False Dichotomy : Presenting only two options when multiple possibilities exist.

Cognitive Biases

Cognitive biases can distort our thinking and decision-making process. Some common biases that can impact inferences are:

• Confirmation Bias : A tendency to search for, interpret, favor, and recall information that confirms one’s preexisting beliefs.
• Anchoring : The inclination to excessively rely on the first piece of information encountered when making decisions.
• Hindsight Bias : The belief that an event was predictable after it has occurred.

Accuracy and Reliability

The accuracy and reliability of an inference depend on the quality of the data and the logical structure applied. Factors affecting accuracy and reliability include:

• Insufficient or outdated data.
• Misinterpretation of data.
• Overgeneralization or oversimplification.

Availability Bias

An individual’s judgement can be swayed by the ease of recall of certain information. This cognitive shortcut is called availability bias.

It can lead to overestimating the likelihood of events that are easily remembered or encountered, and underestimating less memorable events.

Cognitive Dissonance

Cognitive dissonance occurs when an individual holds two or more contradictory beliefs, values, or attitudes.

This mental conflict can cause inconsistencies in the inference process, as individuals may attempt to reconcile their conflicting ideas through biased or illogical reasoning.

Emotions and Feelings

Emotions and feelings can influence how an individual interprets information and forms inferences.

Example : A person in a negative emotional state may more readily make pessimistic inferences, while someone in a positive state may be more prone to optimistic conclusions.

Being aware of emotional factors can help ensure that inferences are based on logical reasoning rather than emotional biases.

Frequently Asked Questions

How does inference help in learning.

In learning, inference enables individuals to utilize their critical thinking and reasoning skills to make connections between new information and existing knowledge.

This process aids in forming associations, understanding complex concepts, and anticipating future events.

How can I improve my inference skills?

To improve inference skills, practice critical thinking exercises, engage in discussions, analyze various scenarios, and make predictions based on available evidence.

Reading comprehension exercises and participating in debate forums can also be beneficial.

What role does inference play in statistical analysis?

In statistical analysis, inference refers to the process of making conclusions about a population based on a sample. It is used to estimate population parameters and test hypotheses, allowing for better decision-making and risk assessments based on available data.

Inference is a powerful cognitive technique that enables individuals to draw conclusions from available evidence. This process forms a vital part of everyday decision-making and spans across various professional fields.

The importance of inference cannot be overstated, as it contributes to the development of critical thinking skills, problem-solving, and decision-making abilities.

By understanding the concept of inference and recognizing its role in processing information, individuals can make better informed decisions and navigate the world with more confidence.

Harnessing the power of inference can add excitement and efficacy to everyday decision-making. Through its application, individuals can generate well-informed conclusions based on the evidence available, making it an invaluable tool in both personal and professional contexts.

Let’s harness the power of inference and make our everyday decision-making more exciting and effective!

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Critical thinking is based on the observation and analysis of facts and evidences to return rational, skeptical and unbiased judgments.   

This type of thinking involves a series of skills that can be created but also improved, as we will see throughout this article in which we will begin by defining the concept and end with tips to build and improve the skills related to critical thinking.

What is critical thinking?

Critical thinking is a discipline based on the ability of people to observe, elucidate and analyze information, facts and evidences in order to judge or decide if it is right or wrong.

It goes beyond mere curiosity, simple knowledge or analysis of any kind of fact or information.

People who develop this type of outlook are able to logically connect ideas and defend them with weighty opinions that ultimately help them make better decisions.

How to build and improve critical thinking skills?

Building and improving critical thinking skills involves focusing on a number of abilities and capacities .

To begin the critical thinking process all ideas must be open and all options must be understood as much as possible.

Even the dumbest or craziest idea can end up being the gateway to the most intelligent and successful conclusion.

The problem with having an open mind is that it is the most difficult path and often involves a greater challenge and effort. It is well known that the easy thing to do is to go with the obvious and the commonly accepted but this has no place in critical thinking.

By contrast, it is helpful not to make hasty decisions and to weigh the problem in its entirety after a first moment of awareness.

Finally, practicing active listening will help you to receive feedback from others and to understand other points of view that may help you as a reference.

Impartiality

An important point in the critical thinking process is the development of the ability to identify biases and maintain an impartial view in evaluations.

To improve this aspect it is advisable to have tools to be able to identify and recognize the prejudices and biases you have and try to leave them completely aside when thinking about the solution.

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Observation

Observation allows you to see each and every detail , no matter how small, subtle or inconsequential they may be or seem to be.

Behind the superficial information hides a universe of data, sources and experiences that help you make the best decision.

One of the pillars of critical thinking is objectivity. This forces you to base your value judgments on established facts that you will have gathered after a correct research process. 

At this point in the process you should also be clear about the influencing factors to be taken into account and those that can be left out.

Remember that your research is not only about gathering a good amount of information that puts the maximum number of options, variables or situations on the table. 

For the information to be of quality, it must be based on reliable and trustworthy sources.

If the information you have to collect is based on the comments and opinions of third parties, try to exercise quality control but without interference. 

To do this, ask open-ended questions that bring all the nuances to the table and at the same time serve to sift out possible biases.

With the research process completed, it is time to analyze the sources and information gathered.

At this point, your analytical skills will help you to discard what does not conform to unconventional thinking, to prioritize among the information that is of value, to identify possible trends and to draw your own conclusions.

One of the skills that characterize a person with critical thinking is their ability to recognize patterns and connections between all the pieces of information they handle in their research.

This allows them to draw conclusions of great relevance on which to base their predictions with weighty foundations.

Analytical thinking is sometimes confused with critical thinking. The former only uses facts and data, while the latter incorporates other nuances such as emotions, experiences or opinions.

One of the problems with critical thinking is that it can be developed to infinity and beyond. You can always keep looking for new avenues of investigation and new lines of argument by stretching inference to limits that may not be necessary.

At this point it is important to clarify that inference is the process of drawing conclusions from initial premises or hypotheses.

Knowing when to stop the research and thinking process and move on to the next stage in which you put into practice the actions considered appropriate is necessary.

Communication

The information you collect in your research is not top secret material. On the contrary, your knowledge sharing with other people who are involved in the next steps of the process is so important.

Think that your analytical ability to extract the information and your conclusions can serve to guide others .

Problem solving

It is important to note at this point that critical thinking can be aimed at solving a problem but can also be used to simply answer questions or even to identify areas for improvement in certain situations. 

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Eighth-graders’ Historical Reading, Thinking, and Writing about Convict-leasing

To best spark students’ critical and historical thinking, teachers must rely on age-appropriate sources and discipline-specific strategies. This article details an eighth-grade class’s guided inquiry into Birmingham’s convict-leasing system, an oft-forgotten era in the Black Freedom Movement. This week-long inquiry centered on close reading, text-based writing, and historical thinking. Researchers extracted meaning from qualitatively analyzing and coding student work samples. Students ably sourced and contextualized complex texts while analyzing causes and consequences; they articulated diverse perspectives and considered elements of continuity and change. Many of students’ text-based writing, however, was brief and underdeveloped. Findings are not generalizable as this was but a single class.

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3 Activities to Enhance Your Inference in Critical Thinking

Practice drawing reasonable conclusions: critical thinking exercise 4.

Posted November 5, 2021 | Reviewed by Tyler Woods

At the beginning of 2021, I posted a piece on this blog asking if any readers wanted to develop their critical thinking as a kind of New Year’s resolution. In light of the positive feedback I received from that piece, I have since posted a series of additional exercises throughout the year—including one on analysis and one on evaluation . Today, I post a set of exercises on inference , which is a critical thinking skill dedicated to the gathering of credible, relevant, logical, balanced, and (as much it can be) unbiased information, for the purpose of drawing a reasonable conclusion (Dwyer, 2017; Facione, 1990).

Critical thinking is a metacognitive process, consisting of a number of skills and dispositions, that when used through self-regulatory reflective judgment, increases the chances of producing a logical conclusion to an argument or solution to a problem (Dwyer, 2017; Dwyer et al., 2016; Dwyer, Hogan & Stewart, 2014; 2015). The purpose of this particular activity set, consistent with the description of inference above, is to provide you with an opportunity to practice drawing reasonable conclusions. If you’re interested in enhancing your critical thinking skills , please start with the first set of exercises and then the second and third, before jumping into this next set below. Remember, when we are given opportunities to think about our thinking , we are engaging our metacognitive processes; and that’s a foundational part of critical thinking.

In the first activity of this exercise, you are asked to infer an appropriate conclusion for each of the three pairs of propositions provided.

Foreign holidays broaden the mind.

I’m going on holiday to Spain.

Conclusion: _____________________________________

The food in the Kebab Hut is terrible.

People don’t want to eat in a restaurant when the food is poor.

Violent television rots the mind.

I don’t like watching violent television.

In the second activity of this exercise, you are asked to gather or develop, a pair of propositions that will appropriately infer each of the three conclusions provided.

1. John’s house will fall down.

Proposition 1: _____________________________________

Proposition 2: _____________________________________

2. Red Rum will win the race.

3. Milk is healthy for humans.

In the third activity of this exercise, you are asked to infer an appropriate conclusion from the first two propositions on level 1. With this resulting conclusion, use the proposition provided on level 2 to infer another conclusion. Finally, use this conclusion, along with the proposition provided on level 3, to infer an overall conclusion. Essentially, what you are doing here is filling-in-the-blanks with your inferences of intermediate conclusions until you reach your overall conclusion.

Proposition: Students who achieve their academic goals report higher life satisfaction.

Proposition: Having higher levels of life satisfaction is associated with lower levels of anxiety .

Intermediate conclusion 1: _______________________________________________

Proposition: Students with lower levels of anxiety do better in exams.

Intermediate conclusion 2: _______________________________________________

Proposition: Students who do better in exams get better jobs and earn more money.

Overall conclusion: _____________________________________________________

I hope you enjoyed this set of activities to exercise your inference skills. Being able to draw reasonable conclusions is an important skill to practice and improve. Though we draw conclusions on a daily basis, quite often they aren't optimal (i.e., either wrong or not entirely accurate) or based on less than credible information. Though it's often the case that some such conclusions will not have a massive impact on decision-making in our lives (e.g., which outfit is best to wear today? ), why take the chance in situations where our conclusions truly do matter (e.g. what should I be looking for in a health insurance policy? )

Along with the completion of the previous exercises, you should be at a stage where you can recognize the cognitive processes necessary in the critical thinking process. However, just because you are able to analyze, evaluate, and infer doesn't ensure that you will approach scenarios that require critical thought. A reflective sensibility— reflective judgment —is also necessary to 'govern' the application of these skills. So, I hope you're looking forward to the final exercise set in this series - on reflective judgment, coming soon.

Dwyer, C.P. (2017). Critical thinking: Conceptual perspectives and practical guidelines.Cambridge, UK: Cambridge University Press.

Dwyer, C. P., Harney, O., Hogan, M. J., & Kavanagh, C. (2016). Facilitating a Student-Educator Conceptual Model of Dispositions towards Critical Thinking through Interactive Management. Educational Technology & Research, doi: 10.1007/s11423-016-9460-7.

Dwyer, C. P., Hogan, M. J., & Stewart, I. (2014). An integrated critical thinking framework for the 21st century. Thinking Skills & Creativity, 12, 43–52.

Dwyer, C. P., Hogan, M. J., & Stewart, I. (2015). The evaluation of argument mapping-infused critical thinking instruction as a method of enhancing reflective judgment performance. Thinking Skills & Creativity, 16, 11–26.

Facione, P.A. (1990). The Delphi report: Committee on pre-college philosophy. Millbrae, CA: California Academic Press.

Christopher Dwyer, Ph.D., is a lecturer at the Technological University of the Shannon in Athlone, Ireland.

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Donkeys Reading Comprehension Worksheet

Subject: English

Age range: 11-14

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Enhance your students’ critical thinking and analytical skills with our comprehensive Donkeys Reading Comprehension worksheet. This engaging resource is specially designed to improve various key skills including word meaning, inference, summarizing, analysis and evaluation, content evaluation, structure comprehension, retrieval skills, prediction, explanation, exploration, as well as comparison and synthesis abilities.

Our worksheet provides a wide range of thought-provoking exercises that encourage students to think deeply about text, strengthen their comprehension skills, and develop their ability to interpret and evaluate information effectively. With a focus on improving not only reading comprehension but also higher-order thinking, this resource is an invaluable tool for educators looking to challenge and inspire their students.

This PDF download is perfect for classroom use or homeschooling and comes ready to use, with no editing required. Suitable for students of varying abilities, this worksheet can be used as part of your lesson plans to support literacy development, critical thinking, and analysis skills across different age groups.

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In the courtyard where Hersh Goldberg-Polin danced on Oct. 6, grief and anger reign after his death

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Shira Ben-Sasson, a founder of the Hakhel synagogue in Jerusalem, lights a candle in memory of Hersh Goldberg-Polin, Sept. 1, 2024. (Deborah Danan)

By Deborah Danan September 1, 2024

( JTA ) — JERUSALEM — Three hundred and thirty-two days after Hersh Goldberg-Polin danced in the courtyard next to his Jerusalem synagogue on the holiday of Simchat Torah, more than a thousand people gathered there in grief and prayer to mourn his murder by Hamas terrorists in Gaza.

During the Sunday night vigil, the courtyard railings were lined with oversized yellow ribbons to symbolize advocacy for the hostages, Hapoel Jerusalem soccer flags — the 23-year-old’s favorite team — and posters that read, “We love you, stay strong, survive,” a mantra coined by his mother, Rachel Goldberg-Polin.

Just hours earlier, one of the posters had been hanging over the balcony of the home of Shira Ben-Sasson, a leader of Hakhel, the Goldberg-Polins’ egalitarian congregation in the Baka neighborhood of Jerusalem.

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“We were sure we would take it down when he came home,” Ben Sasson said.

The community wanted to unite while respecting the Goldberg-Polins’ desire for privacy, she said, prompting them to organize the prayer gathering.

“But it’s like a Band-Aid or giving first aid, it’s what you do in an emergency. I don’t know how we go on after this,” she said.

She added that the community, which has a large contingent of English-speaking immigrants, was not prepared for the High Holidays, which begin in about a month. She said, “Seeing his empty seat is hard.”

For Ben-Sasson, who wore a T-shirt bearing the Talmudic dictum “There is no greater mitzvah than the redeeming of captives,” the tragedy is especially painful because, she said, it could have been avoided with a ceasefire agreement that freed hostages.

“Hersh was alive 48 hours ago. We think a deal could have saved him. There is no military solution to this,” she said.

That feeling of bereavement, often mixed with betrayal, pervaded gatherings across Israel on Sunday, as the country struggled with the news that six hostages who may have been freed in an agreement were now dead as negotiations continue to stall. Speakers at protests in Tel Aviv blamed Israeli Prime Minister Benjamin Netanyahu, who himself apologized for not getting the hostages out alive but blamed Hamas for obstructing a deal. The country’s labor union, the Histadrut, has called a national strike on Monday to demand a deal.

Some at the Jerusalem gathering, including the relative of another former hostage, said Netanyahu had chosen defeating Hamas over freeing the captives.

Josef Avi Yair Engel, whose grandson Ofir was released from Hamas captivity in November during that month’s ceasefire deal, expressed shock over Hersh’s murder but said he was not surprised, given the wartime policies of Netanyahu’s government.

“We knew months ago this was going to happen. Bibi’s formula, to dismantle Hamas and return the hostages, wasn’t logical. It’s an either/or situation,” Engel said, referring to Netanyahu by his nickname. “He’s tearing the country apart. I’m afraid that in the coming months there won’t be a state at all.”

Engel said he felt a close bond with Hersh’s father Jon Polin, not only because of their joint activism in the hostage families’ tent outside the Prime Minister’s Residence, but also because of their shared identity as Jerusalemites.

“There aren’t many of us in the hostage circle,” he said. “We’re like family.”

Sarah Mann, who did not know the family personally, said the weekend’s tragedy reminded her of Oct. 7.

“This day has sparks of the seventh, which created numbness and an inability to talk. Just complete shock,” she said.

Part of the reason for that, Mann said, was Rachel, who she described as a “force of faith.” Goldberg-Polin’s mother emerged as the most prominent advocate for the hostages globally and became a symbol in her own right as she crisscrossed the world calling for her son’s freedom.

“Millions of people around the world held onto her. Once that was cut, people’s ability to hold onto faith was knocked out today. But even though this has shattered us, we need to keep holding onto God,” Mann said.

For Susi Döring Preston, the day called to mind was not Oct. 7 but Yom Kippur, and its communal solemnity.

She said she usually steers clear of similar war-related events because they are too overwhelming for her.

“Before I avoided stuff like this because I guess I still had hope. But now is the time to just give in to needing to be around people because you can’t hold your own self up any more,” she said, tears rolling down her face. “You need to feel the humanity and hang onto that.”

Like so many others, Döring Preston paid tribute to the Goldberg-Polins’ tireless activism. “They needed everyone else’s strength but we drew so much strength from them and their efforts, “she said. “You felt it could change the outcome. But war is more evil than good. I think that’s the crushing thing. You can do everything right, but the outcome is still devastating.”

Guy Gordon, a member of Hakhel who moved to Israel from Dublin, Ireland, in the mid-1990s, said the efforts towards ensuring Hersh’s safe return have been an anchor for the community during the war.

“It gave us something to hope for, and pray for and to demonstrate for,” he said. “We had no choice but to be unreasonably optimistic. Tragically it transpired that he survived until the very end.”

Gordon, like many others in the crowd, wore a piece of duct tape marked with the number of days since Oct. 7 — a gesture initiated by Goldberg-Polin’s mother. Unlike on previous days, though, his tape also featured a broken red heart beside the number.

Nadia Levene, a family friend, also reflected on the improbability of Hersh’s survival.

“He did exactly what his parents begged him to do. He was strong. He did survive. And look what happened,” Levene said.

She hailed Rachel Goldberg-Polin’s “unwavering strength and belief in God,” adding, “There were times I lost faith. I suppose I was angry with God. But she just kept inspiring us all to pray, pray, pray.”

Jerusalem resident Leah Silver rejected politicizing the hostages’ deaths.

“Everything turns political so quickly. I came here because I felt that before all the protests, we need to just mourn for a moment and to pray. And show respect for each other,” she said. “We’ve become confused about who the enemy is. It’s very sad.”

But not everyone at the gathering joined in to sing Israel’s national anthem at the closing of the prayer gathering.

“I’m sorry, I can’t sing ‘Hatikvah,’” Reza Green, a Baka resident who did not know the Goldberg-Polins personally, said. “I’m too angry. We shouldn’t be here.”

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