compare and contrast critical thinking and problem solving

1

Every problem has only one solution (or one right answer)

The goal of problem-solving is to solve the problem, and most problems can be solved in any number of ways. If you discover a solution that works, it’s a good solution. Other people may think up solutions that differ from yours, but that doesn’t make your solution wrong or unimportant. What is the solution to “putting words on paper?” Fountain pen, ballpoint, pencil, marker, typewriter, printer, printing press, word-processing… all are valid solutions!

2

The best answer, solution, or method has already been discovered

Look at the history of any solution and you’ll see that improvements, new solutions, and new right answers are always being found. What is the solution to human transportation? The ox or horse, the cart, the wagon, the train, the car, the airplane, the jet, the space shuttle? What is the best and last?

3

Creative answers are technologically complex

Only a few problems require complex technological solutions. Most problems you’ll encounter need only a thoughtful solution involving personal action and perhaps a few simple tools. Even many problems that seem to require technology can be addressed in other ways.

4

Ideas either come or they don’t. Nothing will help— certainly not structure.

There are many successful techniques for generating ideas. One important technique is to include structure. Create guidelines, limiting parameters, and concrete goals for yourself that stimulate and shape your creativity. This strategy can help you get past the intimidation of “the blank page.” For example, if you want to write a story about a person who gained insight through experience, you can stoke your creativity by limiting or narrowing your theme to “a young girl in Cambodia who escaped the Khmer Rouge to find a new life as a nurse in France.” Apply this specificity and structure to any creative endeavor.

Critical and creative thinking complement each other when it comes to problem-solving. The process of alternatively focusing and expanding your thinking can generate more creative, innovative, and effective outcomes.

Problem-Solving Action Checklist

Problem-solving can be an efficient and rewarding process, especially if you are organized and mindful of critical steps and strategies. Remember to assume the attributes of a good critical thinker: if you are curious, reflective, knowledge-seeking, open to change, probing, organized, and ethical, your challenge or problem will be less of a hurdle, and you’ll be in a good position to find intelligent solutions. The steps outlined in this checklist will help you adhere to these qualities in your approach to any problem:

KEY TAKEAWAYS

• Critical thinking is logical and reflective thinking focused on deciding what to believe or do.
• Critical thinking involves questioning and evaluating information.
• Evaluating information is a complex, but essential, process. You can use the SIFT method to help determine if sources and information are reliable.
• Creative thinking is both a natural aspect of childhood and a re-learnable skill as an adult.
• Creative thinking is as essential a skill as critical thinking and integrating them can contribute to  innovative and rewarding experiences in life.
• Critical and creative thinking both contribute to our ability to solve problems in a variety of contexts.
• You can take specific actions to develop and strengthen your critical and creative thinking skills.

LICENSES AND ATTRIBUTIONS

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• Critical and Creative Thinking  Authored by : Laura Lucas, Tobin Quereau, and Heather Syrett.  Provided by : Austin Community College.  License :  CC BY-NC-SA-4.0

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• Chapter cover image.  Authored by : Hans-Peter Gauster.  Provided by : Unsplash.  Located at :  https://unsplash.com/photos/3y1zF4hIPCg .  License :  CC0: No Rights Reserved
• Creative Thinking Skills  in College Success.  Authored by : Linda Bruce.  Provided by : Lumen Learning.  Located at :  https://courses.lumenlearning.com/collegesuccess-lumen/chapter/creative-thinking-skills/ .  License :  CC BY 4.0
• Critical Thinking Skills  in College Success.   Authored by : Linda Bruce.  Provided by : Lumen Learning.  Located at :  https://courses.lumenlearning.com/collegesuccess-lumen/chapter/critical-thinking-skills/ .  License :  CC BY 4.0
• Evaluate: Assessing Your Research Process and Findings  in Information Literacy.  Authored by : Bernnard, Bobish, Hecker, Holden, Hosier, Jacobsen, Loney, Bullis.  Provided by : Lumen Learning.  Located at :  https://courses.lumenlearning.com/informationliteracy/chapter/evaluate-assessing-your-research-process-and-findings/ .  License :  CC BY-NC-SA-4.0
• The SIFT Method in Introduction to College Research . Authored by:  Walter D. Butler; Aloha Sargent; and Kelsey Smith. Provided by: Pressbooks. Located at : https://oer.pressbooks.pub/collegeresearch/chapter/the-sift-method/ . License: CC BY 4.0
• Why Fact-Checking in Introduction to College Research . Authored by:  Walter D. Butler; Aloha Sargent; and Kelsey Smith. Provided by: Pressbooks. Located at : https://oer.pressbooks.pub/collegeresearch/chapter/why-fact-checking/ . License: CC BY 4.0

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Where Good Ideas Come From.  Authored by : Steven Johnson. Provided by: Riverhead Books.  Located at :  https://www.youtube.com/watch?v=NugRZGDbPFU .  License :  All Rights Reserved .  License Terms : Standard YouTube License

How to Stimulate the Creative Process.  Provided by : Howcast.  Located at :  https://youtu.be/kPC8e-Jk5uw .  License :  All Rights Reserved .  License Terms : Standard YouTube License

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Critical Thinking and Decision-Making  - What is Critical Thinking?

Critical thinking and decision-making  -, what is critical thinking, critical thinking and decision-making what is critical thinking.

Critical Thinking and Decision-Making: What is Critical Thinking?

Lesson 1: what is critical thinking, what is critical thinking.

Critical thinking is a term that gets thrown around a lot. You've probably heard it used often throughout the years whether it was in school, at work, or in everyday conversation. But when you stop to think about it, what exactly is critical thinking and how do you do it ?

Watch the video below to learn more about critical thinking.

Simply put, critical thinking is the act of deliberately analyzing information so that you can make better judgements and decisions . It involves using things like logic, reasoning, and creativity, to draw conclusions and generally understand things better.

This may sound like a pretty broad definition, and that's because critical thinking is a broad skill that can be applied to so many different situations. You can use it to prepare for a job interview, manage your time better, make decisions about purchasing things, and so much more.

The process

As humans, we are constantly thinking . It's something we can't turn off. But not all of it is critical thinking. No one thinks critically 100% of the time... that would be pretty exhausting! Instead, it's an intentional process , something that we consciously use when we're presented with difficult problems or important decisions.

Improving your critical thinking

In order to become a better critical thinker, it's important to ask questions when you're presented with a problem or decision, before jumping to any conclusions. You can start with simple ones like What do I currently know? and How do I know this? These can help to give you a better idea of what you're working with and, in some cases, simplify more complex issues.  

Real-world applications

Let's take a look at how we can use critical thinking to evaluate online information . Say a friend of yours posts a news article on social media and you're drawn to its headline. If you were to use your everyday automatic thinking, you might accept it as fact and move on. But if you were thinking critically, you would first analyze the available information and ask some questions :

• What's the source of this article?
• Is the headline potentially misleading?
• What are my friend's general beliefs?
• Do their beliefs inform why they might have shared this?

After analyzing all of this information, you can draw a conclusion about whether or not you think the article is trustworthy.

Critical thinking has a wide range of real-world applications . It can help you to make better decisions, become more hireable, and generally better understand the world around you.

/en/problem-solving-and-decision-making/why-is-it-so-hard-to-make-decisions/content/

Exploring the Difference: Creative Thinking vs. Critical Thinking

Annie Walls

Creative thinking and critical thinking are two distinct cognitive processes that play important roles in problem-solving and decision-making. While creative thinking involves generating innovative ideas and solutions, critical thinking involves analyzing and evaluating information to make reasoned judgments. Both types of thinking have their unique characteristics and benefits. In this article, we will explore the difference between creative thinking and critical thinking, and how they can be applied in various contexts.

Key Takeaways

• Creative thinking involves generating new ideas and solutions.
• Critical thinking involves analyzing and evaluating information to make reasoned judgments.
• Creative thinkers are characterized by their curiosity, open-mindedness, and willingness to take risks.
• Critical thinkers are characterized by their skepticism, logical reasoning, and attention to detail.
• Creative thinking can lead to innovation and breakthroughs.

Understanding Creative Thinking

Defining creative thinking.

Creative thinking is the ability to think outside the box and generate innovative ideas. It involves breaking free from conventional ways of thinking and exploring new possibilities. Creativity is the key element in creative thinking , as it allows individuals to come up with unique and original solutions to problems.

Creative thinking is not limited to artistic endeavors; it can be applied to various aspects of life, including problem-solving, decision-making, and even everyday tasks. It requires an open mind, a willingness to take risks, and the ability to see things from different perspectives.

In order to foster creative thinking, it is important to create an environment that encourages experimentation and exploration. This can be done by providing opportunities for brainstorming, encouraging collaboration, and embracing failure as a learning opportunity.

Here are some techniques that can enhance creative thinking:

• Mind mapping: A visual tool that helps organize thoughts and generate new ideas.
• Divergent thinking: Generating multiple solutions to a problem.
• Analogical thinking: Drawing connections between unrelated concepts.

Tip: Embrace curiosity and embrace the unknown. Be open to new experiences and ideas, and don't be afraid to take risks.

Characteristics of Creative Thinkers

Creative thinkers possess a unique set of characteristics that set them apart from others. They have the ability to think outside the box and come up with innovative solutions to problems. Imagination plays a crucial role in their thought process, allowing them to envision possibilities that others may not see. They are open-minded and willing to explore different perspectives, which helps them generate fresh ideas. Creative thinkers are also comfortable with ambiguity and uncertainty, as they understand that these conditions can lead to breakthroughs. They are not afraid to take risks and are willing to challenge the status quo.

Benefits of Creative Thinking

Creative thinking offers numerous benefits that can enhance various aspects of life. One of the key advantages of creative thinking is the ability to generate innovative ideas and solutions. Creativity allows individuals to think outside the box and come up with unique approaches to problems. This can lead to breakthroughs and advancements in various fields.

Another benefit of creative thinking is its impact on personal growth and self-expression. By engaging in creative activities, individuals can explore their inner thoughts and emotions, allowing for self-discovery and self-reflection. Creative pursuits such as painting, writing, or playing an instrument can serve as outlets for self-expression and can contribute to overall well-being.

In addition, creative thinking can foster collaboration and teamwork. When individuals approach problems with a creative mindset, they are more likely to seek input and ideas from others. This promotes a collaborative environment where diverse perspectives are valued and innovative solutions are developed.

Furthermore, creative thinking can enhance problem-solving skills. By thinking creatively, individuals are able to consider multiple perspectives and explore alternative solutions. This can lead to more effective problem-solving and decision-making processes.

Overall, creative thinking offers a range of benefits, from generating innovative ideas to fostering collaboration and enhancing problem-solving skills.

Techniques for Enhancing Creative Thinking

In order to enhance creative thinking, there are several techniques that can be employed:

• Mind Mapping : This technique involves visually organizing ideas and concepts in a non-linear manner, allowing for connections and associations to be made.
• Brainstorming : This popular technique involves generating a large number of ideas in a short amount of time, without judgment or evaluation.
• Divergent Thinking : This approach encourages exploring multiple possibilities and perspectives, thinking outside the box, and avoiding conventional solutions.

Tip: When using these techniques, it is important to create a supportive and non-judgmental environment that encourages free thinking and idea generation.

By utilizing these techniques, individuals and teams can unlock their creative potential and generate innovative ideas to drive growth and success.

Exploring Critical Thinking

Defining critical thinking.

Critical thinking is essentially a questioning, challenging approach to knowledge and perceived wisdom. It involves ideas and information from an objective perspective, analyzing and evaluating them to form well-reasoned judgments and decisions. It goes beyond accepting information at face value and encourages a deeper understanding of the subject matter. Critical thinkers are curious, open-minded, and willing to consider different perspectives. They are skilled at identifying biases and assumptions, and they strive to make logical and evidence-based conclusions.

Characteristics of Critical Thinkers

Critical thinkers possess several key characteristics that set them apart:

• Analytical Skills : Critical thinkers are adept at analyzing information and breaking it down into its component parts. They can identify patterns, evaluate evidence, and draw logical conclusions.
• Open-mindedness : Critical thinkers are willing to consider different perspectives and are open to changing their beliefs or opinions based on new evidence or information.
• Skepticism : Critical thinkers approach information with a healthy dose of skepticism. They question assumptions, challenge authority, and seek evidence to support or refute claims.

Tip: Critical thinkers actively engage in critical reflection, constantly questioning their own thinking and seeking to improve their reasoning abilities.

Benefits of Critical Thinking

Critical thinking has numerous benefits that can positively impact various aspects of life. It enhances problem-solving skills, allowing individuals to analyze complex situations and make informed decisions. Analytical thinking is a key component of critical thinking, enabling individuals to break down problems into smaller parts and examine them from different perspectives. This approach helps in identifying potential biases and assumptions, leading to more objective and rational decision-making.

In addition, critical thinking promotes effective communication . By critically evaluating information and arguments, individuals can articulate their thoughts and ideas more clearly and persuasively. They can also identify logical fallacies and inconsistencies in others' arguments, enabling them to engage in meaningful and constructive discussions.

Furthermore, critical thinking fosters creativity and innovation . By questioning assumptions and challenging conventional wisdom, individuals can generate new ideas and approaches. Critical thinkers are more open to exploring alternative solutions and are willing to take risks in order to achieve better outcomes.

Developing Critical Thinking Skills

Developing critical thinking skills is essential for success in both personal and professional life. It involves the ability to analyze information objectively, evaluate arguments and evidence, and make informed decisions. Here are some strategies that can help enhance your critical thinking skills:

• Ask Questions: One of the key aspects of critical thinking is asking thoughtful and probing questions. This helps you gain a deeper understanding of the subject matter and challenges assumptions.
• Seek Different Perspectives: To develop critical thinking skills, it is important to consider multiple viewpoints and perspectives. This allows you to evaluate arguments from different angles and make well-rounded judgments.
• Practice Problem-Solving: Critical thinking involves problem-solving skills. Engaging in activities that require you to analyze and solve problems can help sharpen your critical thinking abilities.
• Reflect on Your Thinking: Take time to reflect on your own thinking process. Consider the biases, assumptions, and logical fallacies that may be influencing your thoughts and decisions.
• Continuous Learning: Critical thinking is a skill that can be developed and improved over time. Engage in continuous learning, read diverse perspectives, and challenge your own beliefs and assumptions.

By incorporating these strategies into your daily life, you can enhance your critical thinking skills and become a more effective problem solver and decision-maker.

Comparing Creative and Critical Thinking

Different approaches to problem solving.

When it comes to problem solving, creative thinking and critical thinking take different approaches. Creative thinkers often rely on their imagination and intuition to generate unique and innovative solutions. They think outside the box and are not afraid to take risks. On the other hand, critical thinkers approach problem solving in a more analytical and logical manner. They carefully analyze the problem, gather information, and evaluate different options before making a decision.

Role of Imagination and Logic

The role of imagination and logic in creative and critical thinking is crucial. Imagination allows us to think outside the box, explore new possibilities, and come up with innovative ideas. It is the fuel that ignites creativity and helps us see beyond the obvious. On the other hand, logic provides the framework for organizing and analyzing information, making rational decisions, and solving problems systematically. It helps us evaluate the feasibility and effectiveness of our ideas.

When it comes to problem-solving, a balance between imagination and logic is essential. While imagination helps generate unique and unconventional solutions, logic ensures that these solutions are practical and viable. By combining the two, we can approach problems with a structured yet imaginative mindset, finding innovative solutions and making connections that others may overlook.

In summary, imagination and logic are two sides of the same coin when it comes to creative and critical thinking. They complement each other and work together to enhance our ability to think creatively and critically.

Balancing Intuition and Analysis

When it comes to problem-solving, finding the right balance between intuition and analysis is crucial. Intuition allows us to tap into our subconscious knowledge and make quick decisions based on gut feelings. On the other hand, analysis involves a systematic and logical approach to gather and evaluate information. Both intuition and analysis have their strengths and weaknesses, and leveraging both can lead to more effective problem-solving.

To strike a balance between intuition and analysis, consider the following:

• Trust your instincts: Pay attention to your gut feelings and initial reactions, as they can provide valuable insights.
• Gather and evaluate data: Take the time to gather relevant information and analyze it objectively.
• Seek different perspectives: Engage with others who have different viewpoints to challenge your assumptions and broaden your thinking.

Tip: Remember that finding the right balance between intuition and analysis is a dynamic process. It requires practice and reflection to develop a nuanced approach to problem-solving.

Collaboration and Individuality in Thinking

Collaboration and individuality are two key aspects of thinking that play a crucial role in both creative and critical thinking. While collaboration allows for the exchange of ideas and perspectives, individuality brings unique insights and approaches to the table. Collaboration fosters a sense of teamwork and encourages diverse thinking, which can lead to innovative solutions. On the other hand, individuality allows individuals to think independently and bring their own creativity and expertise to the problem-solving process.

In order to effectively balance collaboration and individuality in thinking, it is important to create an environment that values both. This can be achieved by promoting open communication and active listening, where team members feel comfortable sharing their ideas and opinions. Additionally, providing opportunities for individual reflection and brainstorming can help stimulate creativity and encourage unique perspectives.

To further enhance collaboration and individuality in thinking, organizations can implement strategies such as group brainstorming sessions , where team members can collectively generate ideas and build upon each other's thoughts. This encourages collaboration while also allowing individuals to contribute their own unique insights. Another strategy is to assign individual tasks within a larger project, giving team members the opportunity to work independently and bring their own creative solutions to the table.

In summary, collaboration and individuality are both essential components of thinking that contribute to creative and critical thinking processes. By fostering a balance between collaboration and individuality, organizations can harness the power of teamwork and individual creativity to drive innovation and problem-solving.

In the article section of my website, I would like to discuss the topic of 'Comparing Creative and Critical Thinking'. Creative thinking and critical thinking are two essential cognitive skills that play a significant role in problem-solving, decision-making, and innovation. While creative thinking involves generating new ideas, thinking outside the box, and exploring different perspectives , critical thinking focuses on analyzing, evaluating, and questioning information to make informed judgments. Both types of thinking are crucial in today's fast-paced and complex world. By understanding the differences and similarities between creative and critical thinking, individuals can enhance their problem-solving abilities and foster a culture of innovation. If you want to learn more about the power of creative thinking and how it can transform your business, visit th website, Creativity Keynote Speaker James Taylor - Inspiring Creative Minds .

In conclusion, both creative thinking and critical thinking are essential skills that complement each other in problem-solving and decision-making. While creative thinking allows for innovative ideas and out-of-the-box solutions, critical thinking provides the necessary analysis and evaluation to ensure the feasibility and effectiveness of those ideas. Flexibility is a key aspect of creative thinking, enabling individuals to adapt and explore different perspectives, while accuracy is a fundamental element of critical thinking, ensuring logical reasoning and evidence-based conclusions. By harnessing the power of both creative and critical thinking, individuals can enhance their problem-solving abilities and make well-informed decisions in various aspects of life.

Frequently Asked Questions

What is the difference between creative thinking and critical thinking.

Creative thinking involves generating new ideas, possibilities, and solutions, while critical thinking involves analyzing, evaluating, and making reasoned judgments.

Can someone be both a creative thinker and a critical thinker?

Yes, individuals can possess both creative and critical thinking skills. They can use creative thinking to generate ideas and critical thinking to evaluate and refine those ideas.

Which is more important, creative thinking or critical thinking?

Both creative thinking and critical thinking are important and complement each other. Creative thinking generates new ideas, while critical thinking helps evaluate and implement those ideas effectively.

How can I enhance my creative thinking skills?

You can enhance your creative thinking skills by engaging in activities that stimulate your imagination, such as brainstorming, mind mapping, and exploring new perspectives.

What are some techniques for developing critical thinking skills?

Techniques for developing critical thinking skills include analyzing arguments, evaluating evidence, questioning assumptions, and considering different perspectives.

Is creative thinking limited to artistic pursuits?

No, creative thinking is not limited to artistic pursuits. It can be applied to various fields and industries, including problem-solving in science, business, technology, and more.

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Chapter 8: Thinking, Communicating & Problem-Solving

Critical thinking & problem-solving, assess your critical thinking strategies.

• Visit the Quia Critical Thinking Quiz page and click on Start Now (you don’t need to enter your name).
• Select the best answer for each question, and then click on Submit Answers. A score of 70 percent or better on this quiz is considered passing.
• Based on the content of the questions, do you feel you use good critical thinking strategies in college? In what ways could you improve as a critical thinker?

The essence of the independent mind lies not in what it thinks, but in how it thinks. —Christopher Hitchens, author and journalist

Critical Thinking

As a college student, you are tasked with engaging and expanding your thinking skills. One of the most important of these skills is critical thinking. Critical thinking is important because it relates to nearly all tasks, situations, topics, careers, environments, challenges, and opportunities. It’s a discipline-general thinking skill, not a thinking skill that’s reserved for a one subject alone or restricted to a particular content area. Of all your thinking skills, critical thinking may have the greatest value.

What Is Critical Thinking?

Critical thinking is clear, reasonable, reflective thinking focused on deciding what to believe or do. It means asking probing questions like, “How do we know?” or “Is this true in every case or just in this instance?” It involves being skeptical and challenging assumptions, rather than simply memorizing facts or blindly accepting what you hear or read. Critical thinking skills will help you in any profession or any circumstance of life, from science to art to business to teaching.

Critical thinkers are curious and reflective people. They explore and probe new areas and seek knowledge, clarification, and solutions. They ask pertinent questions, evaluate statements and arguments, and distinguish between facts and opinion. They are also willing to examine their own beliefs, possessing a manner of humility that allows them to admit lack of knowledge or understanding when needed. Critical thinkers are open to changing their mind. Perhaps most of all, they actively enjoy learning and view seeking new knowledge as a lifelong pursuit.

Thinking critically will help you develop more balanced arguments, express yourself clearly, read more critically, and glean important information efficiently. With critical thinking, you become a clearer thinker and problem solver.

The following video, from Lawrence Bland, presents the major concepts and benefits of critical thinking.

The Role of Logic in Critical Thinking

Critical thinking is fundamentally a process of questioning information and data. You may question the information you read in a textbook, or you may question what a politician or a professor or a classmate says. You can also question a commonly-held belief or a new idea. With critical thinking, anything and everything is subject to question and examination for the purpose of logically constructing reasoned perspectives.

The word logic comes from the Ancient Greek logike , referring to the science or art of reasoning. Using logic, a person evaluates arguments and reasoning and strives to distinguish between good and bad reasoning or between truth and falsehood. Using logic, you can evaluate ideas or claims people make, make good decisions, and form sound beliefs about the world. [1] . Logical thinkers provide reasonable and appropriate evidence to support their claims, acknowledge the strengths of the opposing side’s position, actively investigate a variety of possible outcomes or new solutions, and use measured and objective language to present their positions.

Clarify Thinking

When you use critical thinking to evaluate information, you need to clarify your thinking to yourself and likely to others. Doing this well is mainly a process of asking and answering logical, probing questions. Design your questions to fit your needs, but be sure to cover adequate ground.

• What is the purpose?
• What question are we trying to answer?
• What point of view is being expressed?
• What assumptions are we or others making?
• What are the facts and data we know, and how do we know them?
• What are the concepts we’re working with?
• What are the conclusions, and do they make sense?
• What are the implications?

Avoid Fallacies

You’ll also want to make sure you can avoid and spot logical fallacies. Fallacies are faults in thinking or illogical approaches used to persuade the other side. Statements such as, everyone else is doing it ca n be very persuasive even though they demonstrate faulty logic, in this case, the bandwagon appeal. These fallacies can undermine your authority and weaken your position. Students shouldn’t park in the faculty lot because that lot is for faculty is another example of a logical fallacy, this time circular reasoning.

Consult the two websites below to identify and avoid some of the many kinds of logical fallacies:

• Fallacies Files—Home
• Logical Fallacies Jeopardy

Applying critical thinking

The following questions may apply to formulating a logical, reasoned perspective in the scenario below or any other situation:

• What is happening? Gather the basic information and begin to think of questions.
• Why is it important? Ask yourself why it’s significant and whether or not you agree.
• What don’t I see? Is there anything important missing?
• How do I know? Ask yourself where the information came from and how it was constructed.
• Who is saying it? What’s the position of the speaker and what is influencing them?
• What else? What if? What other ideas exist and are there other possibilities?

A man has a Ph.D. in political science, and he works as a professor at a local college. His wife works at the college, too. They have three young children in the local school system, and their family is well known in the community. The man is now running for political office.

Are his credentials and experience sufficient for entering public office? Will he be effective in political office? Some voters might believe that his personal life and current job, on the surface, suggest he will do well in the position, and they will vote for him. In truth, the characteristics described don’t guarantee that the man will do a good job. The information is somewhat irrelevant.

What else might you want to know? How about whether the man had already held a political office and done a good job? In this case, we want to ask, How much information is adequate in order to make a decision based on logic instead of assumptions?

Problem-Solving with Critical Thinking

For most people, a typical day is filled with critical thinking and problem-solving challenges. In fact, critical thinking and problem-solving go hand-in-hand. They both refer to using knowledge, facts, and data to solve problems effectively, but with problem-solving, you are specifically identifying, selecting, and defending your solution.

Applying the strategies described in the action checklist below can help you utilize critical thinking skills to solve problems.

Problem-solving can be an efficient and rewarding process, especially if you are organized and mindful of critical steps and strategies. Remember, too, to assume the attributes of a good critical thinker. If you are curious, reflective, knowledge-seeking, open to change, probing, organized, and ethical, your challenge or problem will be less of a hurdle, and you’ll be in a good position to find intelligent solutions.

 Developing Yourself As a Critical Thinker and Problem-Solver

Critical thinking is a fundamental skill for college students, but it should also be a lifelong pursuit that we continually refine. Below are additional strategies to develop yourself as a critical thinker in college and in everyday life:

• Reflect and practice : Always reflect on what you’ve learned. Is it true all the time? How did you arrive at your conclusions?
• Use wasted time : It’s certainly important to make time for relaxing, but if you find you are indulging in too much of a good thing, think about using your time more constructively. Determine when you do your best thinking and try to learn something new during that part of the day.
• Redefine the way you see things : It can be very uninteresting to always think the same way. Challenge yourself to see familiar things in new ways. Put yourself in someone else’s shoes and consider a certain situation from a different angle or perspective. If you’re trying to solve a problem, list all your concerns, such as what you need in order to solve it, who can help, and what some possible barriers might be. It’s often possible to reframe a problem as an opportunity. Try to find a solution where there seems to be none.
• Analyze the influences on your thinking and in your life : Why do you think or feel the way you do? Analyze your influences. Think about who in your life influences you. Do you feel or react a certain way because of social convention or because you believe it is what is expected of you? Try to break out of any molds that may be constricting you.
• Express yourself : Critical thinking also involves being able to express yourself clearly. Most important in expressing yourself clearly is stating one point at a time. You might be inclined to argue every thought, but you might have greater impact if you focus only on your main arguments. This will help others to follow your thinking clearly. For more abstract ideas, assume that your audience may not understand. Provide examples, analogies, or metaphors where you can.
• Enhance your wellness : It’s easier to think critically when you take care of your mental and physical health. Try taking 10-minute activity breaks to reach 30 to 60 minutes of physical activity each day . Try taking a break between classes and walk to the coffee shop that’s farthest away. Scheduling physical activity into your day can help lower stress and increase mental alertness.
• Do your most difficult work when you have the most energy: Think about the time of day you are most effective and have the most energy. Plan to do your most difficult thinking during these times.

Reflect on Critical Thinking

• Think about someone whom you consider to be a critical thinker (friend, professor, historical figure, etc). What qualities does he/she have?
• Review some of the critical thinking strategies discussed on this page. Choose one strategy that makes sense to you. How can you apply this critical thinking technique to your academic work?
• Habits of mind are attitudes and beliefs that influence how you approach the world (inquiring attitude, open mind, respect for truth, etc.). What is one habit of mind you would like to actively develop over the next year? How will you develop a daily practice to cultivate this habit?

Cultivate Critical Habits of Mind

Earlier in this text we discussed, “habits of mind,” the personal commitments, values, and standards people have about the principle of good thinking. Consider your intellectual commitments, values, and standards. Do you approach problems with an open mind, a respect for truth, and an inquiring attitude? Some good habits to have when thinking critically are being receptive to having your opinions changed, having respect for others, being independent and not accepting something is true until you’ve had the time to examine the available evidence. Other important habits of mind include being fair-minded, having respect for a reason, having an inquiring mind, not making assumptions, and always, especially, questioning your own conclusions. In their quest towards developing an intellectual work ethic, critical thinkers constantly try to work these qualities into their daily lives.

 problem-solving with critical thinking

Below are some examples of using critical thinking to problem-solve. Can you think of additional action steps to apply to the following situations? You may want to look back to Chapter 2 “Defining Goals” to utilize the five step problem solving strategy described there.

• Your roommate was upset and said some unkind words to you, which has put a crimp in the relationship. You try to see through the angry behaviors to determine how you might best support your roommate and help bring the relationship back to a comfortable spot.
• Your campus club has been languishing on account of lack of participation and funds. The new club president, though, is a marketing major and has identified some strategies to interest students in joining and supporting the club. Implementation is forthcoming.
• Your final art class project challenges you to conceptualize form in new ways. On the last day of class when students present their projects, you describe the techniques you used to fulfill the assignment. You explain why and how you selected that approach.
• Your math teacher sees that the class is not quite grasping a concept. She uses clever questioning to dispel anxiety and guide you to new understanding of the concept.
• You have a job interview for a position that you feel you are only partially qualified for, although you really want the job and you are excited about the prospects. You analyze how you will explain your skills and experiences in a way to show that you are a good match for the prospective employer.
• You are doing well in college, and most of your college and living expenses are covered. But there are some gaps between what you want and what you feel you can afford. You analyze your income, savings, and budget to better calculate what you will need to stay in college and maintain your desired level of spending.
• "logike." Wordnik. n.d. Web. 16 Feb 2016. ↵
• "Student Success-Thinking Critically In Class and Online."  Critical Thinking Gateway . St Petersburg College, n.d. Web. 16 Feb 2016. ↵
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Thinking Vs. Critical Thinking: What’s the Difference?

Thinking and critical thinking do not sound that different in nature. After all, they both include the verb thinking, and therefore, imply that some form of thinking is taking place. If you find yourself wondering, what is the difference between thinking vs critical thinking, you have had an excellent thought.

Going back to your question. When you thought, what is the difference between thinking and critical thinking and you began to weigh the difference, you were performing the action of critical thinking! Let’s take some time to dig further into the differences in thinking and critical thinking.

What is Thinking?

There are many things that can lead to thinking. If you are walking down the street and pass a bakery and you smell the sweet smell of apple pie and you think about being in your grandma’s kitchen, this process of thinking is initiated by something called stimuli.

Have you ever laid in bed trying to go to sleep, but you kept thinking about the pile of papers you left on your desk or the long to-do list you have waiting for you tomorrow? You may be thinking too much because you are stressed or simply because it is difficult for you to turn off your brain, so to speak, at night when it is time to sleep.

What is Critical Thinking?

Since critical thinking goes beyond the basic formation of thought that we do hundreds if not thousands of times a day, it is considered a skill that must be practiced. This is why students study things in school like problem-solving, critical analysis, and how to compare and contrast different things.

Though critical thinking in its most basic form can come naturally, in order to really master and feel comfortable with various aspects of critical thinking, we must learn about the different processes involved in critical thinking. Then we can more confidently apply these individual thinking skills that fall under the umbrella term of critical thinking.

Why do We Use Critical Thinking?

We all have opinions, and when we meet someone with a different opinion, we use critical thinking skills to form arguments. We take our knowledge of a particular subject and logically piece together an argument that supports our opinion of that subject. This can be something a simple as whether pineapple belongs on pizza or something more complex like the causes of global warming.

5 Everyday Critical Thinking Skills

There are more than a dozen different critical thinking skills ranging from analyzing to critiquing. Oftentimes, we use multiple critical thinking skills at one time.

Comparing and Contrasting

When you look at two or more things and decide what is similar and what is different between them, you are using the critical thinking skills of comparing and contrasting. We do this when we look at universities or job options. We look at the majors that are offered or the benefits that come with the job to see how they are similar and different.

Forecasting

If you believe the housing market is going to crash, you sell while you can to get the most for your money. If you believe a particular stock is going to increase in value in the future, you buy now while the prices are low.

Though we may not be movie or food critics professionally, it is human nature to critique things. Though the critical thinking skill of critiquing usually goes much deeper than deciding whether your meal was delicious or not, you still critique things in your daily life.

Have you ever decided that you wanted to buy something online like a computer or a new pair of shoes? Most of the time, when we shop online, we will look at different websites to check customer reviews. Even if you just glance at a product’s star rating or look at the available features for a specific product, you are evaluating the overall product before you decide to purchase.

Similarities and Differences

It is a general belief that every person is capable of thinking. However, the skills of critical thinking take practice. This does not mean some people are incapable of critical thinking. It only means that it may be more difficult for some than others.

If you want to challenge yourself to go beyond just thinking and reach a level of critical thinking, keep pondering questions like what is the difference between thinking and critical thinking? Questions like these will naturally push you to use your critical thinking skills. As you further develop your ability to think critically, you will find that other skills like problem solving and brainstorming come more easily to you.

Difference Between Thinking and Critical Thinking

Critical Thinking vs. Creative Thinking

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The pursuit of performance excellence, critical thinking vs. creative thinking.

Creative thinking is a way of looking at problems or situations from a fresh perspective to conceive of something new or original.

Critical thinking is the logical, sequential disciplined process of rationalizing, analyzing, evaluating, and interpreting information to make informed judgments and/or decisions.

Critical Thinking vs. Creative Thinking – Key Differences

• Creative thinking tries to create something new, while critical thinking seeks to assess worth or validity of something that already exists.
• Creative thinking is generative, while critical thinking is analytical.
• Creative thinking is divergent, while critical thinking is convergent.
• Creative thinking is focused on possibilities, while critical thinking is focused on probability.
• Creative thinking is accomplished by disregarding accepted principles, while critical thinking is accomplished by applying accepted principles.

About Creative Thinking

Creative thinking is a process utilized to generate lists of new, varied and unique ideas or possibilities. Creative thinking brings a fresh perspective and sometimes unconventional solution to solve a problem or address a challenge.  When you are thinking creatively, you are focused on exploring ideas, generating possibilities, and/or developing various theories.

Creative thinking can be performed both by an unstructured process such as brainstorming, or by a structured process such as lateral thinking.

Brainstorming is the process for generating unique ideas and solutions through spontaneous and freewheeling group discussion. Participants are encouraged to think aloud and suggest as many ideas as they can, no matter how outlandish it may seem.

Lateral thinking uses a systematic process that leads to logical conclusions. However, it involves changing a standard thinking sequence and arriving at a solution from completely different angles.

No matter what process you chose, the ultimate goal is to generate ideas that are unique, useful and worthy of further elaboration. Often times, critical thinking is performed after creative thinking has generated various possibilities. Critical thinking is used to vet those ideas to determine if they are practical.

Creative Thinking Skills

• Open-mindedness
• Flexibility
• Imagination
• Adaptability
• Risk-taking
• Originality
• Elaboration
• Brainstorming

About Critical Thinking

Critical thinking is the process of actively analyzing, interpreting, synthesizing, evaluating information gathered from observation, experience, or communication. It is thinking in a clear, logical, reasoned, and reflective manner to make informed judgments and/or decisions.

Critical thinking involves the ability to:

• remain objective

In general, critical thinking is used to make logical well-formed decisions after analyzing and evaluating information and/or an array of ideas.

On a daily basis, it can be used for a variety of reasons including:

• to form an argument
• to articulate and justify a position or point of view
• to reduce possibilities to convergent toward a single answer
• to vet creative ideas to determine if they are practical
• to judge an assumption
• to solve a problem
• to reach a conclusion

Critical Thinking Skills

• Interpreting
• Integrating
• Contrasting
• Classifying
• Forecasting
• Hypothesizing

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Problem-solving, decision-making, and critical thinking: how do they mix and why bother?

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• 1 Sources for Excellence, University of Cincinnati College of Nursing, USA.
• PMID: 11744895
• DOI: 10.1067/mhc.2001.120987

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Enhancing students’ critical thinking skills: is comparing correct and erroneous examples beneficial?

• Original Research
• Open access
• Published: 26 September 2021
• Volume 49 , pages 747–777, ( 2021 )

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• Lara M. van Peppen   ORCID: orcid.org/0000-0002-1219-8267 1   nAff2 ,
• Peter P. J. L. Verkoeijen 1 , 3 ,
• Anita E. G. Heijltjes 3 ,
• Eva M. Janssen 4 &
• Tamara van Gog 4  

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There is a need for effective methods to teach critical thinking (CT). One instructional method that seems promising is comparing correct and erroneous worked examples (i.e., contrasting examples). The aim of the present study, therefore, was to investigate the effect of contrasting examples on learning and transfer of CT-skills, focusing on avoiding biased reasoning. Students ( N  = 170) received instructions on CT and avoiding biases in reasoning tasks, followed by: (1) contrasting examples, (2) correct examples, (3) erroneous examples, or (4) practice problems. Performance was measured on a pretest, immediate posttest, 3-week delayed posttest, and 9-month delayed posttest. Our results revealed that participants’ reasoning task performance improved from pretest to immediate posttest, and even further after a delay (i.e., they learned to avoid biased reasoning). Surprisingly, there were no differences in learning gains or transfer performance between the four conditions. Our findings raise questions about the preconditions of contrasting examples effects. Moreover, how transfer of CT-skills can be fostered remains an important issue for future research.

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Unraveling the effects of critical thinking instructions, practice, and self-explanation on students’ reasoning performance

The effects of learning from correct and erroneous examples in individual and collaborative settings, deliberate erring improves far transfer of learning more than errorless elaboration and spotting and correcting others’ errors.

Avoid common mistakes on your manuscript.

Introduction

Every day, we reason and make many decisions based on previous experiences and existing knowledge. To do so we often rely on a number of heuristics (i.e., mental shortcuts) that ease reasoning processes (Tversky & Kahneman, 1974 ). Usually, these decisions are inconsequential but sometimes they can lead to biases (i.e., deviating from ideal normative standards derived from logic and probability theory) with severe consequences. To illustrate, a forensic expert who misjudges fingerprint evidence because it verifies his or her preexisting beliefs concerning the likelihood of the guilt of a defendant, displays the so-called confirmation bias, which can result in a misidentification and a wrongful conviction (e.g., the Madrid bomber case; Kassin et al., 2013 ). Biases occur when people rely on heuristic reasoning (i.e., Type 1 processing) when that is not appropriate, do not recognize the need for analytical or reflective reasoning (i.e., Type 2 processing), are not willing to switch to Type 2 processing or unable to sustain it, or miss the relevant mindware to come up with a better response (e.g., Evans, 2003 ; Stanovich, 2011 ). Our primary tool for reasoning and making better decisions, and thus to avoid biases in reasoning and decision making, is critical thinking (CT), which is generally characterized as “purposeful, self-regulatory judgment that results in interpretation, analysis, evaluation, and inference, as well as explanation of the evidential, conceptual, methodological, criteriological, or contextual considerations on which that judgment is based” (Facione, 1990 , p. 2).

Because CT is essential for successful functioning in one’s personal, educational, and professional life, fostering students’ CT has become a central aim of higher education (Davies, 2013 ; Halpern, 2014 ; Van Gelder, 2005 ). However, several large-scale longitudinal studies were quite pessimistic that this laudable aim would be realized merely by following a higher education degree program. These studies revealed that CT-skills of many higher education graduates are insufficiently developed (e.g., Arum & Roksa, 2011 ; Flores et al., 2012 ; Pascarella et al., 2011 ; although a more recent meta-analytic study reached the more positive conclusion that students’ do improve their CT-skills over college years: Huber & Kuncel, 2016 ). Hence, there is a growing body of literature on how to teach CT (e.g., Abrami et al., 2008 , 2014 ; Van Peppen et al., 2018 , 2021 ; Angeli & Valanides, 2009 ; Niu et al., 2013 ; Tiruneh et al., 2014 , 2016 ).

However, there are different views on the best way to teach CT; the most well-known debate being whether CT should be taught in a general or content-specific manner (Abrami et al., 2014 ; Davies, 2013 ; Ennis, 1989 ; Moore, 2004 ). This debate has faded away during the last years, since most researchers nowadays commonly agree that CT can be seen in terms of both general skills (e.g., sound argumentation, evaluating statistical information, and evaluating the credibility of sources) and specific skills or knowledge used in the context of disciplines (e.g., diagnostic reasoning). Indeed, it has been shown that the most effective teaching methods combine generic instruction on CT with the opportunity to integrate the general principles that were taught with domain-specific subject matter. It is well established, for instance, that explicit teaching of CT combined with practice improves learning of CT-skills required for unbiased reasoning (e.g., Abrami et al., 2008 ; Heijltjes et al., 2014b ). However, while some effective teaching methods have been identified, it is as yet unclear under which conditions transfer of CT-skills across tasks or domains can be promoted, that is, the ability to apply acquired knowledge and skills to some new context of related materials (e.g., Barnett & Ceci, 2002 ).

Transfer has been described as existing on a continuum from near to far, with lower degrees of similarity between the initial and transfer situation along the way (Salomon & Perkins, 1989 ). Transferring knowledge or skills to a very similar situation, for instance problems in an exam of the same kind as practiced during the lessons, refers to ‘near’ transfer. By contrast, transferring between situations that share similar structural features but, on appearance, seem remote and alien to one another is considered ‘far’ transfer.

Previous research has shown that CT-skills required for unbiased reasoning consistently failed to transfer to novel problem types, i.e., far transfer, even when using instructional methods that proved effective for fostering transfer in various other domains (Van Peppen et al., 2018 , 2021 ; Heijltjes et al., 2014a , 2014b , 2015 , and this also applies to CT-skills more generally, see for example Halpern, 2014 ; Ritchhart & Perkins, 2005 ; Tiruneh et al., 2014 , 2016 ). This lack of transfer of CT-skills is worrisome because it would be unfeasible to train students on each and every type of reasoning bias they will ever encounter. CT-skills acquired in higher education should transfer to other domains and on-the-job and, therefore, it is crucial to acquire more knowledge on how transfer of these skills can be fostered (and this also applies to CT-skills more generally, see for example, Halpern, 2014 ; Beaulac & Kenyon, 2014 ; Lai, 2011 ; Ritchhart & Perkins, 2005 ). One instructional method that seems promising is comparing correct and erroneous worked examples (i.e., contrasting examples; e.g., Durkin & Rittle-Johnson, 2012 ).

Benefits of studying examples

Over the last decades, a large body of research has investigated learning from studying worked examples as opposed to unsupported problem solving. Worked examples consist of a problem statement and an entirely and correctly worked-out solution procedure (in this paper referred to as correct examples; Renkl, 2014 ; Renkl et al., 2009 ; Sweller et al., 1998 ; Van Gog et al., 2019 ). Typically, studying correct examples is more beneficial for learning than problem-solving practice, especially in initial skill acquisition (for reviews, see Atkinson et al., 2003 ; Renkl, 2014 ; Sweller et al., 2011 ; Van Gog et al., 2019 ). Although this worked example effect has been mainly studied in domains such as mathematics and physics, it has also been demonstrated in learning argumentation skills (Schworm & Renkl, 2007 ), learning to reason about legal cases (Nievelstein et al., 2013 ) and medical cases (Ibiapina et al., 2014 ), and novices’ learning to avoid biased reasoning (Van Peppen et al., 2021 ).

The worked example effect can be explained by cognitive load imposed on working memory (Paas et al., 2003a ; Sweller, 1988 ). Cognitive Load Theory (CLT) suggests that—given the limited capacity and duration of our working memory—learning materials should be designed so as to decrease unnecessary cognitive load related to the presentation of the materials (i.e., extraneous cognitive load). Instead, learners’ attention should be devoted towards processes that are directly relevant for learning (i.e., germane cognitive load). When solving practice problems, novices often use general and weak problem-solving strategies that impose high extraneous load. During learning from worked examples, however, the high level of instructional guidance provides learners with the opportunity to focus directly on the problem-solving principles and their application. Accordingly, learners can use the freed up cognitive capacity to engage in generative processing (Wittrock, 2010 ). Generative processing involves actively constructing meaning from to-be-learned information, by mentally organizing it into coherent knowledge structures and integrating these principles with one’s prior knowledge (i.e., Grabowski, 1996 ; Osborne & Wittrock, 1983 ; Wittrock, 1974 , 1990 , 1992 , 2010 ). These knowledge structures in turn can aid future problem solving (Kalyuga, 2011 ; Renkl, 2014 ; Van Gog et al., 2019 ).

A recent study showed that the worked example effect also applies to novices’ learning to avoid biased reasoning (Van Peppen et al., 2021 Footnote 1 ): participants’ performance on isomorphic tasks on a final test improved after studying correct examples, but not after solving practice problems. However, studying correct examples was not sufficient to establish transfer to novel tasks that shared similar features with the isomorphic tasks, but on which participants had not acquired any knowledge during instruction/practice. The latter finding might be explained by the fact that students sometimes process worked examples superficially and do not spontaneously use the freed up cognitive capacity to engage in generative processing needed for successful transfer (Renkl & Atkinson, 2010 ). Another possibility is that these examples did not sufficiently encourage learners to make abstractions of the underlying principles and explore possible connections between problems (e.g., Perkins & Salomon, 1992 ). It seems that to fully take advantage of worked examples in learning unbiased reasoning, students should be encouraged to be actively involved in the learning process and facilitated to focus on the underlying principles (e.g., Van Gog et al., 2004 ).

The potential of erroneous examples

While most of the worked-example research focuses on correct examples, recent research suggests that students learn at a deeper level and may come to understand the principles behind solution steps better when (also) provided with erroneous examples (e.g., Adams et al., 2014 ; Barbieri & Booth, 2016 ; Booth et al., 2013 ; Durkin & Rittle-Johnson, 2012 ; McLaren et al., 2015 ). In studies involving erroneous examples, which are often preceded by correct examples (e.g., Booth et al., 2015 ), students are usually prompted to locate the incorrect solution step and to explain why this step is incorrect or to correct it. This induces generative processing, such as comparison with internally represented correct examples and (self-)explaining (e.g., Chi et al., 1994 ; McLaren et al., 2015 ; Renkl, 1999 ). Students are encouraged to go beyond noticing surface characteristics and to think deeply about how erroneous steps differ from correct ones and why a solution step is incorrect (Durkin & Rittle-Johnson, 2012 ). This might help them to correctly update schemas of correct concepts and strategies and, moreover, to create schemas for erroneous strategies (Durkin & Rittle-Johnson, 2012 ; Große & Renkl, 2007 ; Siegler, 2002 ; Van den Broek & Kendeou, 2008 ; VanLehn, 1999 ), reducing the probability of recurring erroneous solutions in the future (Siegler, 2002 ).

However, erroneous examples are typically presented separately from correct examples, requiring learners to use mental resources to recall the gist of the no longer visible correct solutions (e.g., Große & Renkl, 2007 ; Stark et al., 2011 ). Splitting attention across time increases the likelihood that mental resources will be expended on activities extraneous to learning, which subsequently may hamper learning (i.e., temporal contiguity effect: e.g., Ginns, 2006 ). One could, therefore, argue that the use of erroneous examples could be optimized by providing them side by side with correct examples (e.g., Renkl & Eitel, 2019 ). This would allow learners to focus on activities directly relevant for learning, such as structural alignment and detection of meaningful commonalities and differences between the examples (e.g., Durkin & Rittle-Johnson, 2012 ; Roelle & Berthold, 2015 ). Indeed, studies on comparing correct and erroneous examples revealed positive effects in math learning (Durkin & Rittle-Johnson, 2012 ; Kawasaki, 2010 ; Loibl & Leuders, 2018 , 2019 ; Siegler, 2002 ).

The present study

We already indicated that it is still an important open question, which instructional strategy can be used to enhance transfer of CT skills. To reiterate, previous research demonstrated that practice consisting of worked example study was more effective for novices’ learning than practice problem solving, but it was not sufficient to establish transfer. Recent research has demonstrated the potential of erroneous examples, which are often preceded by correct examples. Comparing correct and erroneous examples (from here on referred to as contrasting examples) when presenting them side-by-side, seems to hold a considerable promise with respect to promoting generative processing and transfer. Hence, the purpose of the present study was to investigate whether contrasting examples of fictitious students’ solutions on ‘heuristics and biases tasks’ (a specific sub-category of CT skills: e.g., Tversky & Kahneman, 1974 ) would be more effective to foster learning and transfer than studying correct examples only, studying erroneous examples only, or solving practice problems. Performance was measured on a pretest, immediate posttest, 3-week delayed posttest, and 9-month delayed posttest (for half of the participants due to practical reasons), to examine effects on learning and transfer.

Based on the literature presented above, we hypothesized that studying correct examples would impose less cognitive load (i.e., lower investment of mental effort during learning ) than solving practice problems (i.e., worked example effect: e.g., Van Peppen et al., 2021 ; Renkl, 2014 ; Hypothesis 1). Whether there would be differences in invested mental effort between contrasting examples, studying erroneous examples, and solving practice problems, however, is an open question. That is, it is possible that these instructional formats impose a similar level of cognitive load, but originating from different processes: while practice problem solving may impose extraneous load that does not contribute to learning, generative processing of contrasting or erroneous examples may impose germane load that is effective for learning (Sweller et al., 2011 ). As such, it is important to consider invested mental effort (i.e., experienced cognitive load) in combination with learning outcomes. Secondly, we hypothesized that students in all conditions would benefit from the CT-instructions combined with the practice activities, as evidenced by pretest to immediate posttest gains in performance on instructed and practiced items (i.e., learning : Hypothesis 2). Furthermore, based on cognitive load theory, we hypothesized that studying correct examples would be more beneficial for learning than solving practice problems (i.e., worked example effect: e.g., Van Peppen et al., 2021 ; Renkl, 2014 ). Based on the aforementioned literature, we expected that studying erroneous examples would promote generative processing more than studying correct examples. Whether that generative processing would actually enhance learning, however, is an open question. This can only be expected to be the case if learners can actually remember and apply the previously studied information on the correct solution, which arguably involves higher cognitive load (i.e., temporal contiguity effect) than studying correct examples or contrasting examples. As contrasting can help learners to focus on key information and thereby induces generative processes directly relevant for learning (e.g., Durkin & Rittle-Johnson, 2012 ), we expected that contrasting examples would be most effective. Thus, we predict the following pattern of results regarding performance gains on learning items (Hypothesis 3): contrasting examples > correct examples > practice problems. As mentioned above, it is unclear how the erroneous examples condition would compare to the other conditions.

Furthermore, we expected that generative processing would promote transfer. Despite findings of previous studies in other domains (e.g., Paas, 1992 ), we found no evidence in a previous study that studying correct examples or solving practice problems would lead to a difference in transfer performance (Van Peppen et al., 2021 ). Therefore, we predict the following pattern of results regarding performance on non-practiced items of the immediate posttest (i.e., transfer , Hypothesis 4): contrasting examples > correct examples ≥ practice problems. Again, it is unclear how the erroneous examples condition would compare to the other conditions.

We expected these effects (Hypotheses 3 and 4) to persist on the delayed posttests. As effects of generative processing (relative to non-generative learning strategies) sometimes increase as time goes by (Dunlosky et al., 2013 ), they may be even greater after a delay. For a schematic overview of the hypotheses, see Table 1 .

We created an Open Science Framework (OSF) page for this project, where all materials, the dataset, and all script files of the experiment are provided (osf.io/8zve4/).

Participants and design

Participants were 182 first-year ‘Public Administration’ and ‘Safety and Security Management’ students of a Dutch university of applied sciences (i.e., higher professional education), both part of the Academy for Security and Governance. These students were approximately 20 years old ( M  = 19.53, SD  = 1.91) and most of them were male (120 male, 62 female). Before they were involved in these study programs, they completed secondary education (senior general secondary education: n  = 122, pre-university: n  = 7) or went to college (secondary vocational education: n  = 28, higher professional education: n  = 24, university education: n  = 1).

Of the 182 students (i.e., total number of students in these cohorts), 173 students (95%) completed the first experimental session (see Fig.  1 for an overview) and 158 students (87%) completed both the first and second experimental session. Additionally, 83 of these students (46%) of the Safety and Security Management program completed the 9-month delayed posttest during the first mandatory CT-lesson of their second study year (we had no access to another CT-lesson of the Public Administration program). The number of absentees during a lesson (about 15 in total) is quite common for mandatory lessons in these programs and often due to illness or personal circumstances. Students who were absent during the first experimental session and returned to the second experimental session could not participate in the study because they had missed the intervention phase.

Overview of the study design. The four conditions differed in practice activities during the practice phase

We defined a priori that participants would be excluded in case of excessively fast reading speed. Considering that even fast readers can read no more than 350 words per minute (e.g., Trauzettel-Klosinski & Dietz, 2012 ), and the text of our instructions additionally required understanding, we assumed that participants who spent < 0.17 s per word (i.e., 60 s/350 words) did not read the instructions seriously. These participants were excluded from the analyses. Due to drop-outs, we decided to split the analyses to include as many participants as possible. We had a final sample of 170 students ( M age  = 19.54, SD = 1.93; 57 female) for the pretest to immediate posttest analyses, a subsample of 155 students for the immediate to 3-week delayed posttest analyses ( M age  = 19.46, SD = 1.91; 54 female), and a subsample of 82 students (46%) for the 3-week delayed to 9-month delayed posttest ( M age  = 19.27, SD = 1.79; 25 female). We calculated a power function of our analyses using the G*Power software (Faul et al., 2009 ) based on these sample sizes. The power for the crucial Practice Type × Test Moment interaction—under a fixed alpha level of 0.05 and with a correlation between measures of 0.3 (e.g., Van Peppen et al., 2018 )—for detecting a small (η p 2  = .01), medium (η p 2  = .06), and large effect (η p 2  = .14) respectively, is estimated at .42, > .99, and 1.00 for the pretest to immediate posttest analyses; .39, > .99, and 1.00 for the immediate to 3-week delayed posttest analyses; and .21, .90, and > .99 for the 3-week to 9-month delayed posttest. Thus, the power of our study should be sufficient to pick up medium-sized interaction effects.

Students participated in a pretest-intervention–posttest design (see Fig.  1 ). After completing the pretest on learning items (i.e., instructed and practiced during the practice phase), all participants received succinct CT instructions and two correct worked examples. Thereafter, they were randomly assigned to one of four conditions that differed in practice activities during the practice phase: they either (1) compared correct and erroneous examples (‘contrasting examples’, n  = 41; n  = 35; n  = 20); (2) studied correct examples (i.e., step-by-step solutions to unbiased reasoning) and explained why these were right (‘correct examples’, n  = 43; n  = 40; n  = 21); (3) studied erroneous examples (i.e., step-by-step incorrect solutions including biased reasoning) and explained why these were wrong (‘erroneous examples’, n  = 43; n  = 40; n  = 18); or (4) solved practice problems and justified their answers (‘practice problems’, n  = 43; n  = 40; n  = 23). A detailed explanation of the practice activities can be found in the CT-practice subsection below. Immediately after the practice phase and after a 3-week delay, participants completed a posttest on learning items (i.e., instructed and practiced during the practice phase) and transfer items (i.e., not instructed and practiced during the practice phase). Additionally, some students took a posttest after a 9-month delay. Further CT-instructions were given (in three lessons of approx. 90 min) in-between the second session of the experiment and the 9-month follow up. In these lessons, for example, the origins of the concept of CT, inductive and deductive reasoning, and the Toulmin model of argument were discussed. Thus, these data were exploratively analyzed and need to be interpreted with caution.

In the following paragraphs, the used learning materials, instruments and associated measures, and characteristics of the experimental conditions are described.

CT-skills tests

The CT-skills tests consisted of classic heuristics and biases tasks that reflected important aspects of CT. In all tasks, belief bias played a role, that is, when the conclusion aligns with prior beliefs or real-world knowledge but is invalid or vice versa (Evans et al., 1983 ; Markovits & Nantel, 1989 ; Newstead et al., 1992 ). These tasks require that one recognizes the need for analytical and reflective reasoning (i.e. based on knowledge and rules of logical reasoning and statistical reasoning) and switches to this type of reasoning. This is only possible when heuristic responses are successfully inhibited.

The pretest consisted of six classic heuristics and biases items, across two categories (see Online Appendix A for an example of each category): syllogistic reasoning (i.e., logical reasoning) and conjunction (i.e., statistical reasoning) items. Three syllogistic reasoning items measured students’ tendency to be influenced by the believability of a conclusion that is inferred from two premises when evaluating the logical validity of that conclusion (adapted from Evans, 2002 ). For instance, the conclusion that cigarettes are healthy is logically valid given the premises that all things you can smoke are healthy and that you can smoke cigarettes. Most people, however, indicate that the conclusion is invalid because it does not align with their prior beliefs or real-world knowledge (i.e., belief bias, Evans et al., 1983 ). Three conjunction items examined to what extent the conjunction rule ( P (A&B) ≤  P (B))—which states that the probability of multiple specific events both occurring must be lower than the probability of one of these events occurring alone—is neglected (Tversky & Kahneman, 1983 ). To illustrate, people have the tendency to judge two things with a causal or correlational link, for example advanced age and occurrence of heart attacks, as more probable than one of these on its own.

The posttests consisted of parallel versions (i.e., structurally equivalent but different surface features) of the six pretest items which were instructed and practiced and, thus, served to assess differences in learning outcomes. Additionally, the posttests contained six items across two non-practiced categories that served to assess differences in transfer performance (see Online Appendix A for an example of each category). Three Wason selection items measured students’ tendency to disprove a hypothesis by verifying rules rather than falsifying them (i.e., confirmation bias, adapted from Stanovich, 2011 ). Three base-rate items examined students’ tendency to incorrectly judge the likelihood of individual-case evidence (e.g., from personal experience, a single case, or prior beliefs) by not considering all relevant statistical information (i.e., base-rate neglect, adapted from Fong et al., 1986 ; Stanovich & West, 2000 ; Stanovich et al., 2016 ; Tversky & Kahneman, 1974 ). These transfer items shared similar features with the learning categories, namely, one category requiring knowledge and rules of logic (i.e., Wason selection tasks can be solved by applying syllogism rules) and one category requiring knowledge and rules of statistics (i.e., base-rate tasks can be solved by appropriate probability and data interpretation).

The cover stories of all test items were adapted to the domain of participants’ study program (i.e., Public Administration and Safety and Security Management). A multiple-choice (MC) format with different numbers of alternatives per item was used, with only one correct alternative for each item.

CT-instructions

All participants received a 12 min video-based instruction that started with emphasizing the importance of CT in general, describing the features of CT, and explaining which skills and attitudes are needed to think critically. Thereafter, explicit instructions on how to avoid biases in syllogistic reasoning and conjunction fallacies followed, consisting of two worked examples that showed the correct line of reasoning. The purpose of these explicit instructions was to provide students with knowledge on CT and to allow them to mentally correct initially incorrect responses on the items seen in the pretest.

CT-practice

Participants performed practice activities on the task categories that they were given instructions on (i.e., syllogistic reasoning and conjunction tasks). The CT-practice consisted of four practice tasks, two of each of the task categories. Each practice task was again adapted to the study domain and started with the problem statement (see Online Appendix B for an example of a practice task of each condition). Participants in the correct examples condition were provided with a fictitious student’s correct solution and explanation to the problem, including auxiliary representations, and were prompted to explain why the solution steps were correct. Participants in the erroneous examples condition received a fictitious student’s erroneous solution to the problem, again including auxiliary representations. They were prompted to indicate the erroneous solution step and to provide the correct solution themselves. In the contrasting examples , participants were provided fictitious students’ correct and erroneous solutions to the problem and were prompted to compare the two solutions and to indicate the erroneous solution and the erroneous solution step. Participants in the practice problems condition had to solve the problems themselves, that is, they were instructed to choose the best answer option and were asked to explain how the answer was obtained. Participants in all conditions were asked to read the practice tasks thoroughly. To minimize differences in time investment (i.e., the contrasting examples consisted of considerably more text), we have added self-explanation prompts in the correct examples, erroneous examples, and practice problem conditions.

Mental effort

After each test item and practice-task, participants were asked to report how much effort they invested in completing that task or item on a 9-point subjective rating scale ranging from (1) very, very low effort to (9) very, very high effort (Paas, 1992 ). This widely used scale in educational research (for overviews, see Paas et al., 2003b ; Van Gog & Paas, 2008 ), is assumed to reflect the cognitive capacity actually allocated to accommodate the demands imposed by the task or item (Paas et al., 2003a ).

The study was run during the first two lessons of a mandatory first-year CT-course in two, very similar, Security and Governance study programs. Participants were not given CT-instructions in between these lessons. They completed the study in a computer classroom at the participants’ university with an entire class of students, their teacher, and the experiment leader (first author) present. When entering the classroom, participants were instructed to sit down at one of the desks and read an A4-paper containing some general instructions and a link to the computer-based environment (Qualtrics platform). The first experimental session (ca. 90 min) began with obtaining written consent from all participants. Then, participants filled out a demographic questionnaire and completed the pretest. Next, participants entered the practice phase in which they first viewed the video-based CT-instructions and then were assigned to one of the four practice conditions. Immediately after the practice phase, participants completed the immediate posttest. Approximately 3 weeks later, participants took the delayed posttest (ca. 20 min) in their computer classrooms. Additionally, students of the Safety and Security Management program took the 9-month delayed posttest during the first mandatory CT-lesson of their second study year, Footnote 2 which was exactly the same as the 3-week delayed posttest. During all experimental sessions, participants could work at their own pace and were allowed to use scrap paper. Time-on-task was logged during all phase and participants had to indicate after each test item and practice-task how much effort they invested. Participants had to wait (in silence) until the last participants had finished before they were allowed to leave the classroom.

Data analysis

All test items were MC-only questions, except for one learning item and one transfer items with only two alternatives (conjunction item and base-rate item) that were MC-plus-motivation questions to prevent participants from guessing. Items were scored for accuracy, that is, unbiased reasoning; 1 point for each correct alternative on the MC-only questions or a maximum of 1 point (increasing in steps of 0.5) for the correct explanation for the MC-plus-motivation question using a coding scheme that can be found on our OSF-page. Because two transfer items (i.e., one Wason selection item and one base-rate item) appeared to substantially reduce the reliability of the transfer performance measure, presumably as a result of low variance due to floor effects, we decided to omit these items from our analyses. As a result, participants could attain a maximum total score of 6 on the learning items and a maximum score of 4 on the transfer items. For comparability, learning and transfer outcomes were computed as percentage correct scores instead of total scores. Participants’ explanations on the open questions of the tests were coded by one rater and another rater (the first author) coded 25% of the explanations of the immediate posttest. Intra-class correlation coefficients were 0.990 for the learning test items and 0.957 for the transfer test items. After the discrepancies were resolved by discussion, the primary rater’s codes were used in the analyses.

Cronbach’s alpha on invested mental effort ratings during studying correct examples, studying erroneous examples, contrasting examples, and solving practice problems, respectively, was .87, .76, .77, and .65. Cronbach’s alpha on the learning items was .21, .42, .58, and .31 on the pretest, immediate posttest, 3-week delayed posttest, and 9-month delayed posttest, respectively. The low reliability on the pretest might be explained by the fact that a lack of prior knowledge requires guessing of answers. As such, inter-item correlations are low, resulting in a low Cronbach’s alpha. Cronbach’s alpha on the transfer items was .31, .12, and .29 on the immediate, 3-week delayed, and 9-month delayed posttest, respectively. Cronbach’s alpha on the mental effort items belonging to the learning items was .73, .79, .81, and .76 on the pretest, immediate posttest, 3-week delayed posttest, and 9-month delayed posttest, respectively. Cronbach’s alpha on the mental effort items belonging to the transfer items was .71, .75, and .64 on the immediate posttest, 3-week delayed posttest, and 9-month delayed posttest, respectively. However, caution is required in interpreting the above values because sample sizes as in studies like this do not seem to produce sufficiently precise alpha coefficients (e.g. Charter, 2003 ). Cronbach’s alpha is a statistic and therefore subject to sample fluctuations. Hence, one should be careful with drawing firm conclusions about the precision of Cronbach’s alpha in the population (the parameter) based on small sample sizes (i.e., in reliability literature, samples of 300–400 are considered small, see for instance Charter, 2003 ; Nunally & Bernstein, 1994 ; Segall, 1994 ).

There was no significant difference on pretest performance between participants who stayed in the study and those who dropped out after the first session, t (172) = .38, p  = .706, and those who dropped out after the second session, t (172) = − 1.46, p  = .146. Furthermore, there was no significant difference in educational background between participants who stayed in the study and those who dropped out after the first session, r (172) = .13, p  = .087, and those who dropped out after the second session, r (172) = − .01, p  = .860. Finally, there was no significant difference in age between participants who stayed in the study and those who dropped out after the first session, t (172) = − 1.51, p  = .134, but there was a difference between participants who stayed in the study and those who dropped out after the second session, t (172) = − 2.02, p  = .045. However, age did not correlate significantly with learning performance (minimum p  = .553) and was therefore not a confounding variable.

Additionally, participants’ performance during the practice phase was scored for accuracy, that is, unbiased reasoning. In each condition, participants could attain a maximum score of 2 points (increasing in steps of 0.5) for the correct answer on each problem (either MC-only answers or MC-plus-explanation answers), resulting in a maximum total score of 8. The explanations given during practice were coded for explicit relations to the principles that were communicated in the instructions (i.e., principle-based explanations; Renkl, 2014 ). For instance, participants earned the full 2 points if they explained in a conjunction task that the first statement is part of the second statement and that the first statement therefore can never be more likely than the two statements combined. Participants’ explanations were coded by the first author and another rater independently coded 25% of the explanations. Intra-class correlation coefficients were 0.941, 0.946, and 0.977 for performance in the correct examples, erroneous examples, and practice problems conditions respectively (contrasting examples consisted of MC-only questions). After a discussion between the raters about the discrepancies, the primary rater’s codes were updated and used in the exploratory analyses.

For all analyses in this paper, a p -value of .05 was used a threshold for statistical significance. Partial eta-squared (η p 2 ) is reported as an effect size for all ANOVAs (see Table 3 ) with η p 2  = .01, η p 2  = .06, and η p 2  = .14 denoting small, medium, and large effects, respectively (Cohen, 1988 ). Cramer’s V is reported as an effect size for chi-square tests with (having 2 degrees of freedom) V  = .07, V  = .21, and V  = .35 denoting small, medium, and large effects, respectively.

Preliminary analyses

Check on condition equivalence.

Before running any of the main analyses, we checked our conditions on equivalence. Preliminary analyses confirmed that there were no a-priori differences between the conditions in educational background, χ 2 (15) = 15.57, p  = .411, V  = .18; gender, χ 2 (3) = 1.21, p  = .750, V  = .08; performance on the pretest, F (3, 165) = 0.42, p  = .739, η p 2  = .01; time spent on the pretest, F (3, 165) = 0.16, p  = .926, η 2  < .01; and mental effort invested on the pretest, F (3, 165) = 0.80, p  = .498, η 2  = .01. Further, we estimated two multiple regression models (learning and transfer) with practice type and performance on the pretest as explanatory variables, including the interaction between practice type and performance on the pretest. There was no evidence of an interaction effect (learning: R 2  = .07, F (1, 166) = .296, p  = .587; transfer: R 2  = .07, F (1, 166) = .260, p  = .611) and we can, therefore, conclude that the relationship between practice type and performance on the posttest does not depend on performance on the pretest.

Check on time-on-task

The Levene’s test for equality of variances was significant, F (3, 166) = 9.57, p  < .001. Therefore, a Brown–Forsythe one-way ANOVA was conducted. This analysis revealed a significant time-on-task (in seconds) difference between the conditions during practice, F (3, 120.28) = 16.19, p  < .001, η 2  = .22. Pairwise comparisons showed that time-on-task was comparable between erroneous examples ( M  = 862.79, SD  = 422.43) and correct examples ( M  = 839.58, SD  = 298.33) and between contrasting examples ( M  = 512.29, SD  = 130.21) and practice problems ( M  = 500.41, SD  = 130.21). However, time-on-task was significantly higher in the first two conditions compared to the latter two conditions (erroneous examples = correct examples > contrasting examples = practice problems), all p ’s < .001. This should be considered when interpreting the results on effort and posttest performance.

Main analyses

Descriptive and test statistics are presented in Table 2 , 3 , and 4 . Correlations between several variables are presented in Table 5 . It is important to realize that we measured mental effort as an indicator of overall experienced cognitive load. It is known, though, that the relation with learning depends on the origin of the experienced cognitive load. That is, if it originates mainly from germane processes that contribute to learning, high load would positively correlate with test performance, if it originates from extraneous processes, it would negatively correlate with test performance. Caution is warranted in interpreting these correlations, however, because of the exploratory nature of these correlation analyses, which makes it impossible to control for the probability of type 1 errors. We also exploratively analyzed invested mental effort and time-on-task data on the posttest; however, these analyses did not have much added value for this paper and, therefore, are not reported here but will be provided on our OSF-project page.

Performance during the practice phase

As each condition received different prompts during practice, performance during the practice phase could not be meaningfully compared between conditions and, therefore, we decided to report descriptive statistics only to describe the level of performance during the practice phase per condition (see Table 2 ). Descriptive statistics showed that participants earned more than half of the maximum total score while studying correct examples or engaging in contrasting examples. Participants who studied erroneous examples or solved practice problems performed worse during practice.

Mental effort during learning

A one-way ANOVA revealed a significant main effect of Practice Type on mental effort invested in the practice tasks. Contrary to hypothesis 1, a Tukey post hoc test revealed that participants who solved practice problems invested significantly less effort ( M  = 4.28, SD  = 1.11) than participants who engaged in contrasting examples ( M  = 5.08, SD  = 1.29, p  = .022) or studied erroneous examples ( M  = 5.17, SD  = 1.19, p  = .008). There were no other significant differences in effort investment between conditions. Interestingly, invested mental effort during contrasting examples correlated negatively with pretest to posttest performance gains on learning items, indicating that the experienced load originated mainly from extraneous processes (see Table 5 ).

Test performance

The data on learning items were analyzed with two 2 × 4 mixed ANOVAs with Test Moment (pretest and immediate posttest/immediate posttest and 3-week delayed posttest) as within-subjects factor and Practice Type (correct examples, erroneous examples, contrasting examples, and practice problems) as between-subjects factor. Because transfer items were not included in the pretest, the data on transfer items were analyzed by a 2 × 4 mixed ANOVA with Test Moment (immediate posttest and 3-week delayed posttest) as within-subjects factor and Practice Type (correct examples, erroneous examples, contrasting examples, and practice problems) as between-subjects factor.

Performance on learning items

In line with Hypothesis 2, the pretest-immediate posttest analysis showed a main effect of Test Moment on performance on learning items: participants’ performance improved from pretest ( M  = 27.26, SE  = 1.43) to immediate posttest ( M  = 49.98, SE  = 1.87). In contrast to Hypothesis 3, the results did not reveal a main effect of Practice Type, nor an interaction between Practice Type and Test Moment. The second analysis ( N  = 154)—to test whether effects are still present after 3 weeks—showed a main effect of Test Moment: participants performed better on the delayed posttest ( M  = 55.54, SE  = 2.16) compared to the immediate posttest ( M  = 50.95, SE  = 2.00). Again, contrary to our hypothesis, there was no main effect of Practice Type, nor an interaction between Practice Type and Test Moment.

Performance on transfer items

The results revealed no main effect of Test Moment. Moreover, in contrast to Hypothesis 4, the results did not reveal a main effect of Practice Type, nor an interaction between Practice Type and Test Moment. Footnote 3

Exploratory analyses

Participants from one of the study programs were tested again after a 9-month delay. Regarding performance on learning items, a 2 × 4 mixed ANOVA with Test Moment (3-week delayed posttest or 9-month delayed posttest) as within-subjects factor and Practice Type (correct examples, erroneous examples, contrasting examples, and practice problems) as between-subjects factor revealed a main effect of Test Moment (see Table 2 ): participants’ performance improved from 3-week delayed posttest ( M  = 53.30, SE  = 2.69) to 9-month delayed posttest ( M  = 63.00, SE  = 2.24). The results did not reveal a main effect of Practice Type, nor an interaction between Practice Type and Test Moment.

Regarding performance on transfer items , a 2 × 4 mixed ANOVA with Test Moment (3-week delayed posttest and 9-month delayed posttest) as within-subjects factor and Practice Type (correct examples, erroneous examples, contrasting examples, and practice problems) as between-subjects factor revealed a main effect of Test Moment (see Table 2 ): participants performed lower on the 3-week delayed test ( M  = 19.25, SE  = 1.60) than the 9-month delayed test ( M  = 24.84, SE  = 1.67). The results did not reveal a main effect of Practice Type, nor an interaction between Practice Type and Test Moment.

Previous research has demonstrated that providing students with explicit instructions combined with practice on domain-relevant tasks was beneficial for learning to reason in an unbiased manner (Heijltjes et al., 2014a , 2014b , 2015 ), and that practice consisting of worked example study was more effective for novices’ learning than practice problem solving (Van Peppen et al., 2021 ). However, this was not sufficient to establish transfer to novel tasks. With the present study, we aimed to find out whether contrasting examples—which has been proven effective for promoting transfer in other learning domains—would promote learning and transfer of reasoning skills.

Findings and implications

Our results corroborate the finding of previous studies (e.g., Heijltjes et al., 2015 ; Van Peppen et al., 2018 , 2021 ) that providing students with explicit instructions and practice activities is effective for learning to avoid biased reasoning (Hypothesis 1), since we found considerable pretest to immediate posttest gains on practiced items. Moreover, our results revealed that participants’ performance improved even further after a 3-week and a 9-month delay, although the latter finding could also be attributed to the further instructions that were given in courses in-between the 3-week and 9-month follow up. That students improved in the longer term seems to indicate that our instructional intervention triggered active and deep processing and contributed to storage strength. Hence, our findings provide further evidence that a relatively brief instructional intervention including explicit instructions and practice opportunities is effective for learning of CT-skills, which is promising for educational practice.

In contrast to our expectations, however, we did not find any differences among conditions on either learning or transfer (Hypothesis 3). It is surprising that the present study did not reveal a beneficial effect of studying correct examples as opposed to practicing with problems, as this worked example effect has been demonstrated with many different tasks (Renkl, 2014 ; Van Gog et al., 2019 ), including heuristics-and-biases tasks (Van Peppen et al., 2021 ).

Given that most studies on the worked example effect use pure practice conditions or give minimal instructions prior to practice (e.g., Van Gog et al., 2019 ), whereas the current study was preceded by instructions including two worked examples, one might wonder whether this contributed to the lack of effect. That is, the effects are usually not investigated in a context in which elaborate processing of instructions precedes practice, as in the current (classroom) study, and this may have affected the results. It seems possible that the CT-instructions already had a substantial effect on learning unbiased reasoning, making it difficult to find differential effects of different types of practice activities. This suggestion, however, contradicts the relatively low performance during the practice phase. Moreover, one could argue that if these instructions would lead to higher prior knowledge, it should render the correct worked examples less useful (cf. research on the ‘expertise reversal effect’) and should help those in the other practice conditions perform better on the practice problems, but we did not find that either. Furthermore, these instructions were also provided in a previous study in which a worked example effect was found in two experiments (Van Peppen et al., 2021 ). A major difference between that prior study and this one, however, is that in the present study, participants were prompted to self-explain while studying examples or solving practice problems. Prompting self-explanations, however, seems to encourage students to engage in deep processing during learning (Chi et al., 1994 ), especially for students with sufficient prior knowledge (Renkl & Atkinson, 2010 ). In the present study, this might have interfered with the usual worked-example effect. However, the quality of the self-explanations was higher in the correct example condition than in the problem-solving condition (i.e., performance during the practice phase scores), making the absence of a worked example effect even more remarkable. Given that the worked example effect mainly occurs for novices, one could argue that participants in the current study had more prior knowledge than participants in that prior study; however, it concerned a similar group of students and descriptive statistics showed that students performed comparable on average in both studies.

Another potential explanation might lie in the number of practice tasks, which differed between the prior study (nine tasks: Van Peppen et al., 2021 ) and present study (four tasks), and which might moderate the effect of worked examples. The mean scores on the pretests as well as the performance progress in the practice problem condition was comparable with the previous study, but the progress of the worked example condition was considerably smaller. As it is crucial for a worked example effect that the worked-out solution procedures are understood, it might be that the effect did not emerge in the present study because participants did not get sufficient worked examples during practice.

This might perhaps also explain why contrasting examples did not benefit learning or transfer in the present study. Possibly, students first need to gain a better understanding of the subject matter with heuristics-and-biases tasks before they are able to benefit from aligning the examples (Rittle-Johnson et al., 2009 ). In particular the lack of transfer effects might be related to the duration or extensiveness of the practice activities; even though students learned to solve reasoning tasks, their subject knowledge may have been insufficient to solve novel tasks. As such, it can be argued that establishing transfer needs longer or more extensive practice. Contrasting examples seem to help students extend and refine their knowledge and skills through engaging in comparing activities and analyzing errors, that is, they seem to help them to correctly update schemas of correct concepts and strategies and to create schemas for erroneous strategies reducing the probability of recurring erroneous solutions in the future. However, more attention may need to be paid to the acquisition of the new knowledge and integration with wat students already know (see the Dimensions of Learning framework; Marzano et al., 1993 ). Potentially, having contrasting examples preceded by a more extensive instruction phase to guarantee a better understanding of logical and statistical reasoning would enhance learning and establish transfer. Another possibility would be to provide more guidance in the contrasting examples, as has been done in previous studies by explicitly marking the erroneous examples as incorrect and prompting students to reflect or elaborate on the examples (e.g., Durkin & Rittle-Johnson, 2012 ; Loibl & Leuders, 2018 , 2019 ). It should be noted though, that the lower time on task in the contrasting condition might also be indicative of a motivational problem; whereas the side-by-side presentation was intended to encourage deep processing, it might have had the opposite effect that students might have engaged in superficial processing, just scanning to see where differences in the examples lay, without thinking much about the underlying principles. This idea is confirmed by the finding that invested mental effort during comparing correct and erroneous examples correlated negatively with performance gains on learning items, indicating that the experienced load originated mainly from extraneous processes. It would be interesting in future research to manipulate knowledge gained during instruction to investigate whether prior knowledge indeed moderates the effect of contrasting examples and to examine the interplay between contrasting examples, reflection/elaboration prompts, and final test performance.

Another possible explanation for the lack of a beneficial effect of contrasting examples might be related to the self-explanations prompts that were provided in the correct examples, erroneous examples, and practice problems conditions. Although the prompts differ, it is important to note that the explicit instruction to compare the solution process likely evokes self-explaining processes as well. The reason we added self-explanation prompts to the other conditions was to rule out an effect of prompting as such, as well as a potential effect of time on task (i.e., the text length in the contrasting examples condition was considerably longer than in the other conditions). The positive effect of contrasting examples might have been negated by a positive effect of the self-explanation prompts given in the other conditions. However, had we found a positive effect of comparing, as we expected, our design would have increased the likelihood that this was due to the comparison process and not just to more in-depth processing or higher processing time through self-explaining. Unexpectedly, we did find time-on-task differences between conditions during practice, but this does not seem to affect our findings. Time-on-task during practice was not correlated with learning and transfer posttest performance. This also becomes apparent from the condition means, i.e., the conditions with the lowest time-on-task means did not differ on learning and transfer compared to the conditions with the highest time-on-task means.

The classroom setting might also explain why there were no differential effects of contrasting examples. This study was conducted as part of an existing course and the learning materials were relevant for the course/exam and. Because of that, students’ willingness to invest effort in their performance may have been higher than is generally the case in psychological laboratory studies: their performance on such tasks actually mattered (intrinsically or extrinsically) to them. As such, students in the control conditions may have engaged in generative processing themselves, for instance by trying to compare the given correct (or erroneous) examples with internally represented erroneous (or correct) solutions. Therefore, it is possible that effects of generative processing strategies such as comparing correct and erroneous examples found in the psychological laboratory—where students participate to earn required research credits and the learning materials are not part of their study program—might not readily transfer to field experiments conducted in real classrooms.

The absence of differential effects of the practice activities on learning and transfer may also be related to the affective and attitudinal dimension of CT. Attitudes and perceptions about learning affect learning (Marzano et al., 1993 ), probably even more so in the CT-domain than in other learning domains. Being able to think critically relies heavily on the extent to which one possesses the requisite skills and is able to use these skills, but also on whether one is inclined to use these skills (i.e., thinking dispositions; Perkins et al., 1993 ).

The present study raises further questions about how transfer of CT-skills can be promoted. Although several studies have shown that to enhance transfer of knowledge or skills, instructional strategies should contribute to storage strength by effortful learning conditions that trigger active and deep processing ( desirable difficulties ; e.g., Bjork & Bjork, 2011 ), the present study—once again (Van Peppen et al., 2018 , 2021 ; Heijltjes et al., 2014a , 2014b , 2015 )—showed that this may not apply to transfer of CT-skills. This lack of transfer could lie in inadequate recall of the acquired knowledge, recognition that the acquired knowledge is relevant to the new task, and/or the ability to actually map that knowledge onto the new task (Barnett & Ceci, 2002 ). Following this, a further study should elucidate what the underlying mechanism(s) is/are to shed more light on how to promote transfer of CT-skills.

Limitations and strengths

One limitation of this study is that our measures showed low levels of reliability. Under these circumstances, the probability of detecting a significant effect—given one exists—are low (e.g., Cleary et al., 1970 ; Rogers & Hopkins, 1988 ), and subsequently, the chance that Type 2 errors have occurred in the current study is relatively high. In our study, the low levels of reliability can probably be explained by the multidimensional nature of the CT-test, that is, it represents multiple constructs that do not correlate with each other. Performance on these tasks depends not only on the extent to which that task elicits a bias (resulting from heuristic reasoning), but also on the extent to which a person possesses the requisite mindware (e.g., rules or logic or probability). Thus, systematic variance in performance on such tasks can either be explained by a person’s use of heuristics or his/her available mindware. If it differs per item to what extent a correct answer depends on these two aspects, and if these aspects are not correlated, there may not be a common factor explaining all interrelationships between the measured items. Moreover, the reliability issue may have increased even more since multiple task types were included in the CT-skills tests, requiring different, and perhaps uncorrelated, types of mindware (e.g., rules of logic or probability). Future research, therefore, would need to find ways to improve CT measures (i.e., decrease measurement error), for instance by narrowing down the test into a single measurable construct, or should utilize measures known to have acceptable levels of reliability (LeBel & Paunonen, 2011 ). The latter option seems challenging, however, as multiple studies report rather low levels of reliability of tests consisting of heuristics and biases tasks (Aczel et al., 2015 ; West et al., 2008 ) and revealed concerns with the reliability of widely used standardized CT tests, particularly with regard to subscales (Bernard et al., 2008 ; Bondy et al., 2001 ; Ku, 2009 ; Leppa, 1997 ; Liu et al., 2014 ; Loo & Thorpe, 1999 ). This raises the question whether these issues are related to the general construct CT. To achieve further progress in research on instructional methods for teaching CT, more knowledge on the construct validity of CT in general and unbiased reasoning in particular is needed. When the aim is to evaluate CT as a whole, one should perhaps move towards a more holistic measurement method, for instance by performing pairwise comparisons (i.e., comparative judgment; Bramley & Vitello, 2018 ; Lesterhuis et al., 2017 ). If, however, the intention is to measure specific aspects of CT, one should indicate specifically which aspect of CT to measure and select a suitable test for that aspect. Mainly considering that individual aspects of CT may not be as strongly correlated as thought and then could not be included in one scale.

Another point worth mentioning, is that we opted for assessing invested mental effort, which reflects the amount of cognitive load students experienced. This is informative when combined with their performance (for a more elaborate discussion, see Van Gog & Paas, 2008 ). Moreover, research has shown that it is important to measure cognitive load immediately after each task (e.g., Schmeck et al., 2015 ; Van Gog et al., 2012 ) and the mental effort rating scale (Paas, 1992 ) is easy to apply after each task. However, it unfortunately does not allow us to distinguish between different types of load. It should be noted, though, that it seems very challenging to do this with other measurement instruments (e.g., Skulmowski & Rey, 2017 ). Also, instruments that might be suited for this purpose, for example the rating scale developed by Leppink et al. ( 2013 ), would have been too long to apply after each task in the present study.

A strength of the current study is that it was conducted in a real educational setting as part of an existing CT course, which increases ecological validity. Despite the wealth of worked examples research, classroom studies are relatively rare. Interestingly, (multi-session) classroom studies on math and chemistry have also failed to find the worked example effect, although—in contrast to the present study—worked examples often did show clear efficiency benefits compared to practice problems (McLaren et al., 2016 ; Van Loon-Hillen et al., 2012 ). In line with our finding, a classroom study by Isotani et al. ( 2011 ) indicated that (high prior knowledge) students did not benefit more from studying erroneous examples than from correct examples or practice problems. As discussed earlier in the discussion, the classroom setting might explain the absence of generative processing strategies on learning and transfer. This suggests a theoretical implication, namely that beneficial effects of such strategies might become smaller when the willingness to invest increases and vice versa.

To conclude, based on the findings of the present study, comparing correct and erroneous examples (i.e., contrasting examples) does not seem to be a promising instructional method to further enhance learning and transfer of specific—and specifically tested—CT skills. Consequently, our findings raise questions about the preconditions of contrasting examples effects and effects of generative processing strategies in general, such as the setting in which they are presented to students. Further research on the exact boundary conditions, through solid laboratory and classroom studies, is therefore recommended. Moreover, this study provides valuable insights for educational practice. That is, providing students with explicit CT-instruction and the opportunity to practice with domain-relevant problems in a relatively short instructional intervention has the potential to improve learning. The format of the practice tasks does not seem to matter much, although a prior study did find a benefit of studying correct examples, which might therefore be the safest bet. Finally, this study again underlines the great difficulty of designing instructions to enhance CT-skills in such a way that these would also transfer across tasks/domains.

Data availability

All data, script files, and materials are provided on the Open Science Framework (OSF) project page that we created for this study (anonymized view-only link: https://osf.io/8zve4/?view_only=ca500b3aeab5406290310de34323457b ).

Code availability

Not applicable.

This study investigated effects of interleaved practice (as opposed to blocked practice) on students’ learning and transfer of unbiased reasoning. Given that interleaved practice seems to impose high cognitive load, which may hinder learning, it was additionally tested whether this effect interacts with the format of the practice tasks (i.e., correct examples or practice problems).

We had no access to another CT-lesson of the Public Administration program, so due to practical reasons, students of this program were not administered to the 9-month delayed posttest.

We also exploratively analyzed the learning and transfer data for each individual measurement point and we analyzed performance on single learning and transfer items. The outcomes did not deviate markedly from the findings on sum scores (i.e., no effects of Practice Type were found). Test statistics can be found on our OSF-project page and the descriptive statistics of performance per single item can be found in Table 4 .

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Acknowledgements

This research was funded by The Netherlands Organisation for Scientific Research (Project Number 409-15-203). The authors would like to thank Stefan V. Kolenbrander for his help with running this study and Esther Stoop and Marjolein Looijen for their assistance with coding the data.

This research was funded by The Netherlands Organisation for Scientific Research (Project Number 409-15-203).

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Lara M. van Peppen

Present address: Institute of Medical Education Research, Erasmus University Medical Center Rotterdam, Doctor Molewaterplein 40, 3051 GD, Rotterdam, The Netherlands

Authors and Affiliations

Department of Psychology, Education and Child Studies, Erasmus University Rotterdam, Burgemeester Oudlaan 50, 3062 PA, Rotterdam, The Netherlands

Lara M. van Peppen & Peter P. J. L. Verkoeijen

Learning and Innovation Center, Avans University of Applied Sciences, Hogeschoollaan 1, 4818 CR, Breda, The Netherlands

Peter P. J. L. Verkoeijen & Anita E. G. Heijltjes

Department of Education, Utrecht University, Heidelberglaan 1, 3584 CS, Utrecht, The Netherlands

Eva M. Janssen & Tamara van Gog

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LP, PV, AH, and TG contributed to the conception and design of the study. LP and EM prepared the materials. LP collected the data, organized the database, and performed the statistical analyses. LP, PV, and TG interpreted the data. LP wrote the original draft of the manuscript and PV, AH, EM, and TG provided critical revision of the manuscript. All authors read and approved the submitted version of the manuscript.

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Correspondence to Lara M. van Peppen .

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In accordance with the guidelines of the ethical committee at the Department of Psychology, Education and Child studies, Erasmus University Rotterdam, the study was exempt from ethical approval procedures because the materials and procedures were not invasive. All subjects gave written informed consent prior to participating in this study.

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van Peppen, L.M., Verkoeijen, P.P.J.L., Heijltjes, A.E.G. et al. Enhancing students’ critical thinking skills: is comparing correct and erroneous examples beneficial?. Instr Sci 49 , 747–777 (2021). https://doi.org/10.1007/s11251-021-09559-0

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Received : 14 February 2020

Accepted : 11 August 2021

Published : 26 September 2021

Issue Date : December 2021

DOI : https://doi.org/10.1007/s11251-021-09559-0

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