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Critical Thinking in Science: Fostering Scientific Reasoning Skills in Students

ALI Staff | Published  July 13, 2023

Thinking like a scientist is a central goal of all science curricula.

As students learn facts, methodologies, and methods, what matters most is that all their learning happens through the lens of scientific reasoning what matters most is that it’s all through the lens of scientific reasoning.

That way, when it comes time for them to take on a little science themselves, either in the lab or by theoretically thinking through a solution, they understand how to do it in the right context.

One component of this type of thinking is being critical. Based on facts and evidence, critical thinking in science isn’t exactly the same as critical thinking in other subjects.

Students have to doubt the information they’re given until they can prove it’s right.

They have to truly understand what’s true and what’s hearsay. It’s complex, but with the right tools and plenty of practice, students can get it right.

What is critical thinking?

This particular style of thinking stands out because it requires reflection and analysis. Based on what's logical and rational, thinking critically is all about digging deep and going beyond the surface of a question to establish the quality of the question itself.

It ensures students put their brains to work when confronted with a question rather than taking every piece of information they’re given at face value.

It’s engaged, higher-level thinking that will serve them well in school and throughout their lives.

Why is critical thinking important?

Critical thinking is important when it comes to making good decisions.

It gives us the tools to think through a choice rather than quickly picking an option — and probably guessing wrong. Think of it as the all-important ‘why.’

Why is that true? Why is that right? Why is this the only option?

Finding answers to questions like these requires critical thinking. They require you to really analyze both the question itself and the possible solutions to establish validity.

Will that choice work for me? Does this feel right based on the evidence?

How does critical thinking in science impact students?

Critical thinking is essential in science.

It’s what naturally takes students in the direction of scientific reasoning since evidence is a key component of this style of thought.

It’s not just about whether evidence is available to support a particular answer but how valid that evidence is.

It’s about whether the information the student has fits together to create a strong argument and how to use verifiable facts to get a proper response.

Critical thinking in science helps students:

• Actively evaluate information
• Identify bias
• Separate the logic within arguments
• Analyze evidence

4 Ways to promote critical thinking

Figuring out how to develop critical thinking skills in science means looking at multiple strategies and deciding what will work best at your school and in your class.

Based on your student population, their needs and abilities, not every option will be a home run.

These particular examples are all based on the idea that for students to really learn how to think critically, they have to practice doing it. 

Each focuses on engaging students with science in a way that will motivate them to work independently as they hone their scientific reasoning skills.

Project-Based Learning

Project-based learning centers on critical thinking.

Teachers can shape a project around the thinking style to give students practice with evaluating evidence or other critical thinking skills.

Critical thinking also happens during collaboration, evidence-based thought, and reflection.

For example, setting students up for a research project is not only a great way to get them to think critically, but it also helps motivate them to learn.

Allowing them to pick the topic (that isn’t easy to look up online), develop their own research questions, and establish a process to collect data to find an answer lets students personally connect to science while using critical thinking at each stage of the assignment.

They’ll have to evaluate the quality of the research they find and make evidence-based decisions.

Self-Reflection

Adding a question or two to any lab practicum or activity requiring students to pause and reflect on what they did or learned also helps them practice critical thinking.

At this point in an assignment, they’ll pause and assess independently. 

You can ask students to reflect on the conclusions they came up with for a completed activity, which really makes them think about whether there's any bias in their answer.

Addressing Assumptions

One way critical thinking aligns so perfectly with scientific reasoning is that it encourages students to challenge all assumptions. 

Evidence is king in the science classroom, but even when students work with hard facts, there comes the risk of a little assumptive thinking.

Working with students to identify assumptions in existing research or asking them to address an issue where they suspend their own judgment and simply look at established facts polishes their that critical eye.

They’re getting practice without tossing out opinions, unproven hypotheses, and speculation in exchange for real data and real results, just like a scientist has to do.

Lab Activities With Trial-And-Error

Another component of critical thinking (as well as thinking like a scientist) is figuring out what to do when you get something wrong.

Backtracking can mean you have to rethink a process, redesign an experiment, or reevaluate data because the outcomes don’t make sense, but it’s okay.

The ability to get something wrong and recover is not only a valuable life skill, but it’s where most scientific breakthroughs start. Reminding students of this is always a valuable lesson.

Labs that include comparative activities are one way to increase critical thinking skills, especially when introducing new evidence that might cause students to change their conclusions once the lab has begun.

For example, you provide students with two distinct data sets and ask them to compare them.

With only two choices, there are a finite amount of conclusions to draw, but then what happens when you bring in a third data set? Will it void certain conclusions? Will it allow students to make new conclusions, ones even more deeply rooted in evidence?

Thinking like a scientist

When students get the opportunity to think critically, they’re learning to trust the data over their ‘gut,’ to approach problems systematically and make informed decisions using ‘good’ evidence.

When practiced enough, this ability will engage students in science in a whole new way, providing them with opportunities to dig deeper and learn more.

It can help enrich science and motivate students to approach the subject just like a professional would.

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Teaching Creativity and Inventive Problem Solving in Science

• Robert L. DeHaan

Division of Educational Studies, Emory University, Atlanta, GA 30322

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Engaging learners in the excitement of science, helping them discover the value of evidence-based reasoning and higher-order cognitive skills, and teaching them to become creative problem solvers have long been goals of science education reformers. But the means to achieve these goals, especially methods to promote creative thinking in scientific problem solving, have not become widely known or used. In this essay, I review the evidence that creativity is not a single hard-to-measure property. The creative process can be explained by reference to increasingly well-understood cognitive skills such as cognitive flexibility and inhibitory control that are widely distributed in the population. I explore the relationship between creativity and the higher-order cognitive skills, review assessment methods, and describe several instructional strategies for enhancing creative problem solving in the college classroom. Evidence suggests that instruction to support the development of creativity requires inquiry-based teaching that includes explicit strategies to promote cognitive flexibility. Students need to be repeatedly reminded and shown how to be creative, to integrate material across subject areas, to question their own assumptions, and to imagine other viewpoints and possibilities. Further research is required to determine whether college students' learning will be enhanced by these measures.

INTRODUCTION

Dr. Dunne paces in front of his section of first-year college students, today not as their Bio 110 teacher but in the role of facilitator in their monthly “invention session.” For this meeting, the topic is stem cell therapy in heart disease. Members of each team of four students have primed themselves on the topic by reading selected articles from accessible sources such as Science, Nature, and Scientific American, and searching the World Wide Web, triangulating for up-to-date, accurate, background information. Each team knows that their first goal is to define a set of problems or limitations to overcome within the topic and to begin to think of possible solutions. Dr. Dunne starts the conversation by reminding the group of the few ground rules: one speaker at a time, listen carefully and have respect for others' ideas, question your own and others' assumptions, focus on alternative paths or solutions, maintain an atmosphere of collaboration and mutual support. He then sparks the discussion by asking one of the teams to describe a problem in need of solution.

Science in the United States is widely credited as a major source of discovery and economic development. According to the 2005 TAP Report produced by a prominent group of corporate leaders, “To maintain our country's competitiveness in the twenty-first century, we must cultivate the skilled scientists and engineers needed to create tomorrow's innovations.” ( www.tap2015.org/about/TAP_report2.pdf ). A panel of scientists, engineers, educators, and policy makers convened by the National Research Council (NRC) concurred with this view, reporting that the vitality of the nation “is derived in large part from the productivity of well-trained people and the steady stream of scientific and technical innovations they produce” ( NRC, 2007 ).

For many decades, science education reformers have promoted the idea that learners should be engaged in the excitement of science; they should be helped to discover the value of evidence-based reasoning and higher-order cognitive skills, and be taught to become innovative problem solvers (for reviews, see DeHaan, 2005 ; Hake, 2005 ; Nelson, 2008 ; Perkins and Wieman, 2008 ). But the means to achieve these goals, especially methods to promote creative thinking in scientific problem solving, are not widely known or used. An invention session such as that led by the fictional Dr. Dunne, described above, may seem fanciful as a means of teaching students to think about science as something more than a body of facts and terms to memorize. In recent years, however, models for promoting creative problem solving were developed for classroom use, as detailed by Treffinger and Isaksen (2005) , and such techniques are often used in the real world of high technology. To promote imaginative thinking, the advertising executive Alex F. Osborn invented brainstorming ( Osborn, 1948 , 1979 ), a technique that has since been successful in stimulating inventiveness among engineers and scientists. Could such strategies be transferred to a class for college students? Could they serve as a supplement to a high-quality, scientific teaching curriculum that helps students learn the facts and conceptual frameworks of science and make progress along the novice–expert continuum? Could brainstorming or other instructional strategies that are specifically designed to promote creativity teach students to be more adaptive in their growing expertise, more innovative in their problem-solving abilities? To begin to answer those questions, we first need to understand what is meant by “creativity.”

What Is Creativity? Big-C versus Mini-C Creativity

How to define creativity is an age-old question. Justice Potter Stewart's famous dictum regarding obscenity “I know it when I see it” has also long been an accepted test of creativity. But this is not an adequate criterion for developing an instructional approach. A scientist colleague of mine recently noted that “Many of us [in the scientific community] rarely give the creative process a second thought, imagining one either ‘has it’ or doesn't.” We often think of inventiveness or creativity in scientific fields as the kind of gift associated with a Michelangelo or Einstein. This is what Kaufman and Beghetto (2008) call big-C creativity, borrowing the term that earlier workers applied to the talents of experts in various fields who were identified as particularly creative by their expert colleagues ( MacKinnon, 1978 ). In this sense, creativity is seen as the ability of individuals to generate new ideas that contribute substantially to an intellectual domain. Howard Gardner defined such a creative person as one who “regularly solves problems, fashions products, or defines new questions in a domain in a way that is initially considered novel but that ultimately comes to be accepted in a particular cultural setting” ( Gardner, 1993 , p. 35).

But there is another level of inventiveness termed by various authors as “little-c” ( Craft, 2000 ) or “mini-c” ( Kaufman and Beghetto, 2008 ) creativity that is widespread among all populations. This would be consistent with the workplace definition of creativity offered by Amabile and her coworkers: “coming up with fresh ideas for changing products, services and processes so as to better achieve the organization's goals” ( Amabile et al. , 2005 ). Mini-c creativity is based on what Craft calls “possibility thinking” ( Craft, 2000 , pp. 3–4), as experienced when a worker suddenly has the insight to visualize a new, improved way to accomplish a task; it is represented by the “aha” moment when a student first sees two previously disparate concepts or facts in a new relationship, an example of what Arthur Koestler identified as bisociation: “perceiving a situation or event in two habitually incompatible associative contexts” ( Koestler, 1964 , p. 95).

In this essay, I maintain that mini-c creativity is not a mysterious, innate endowment of rare individuals. Instead, I argue that creative thinking is a multicomponent process, mediated through social interactions, that can be explained by reference to increasingly well-understood mental abilities such as cognitive flexibility and cognitive control that are widely distributed in the population. Moreover, I explore some of the recent research evidence (though with no effort at a comprehensive literature review) showing that these mental abilities are teachable; like other higher-order cognitive skills (HOCS), they can be enhanced by explicit instruction.

Creativity Is a Multicomponent Process

Efforts to define creativity in psychological terms go back to J. P. Guilford ( Guilford, 1950 ) and E. P. Torrance ( Torrance, 1974 ), both of whom recognized that underlying the construct were other cognitive variables such as ideational fluency, originality of ideas, and sensitivity to missing elements. Many authors since then have extended the argument that a creative act is not a singular event but a process, an interplay among several interactive cognitive and affective elements. In this view, the creative act has two phases, a generative and an exploratory or evaluative phase ( Finke et al. , 1996 ). During the generative process, the creative mind pictures a set of novel mental models as potential solutions to a problem. In the exploratory phase, we evaluate the multiple options and select the best one. Early scholars of creativity, such as J. P. Guilford, characterized the two phases as divergent thinking and convergent thinking ( Guilford, 1950 ). Guilford defined divergent thinking as the ability to produce a broad range of associations to a given stimulus or to arrive at many solutions to a problem (for overviews of the field from different perspectives, see Amabile, 1996 ; Banaji et al. , 2006 ; Sawyer, 2006 ). In neurocognitive terms, divergent thinking is referred to as associative richness ( Gabora, 2002 ; Simonton, 2004 ), which is often measured experimentally by comparing the number of words that an individual generates from memory in response to stimulus words on a word association test. In contrast, convergent thinking refers to the capacity to quickly focus on the one best solution to a problem.

The idea that there are two stages to the creative process is consistent with results from cognition research indicating that there are two distinct modes of thought, associative and analytical ( Neisser, 1963 ; Sloman, 1996 ). In the associative mode, thinking is defocused, suggestive, and intuitive, revealing remote or subtle connections between items that may be correlated, or may not, and are usually not causally related ( Burton, 2008 ). In the analytical mode, thought is focused and evaluative, more conducive to analyzing relationships of cause and effect (for a review of other cognitive aspects of creativity, see Runco, 2004 ). Science educators associate the analytical mode with the upper levels (analysis, synthesis, and evaluation) of Bloom's taxonomy (e.g., Crowe et al. , 2008 ), or with “critical thinking,” the process that underlies the “purposeful, self-regulatory judgment that drives problem-solving and decision-making” ( Quitadamo et al. , 2008 , p. 328). These modes of thinking are under cognitive control through the executive functions of the brain. The core executive functions, which are thought to underlie all planning, problem solving, and reasoning, are defined ( Blair and Razza, 2007 ) as working memory control (mentally holding and retrieving information), cognitive flexibility (considering multiple ideas and seeing different perspectives), and inhibitory control (resisting several thoughts or actions to focus on one). Readers wishing to delve further into the neuroscience of the creative process can refer to the cerebrocerebellar theory of creativity ( Vandervert et al. , 2007 ) in which these mental activities are described neurophysiologically as arising through interactions among different parts of the brain.

The main point from all of these works is that creativity is not some single hard-to-measure property or act. There is ample evidence that the creative process requires both divergent and convergent thinking and that it can be explained by reference to increasingly well-understood underlying mental abilities ( Haring-Smith, 2006 ; Kim, 2006 ; Sawyer, 2006 ; Kaufman and Sternberg, 2007 ) and cognitive processes ( Simonton, 2004 ; Diamond et al. , 2007 ; Vandervert et al. , 2007 ).

Creativity Is Widely Distributed and Occurs in a Social Context

Although it is understandable to speak of an aha moment as a creative act by the person who experiences it, authorities in the field have long recognized (e.g., Simonton, 1975 ) that creative thinking is not so much an individual trait but rather a social phenomenon involving interactions among people within their specific group or cultural settings. “Creativity isn't just a property of individuals, it is also a property of social groups” ( Sawyer, 2006 , p. 305). Indeed, Osborn introduced his brainstorming method because he was convinced that group creativity is always superior to individual creativity. He drew evidence for this conclusion from activities that demand collaborative output, for example, the improvisations of a jazz ensemble. Although each musician is individually creative during a performance, the novelty and inventiveness of each performer's playing is clearly influenced, and often enhanced, by “social and interactional processes” among the musicians ( Sawyer, 2006 , p. 120). Recently, Brophy (2006) offered evidence that for problem solving, the situation may be more nuanced. He confirmed that groups of interacting individuals were better at solving complex, multipart problems than single individuals. However, when dealing with certain kinds of single-issue problems, individual problem solvers produced a greater number of solutions than interacting groups, and those solutions were judged to be more original and useful.

Consistent with the findings of Brophy (2006) , many scholars acknowledge that creative discoveries in the real world such as solving the problems of cutting-edge science—which are usually complex and multipart—are influenced or even stimulated by social interaction among experts. The common image of the lone scientist in the laboratory experiencing a flash of creative inspiration is probably a myth from earlier days. As a case in point, the science historian Mara Beller analyzed the social processes that underlay some of the major discoveries of early twentieth-century quantum physics. Close examination of successive drafts of publications by members of the Copenhagen group revealed a remarkable degree of influence and collaboration among 10 or more colleagues, although many of these papers were published under the name of a single author ( Beller, 1999 ). Sociologists Bruno Latour and Steve Woolgar's study ( Latour and Woolgar, 1986 ) of a neuroendocrinology laboratory at the Salk Institute for Biological Studies make the related point that social interactions among the participating scientists determined to a remarkable degree what discoveries were made and how they were interpreted. In the laboratory, researchers studied the chemical structure of substances released by the brain. By analysis of the Salk scientists' verbalizations of concepts, theories, formulas, and results of their investigations, Latour and Woolgar showed that the structures and interpretations that were agreed upon, that is, the discoveries announced by the laboratory, were mediated by social interactions and power relationships among members of the laboratory group. By studying the discovery process in other fields of the natural sciences, sociologists and anthropologists have provided more cases that further illustrate how social and cultural dimensions affect scientific insights (for a thoughtful review, see Knorr Cetina, 1995 ).

In sum, when an individual experiences an aha moment that feels like a singular creative act, it may rather have resulted from a multicomponent process, under the influence of group interactions and social context. The process that led up to what may be sensed as a sudden insight will probably have included at least three diverse, but testable elements: 1) divergent thinking, including ideational fluency or cognitive flexibility, which is the cognitive executive function that underlies the ability to visualize and accept many ideas related to a problem; 2) convergent thinking or the application of inhibitory control to focus and mentally evaluate ideas; and 3) analogical thinking, the ability to understand a novel idea in terms of one that is already familiar.

LITERATURE REVIEW

What do we know about how to teach creativity.

The possibility of teaching for creative problem solving gained credence in the 1960s with the studies of Jerome Bruner, who argued that children should be encouraged to “treat a task as a problem for which one invents an answer, rather than finding one out there in a book or on the blackboard” ( Bruner, 1965 , pp. 1013–1014). Since that time, educators and psychologists have devised programs of instruction designed to promote creativity and inventiveness in virtually every student population: pre–K, elementary, high school, and college, as well as in disadvantaged students, athletes, and students in a variety of specific disciplines (for review, see Scott et al. , 2004 ). Smith (1998) identified 172 instructional approaches that have been applied at one time or another to develop divergent thinking skills.

Some of the most convincing evidence that elements of creativity can be enhanced by instruction comes from work with young children. Bodrova and Leong (2001) developed the Tools of the Mind (Tools) curriculum to improve all of the three core mental executive functions involved in creative problem solving: cognitive flexibility, working memory, and inhibitory control. In a year-long randomized study of 5-yr-olds from low-income families in 21 preschool classrooms, half of the teachers applied the districts' balanced literacy curriculum (literacy), whereas the experimenters trained the other half to teach the same academic content by using the Tools curriculum ( Diamond et al. , 2007 ). At the end of the year, when the children were tested with a battery of neurocognitive tests including a test for cognitive flexibility ( Durston et al. , 2003 ; Davidson et al. , 2006 ), those exposed to the Tools curriculum outperformed the literacy children by as much as 25% ( Diamond et al. , 2007 ). Although the Tools curriculum and literacy program were similar in academic content and in many other ways, they differed primarily in that Tools teachers spent 80% of their time explicitly reminding the children to think of alternative ways to solve a problem and building their executive function skills.

Teaching older students to be innovative also demands instruction that explicitly promotes creativity but is rigorously content-rich as well. A large body of research on the differences between novice and expert cognition indicates that creative thinking requires at least a minimal level of expertise and fluency within a knowledge domain ( Bransford et al. , 2000 ; Crawford and Brophy, 2006 ). What distinguishes experts from novices, in addition to their deeper knowledge of the subject, is their recognition of patterns in information, their ability to see relationships among disparate facts and concepts, and their capacity for organizing content into conceptual frameworks or schemata ( Bransford et al. , 2000 ; Sawyer, 2005 ).

Such expertise is often lacking in the traditional classroom. For students attempting to grapple with new subject matter, many kinds of problems that are presented in high school or college courses or that arise in the real world can be solved merely by applying newly learned algorithms or procedural knowledge. With practice, problem solving of this kind can become routine and is often considered to represent mastery of a subject, producing what Sternberg refers to as “pseudoexperts” ( Sternberg, 2003 ). But beyond such routine use of content knowledge the instructor's goal must be to produce students who have gained the HOCS needed to apply, analyze, synthesize, and evaluate knowledge ( Crowe et al. , 2008 ). The aim is to produce students who know enough about a field to grasp meaningful patterns of information, who can readily retrieve relevant knowledge from memory, and who can apply such knowledge effectively to novel problems. This condition is referred to as adaptive expertise ( Hatano and Ouro, 2003 ; Schwartz et al. , 2005 ). Instead of applying already mastered procedures, adaptive experts are able to draw on their knowledge to invent or adapt strategies for solving unique or novel problems within a knowledge domain. They are also able, ideally, to transfer conceptual frameworks and schemata from one domain to another (e.g., Schwartz et al. , 2005 ). Such flexible, innovative application of knowledge is what results in inventive or creative solutions to problems ( Crawford and Brophy, 2006 ; Crawford, 2007 ).

Promoting Creative Problem Solving in the College Classroom

In most college courses, instructors teach science primarily through lectures and textbooks that are dominated by facts and algorithmic processing rather than by concepts, principles, and evidence-based ways of thinking. This is despite ample evidence that many students gain little new knowledge from traditional lectures ( Hrepic et al. , 2007 ). Moreover, it is well documented that these methods engender passive learning rather than active engagement, boredom instead of intellectual excitement, and linear thinking rather than cognitive flexibility (e.g., Halpern and Hakel, 2003 ; Nelson, 2008 ; Perkins and Wieman, 2008 ). Cognitive flexibility, as noted, is one of the three core mental executive functions involved in creative problem solving ( Ausubel, 1963 , 2000 ). The capacity to apply ideas creatively in new contexts, referred to as the ability to “transfer” knowledge (see Mestre, 2005 ), requires that learners have opportunities to actively develop their own representations of information to convert it to a usable form. Especially when a knowledge domain is complex and fraught with ill-structured information, as in a typical introductory college biology course, instruction that emphasizes active-learning strategies is demonstrably more effective than traditional linear teaching in reducing failure rates and in promoting learning and transfer (e.g., Freeman et al. , 2007 ). Furthermore, there is already some evidence that inclusion of creativity training as part of a college curriculum can have positive effects. Hunsaker (2005) has reviewed a number of such studies. He cites work by McGregor (2001) , for example, showing that various creativity training programs including brainstorming and creative problem solving increase student scores on tests of creative-thinking abilities.

Model creativity—students develop creativity when instructors model creative thinking and inventiveness.

Repeatedly encourage idea generation—students need to be reminded to generate their own ideas and solutions in an environment free of criticism.

Cross-fertilize ideas—where possible, avoid teaching in subject-area boxes: a math box, a social studies box, etc; students' creative ideas and insights often result from learning to integrate material across subject areas.

Build self-efficacy—all students have the capacity to create and to experience the joy of having new ideas, but they must be helped to believe in their own capacity to be creative.

Constantly question assumptions—make questioning a part of the daily classroom exchange; it is more important for students to learn what questions to ask and how to ask them than to learn the answers.

Imagine other viewpoints—students broaden their perspectives by learning to reflect upon ideas and concepts from different points of view.

How Is Creativity Related to Critical Thinking and the Higher-Order Cognitive Skills?

It is not uncommon to associate creativity and ingenuity with scientific reasoning ( Sawyer, 2005 ; 2006 ). When instructors apply scientific teaching strategies ( Handelsman et al. , 2004 ; DeHaan, 2005 ; Wood, 2009 ) by using instructional methods based on learning research, according to Ebert-May and Hodder ( 2008 ), “we see students actively engaged in the thinking, creativity, rigor, and experimentation we associate with the practice of science—in much the same way we see students learn in the field and in laboratories” (p. 2). Perkins and Wieman (2008) note that “To be successful innovators in science and engineering, students must develop a deep conceptual understanding of the underlying science ideas, an ability to apply these ideas and concepts broadly in different contexts, and a vision to see their relevance and usefulness in real-world applications … An innovator is able to perceive and realize potential connections and opportunities better than others” (pp. 181–182). The results of Scott et al. (2004) suggest that nontraditional courses in science that are based on constructivist principles and that use strategies of scientific teaching to promote the HOCS and enhance content mastery and dexterity in scientific thinking ( Handelsman et al. , 2007 ; Nelson, 2008 ) also should be effective in promoting creativity and cognitive flexibility if students are explicitly guided to learn these skills.

Creativity is an essential element of problem solving ( Mumford et al. , 1991 ; Runco, 2004 ) and of critical thinking ( Abrami et al. , 2008 ). As such, it is common to think of applications of creativity such as inventiveness and ingenuity among the HOCS as defined in Bloom's taxonomy ( Crowe et al. , 2008 ). Thus, it should come as no surprise that creativity, like other elements of the HOCS, can be taught most effectively through inquiry-based instruction, informed by constructivist theory ( Ausubel, 1963 , 2000 ; Duch et al. , 2001 ; Nelson, 2008 ). In a survey of 103 instructors who taught college courses that included creativity instruction, Bull et al. (1995) asked respondents to rate the importance of various course characteristics for enhancing student creativity. Items ranking high on the list were: providing a social climate in which students feels safe, an open classroom environment that promotes tolerance for ambiguity and independence, the use of humor, metaphorical thinking, and problem defining. Many of the responses emphasized the same strategies as those advanced to promote creative problem solving (e.g., Mumford et al. , 1991 ; McFadzean, 2002 ; Treffinger and Isaksen, 2005 ) and critical thinking ( Abrami et al. , 2008 ).

In a careful meta-analysis, Scott et al. (2004) examined 70 instructional interventions designed to enhance and measure creative performance. The results were striking. Courses that stressed techniques such as critical thinking, convergent thinking, and constraint identification produced the largest positive effect sizes. More open techniques that provided less guidance in strategic approaches had less impact on the instructional outcomes. A striking finding was the effectiveness of being explicit; approaches that clearly informed students about the nature of creativity and offered clear strategies for creative thinking were most effective. Approaches such as social modeling, cooperative learning, and case-based (project-based) techniques that required the application of newly acquired knowledge were found to be positively correlated to high effect sizes. The most clear-cut result to emerge from the Scott et al. (2004) study was simply to confirm that creativity instruction can be highly successful in enhancing divergent thinking, problem solving, and imaginative performance. Most importantly, of the various cognitive processes examined, those linked to the generation of new ideas such as problem finding, conceptual combination, and idea generation showed the greatest improvement. The success of creativity instruction, the authors concluded, can be attributed to “developing and providing guidance concerning the application of requisite cognitive capacities … [and] a set of heuristics or strategies for working with already available knowledge” (p. 382).

Many of the scientific teaching practices that have been shown by research to foster content mastery and HOCS, and that are coming more widely into use, also would be consistent with promoting creativity. Wood (2009) has recently reviewed examples of such practices and how to apply them. These include relatively small modifications of the traditional lecture to engender more active learning, such as the use of concept tests and peer instruction ( Mazur, 1996 ), Just-in-Time-Teaching techniques ( Novak et al. , 1999 ), and student response systems known as “clickers” ( Knight and Wood, 2005 ; Crossgrove and Curran, 2008 ), all designed to allow the instructor to frequently and effortlessly elicit and respond to student thinking. Other strategies can transform the lecture hall into a workshop or studio classroom ( Gaffney et al. , 2008 ) where the teaching curriculum may emphasize problem-based (also known as project-based or case-based) learning strategies ( Duch et al. , 2001 ; Ebert-May and Hodder, 2008 ) or “community-based inquiry” in which students engage in research that enhances their critical-thinking skills ( Quitadamo et al. , 2008 ).

Another important approach that could readily subserve explicit creativity instruction is the use of computer-based interactive simulations, or “sims” ( Perkins and Wieman, 2008 ) to facilitate inquiry learning and effective, easy self-assessment. An example in the biological sciences would be Neurons in Action ( http://neuronsinaction.com/home/main ). In such educational environments, students gain conceptual understanding of scientific ideas through interactive engagement with materials (real or virtual), with each other, and with instructors. Following the tenets of scientific teaching, students are encouraged to pose and answer their own questions, to make sense of the materials, and to construct their own understanding. The question I pose here is whether an additional focus—guiding students to meet these challenges in a context that explicitly promotes creativity—would enhance learning and advance students' progress toward adaptive expertise?

Assessment of Creativity

To teach creativity, there must be measurable indicators to judge how much students have gained from instruction. Educational programs intended to teach creativity became popular after the Torrance Tests of Creative Thinking (TTCT) was introduced in the 1960s ( Torrance, 1974 ). But it soon became apparent that there were major problems in devising tests for creativity, both because of the difficulty of defining the construct and because of the number and complexity of elements that underlie it. Tests of intelligence and other personality characteristics on creative individuals revealed a host of related traits such as verbal fluency, metaphorical thinking, flexible decision making, tolerance of ambiguity, willingness to take risks, autonomy, divergent thinking, self-confidence, problem finding, ideational fluency, and belief in oneself as being “creative” ( Barron and Harrington, 1981 ; Tardif and Sternberg, 1988 ; Runco and Nemiro, 1994 ; Snyder et al. , 2004 ). Many of these traits have been the focus of extensive research of recent decades, but, as noted above, creativity is not defined by any one trait; there is now reason to believe that it is the interplay among the cognitive and affective processes that underlie inventiveness and the ability to find novel solutions to a problem.

Although the early creativity researchers recognized that assessing divergent thinking as a measure of creativity required tests for other underlying capacities ( Guilford, 1950 ; Torrance, 1974 ), these workers and their colleagues nonetheless believed that a high score for divergent thinking alone would correlate with real creative output. Unfortunately, no such correlation was shown ( Barron and Harrington, 1981 ). Results produced by many of the instruments initially designed to measure various aspects of creative thinking proved to be highly dependent on the test itself. A review of several hundred early studies showed that an individual's creativity score could be affected by simple test variables, for example, how the verbal pretest instructions were worded ( Barron and Harrington, 1981 , pp. 442–443). Most scholars now agree that divergent thinking, as originally defined, was not an adequate measure of creativity. The process of creative thinking requires a complex combination of elements that include cognitive flexibility, memory control, inhibitory control, and analogical thinking, enabling the mind to free-range and analogize, as well as to focus and test.

More recently, numerous psychometric measures have been developed and empirically tested (see Plucker and Renzulli, 1999 ) that allow more reliable and valid assessment of specific aspects of creativity. For example, the creativity quotient devised by Snyder et al. (2004) tests the ability of individuals to link different ideas and different categories of ideas into a novel synthesis. The Wallach–Kogan creativity test ( Wallach and Kogan, 1965 ) explores the uniqueness of ideas associated with a stimulus. For a more complete list and discussion, see the Creativity Tests website ( www.indiana.edu/∼bobweb/Handout/cretv_6.html ).

The most widely used measure of creativity is the TTCT, which has been modified four times since its original version in 1966 to take into account subsequent research. The TTCT-Verbal and the TTCT-Figural are two versions ( Torrance, 1998 ; see http://ststesting.com/2005giftttct.html ). The TTCT-Verbal consists of five tasks; the “stimulus” for each task is a picture to which the test-taker responds briefly in writing. A sample task that can be viewed from the TTCT Demonstrator website asks, “Suppose that people could transport themselves from place to place with just a wink of the eye or a twitch of the nose. What might be some things that would happen as a result? You have 3 min.” ( www.indiana.edu/∼bobweb/Handout/d3.ttct.htm ).

In the TTCT-Figural, participants are asked to construct a picture from a stimulus in the form of a partial line drawing given on the test sheet (see example below; Figure 1 ). Specific instructions are to “Add lines to the incomplete figures below to make pictures out of them. Try to tell complete stories with your pictures. Give your pictures titles. You have 3 min.” In the introductory materials, test-takers are urged to “… think of a picture or object that no one else will think of. Try to make it tell as complete and as interesting a story as you can …” ( Torrance et al. , 2008 , p. 2).

Figure 1. Sample figural test item from the TTCT Demonstrator website ( www.indiana.edu/∼bobweb/Handout/d3.ttct.htm ).

How would an instructor in a biology course judge the creativity of students' responses to such an item? To assist in this task, the TTCT has scoring and norming guides ( Torrance, 1998 ; Torrance et al. , 2008 ) with numerous samples and responses representing different levels of creativity. The guides show sample evaluations based upon specific indicators such as fluency, originality, elaboration (or complexity), unusual visualization, extending or breaking boundaries, humor, and imagery. These examples are easy to use and provide a high degree of validity and generalizability to the tests. The TTCT has been more intensively researched and analyzed than any other creativity instrument, and the norming samples have longitudinal validations and high predictive validity over a wide age range. In addition to global creativity scores, the TTCT is designed to provide outcome measures in various domains and thematic areas to allow for more insightful analysis ( Kaufman and Baer, 2006 ). Kim (2006) has examined the characteristics of the TTCT, including norms, reliability, and validity, and concludes that the test is an accurate measure of creativity. When properly used, it has been shown to be fair in terms of gender, race, community status, and language background. According to Kim (2006) and other authorities in the field ( McIntyre et al. , 2003 ; Scott et al. , 2004 ), Torrance's research and the development of the TTCT have provided groundwork for the idea that creative levels can be measured and then increased through instruction and practice.

SCIENTIFIC TEACHING TO PROMOTE CREATIVITY

How could creativity instruction be integrated into scientific teaching.

Guidelines for designing specific course units that emphasize HOCS by using strategies of scientific teaching are now available from the current literature. As an example, Karen Cloud-Hansen and colleagues ( Cloud-Hansen et al. , 2008 ) describe a course titled, “Ciprofloxacin Resistance in Neisseria gonorrhoeae .” They developed this undergraduate seminar to introduce college freshmen to important concepts in biology within a real-world context and to increase their content knowledge and critical-thinking skills. The centerpiece of the unit is a case study in which teams of students are challenged to take the role of a director of a local public health clinic. One of the county commissioners overseeing the clinic is an epidemiologist who wants to know “how you plan to address the emergence of ciprofloxacin resistance in Neisseria gonorrhoeae ” (p. 304). State budget cuts limit availability of expensive antibiotics and some laboratory tests to patients. Student teams are challenged to 1) develop a plan to address the medical, economic, and political questions such a clinic director would face in dealing with ciprofloxacin-resistant N. gonorrhoeae ; 2) provide scientific data to support their conclusions; and 3) describe their clinic plan in a one- to two-page referenced written report.

Throughout the 3-wk unit, in accordance with the principles of problem-based instruction ( Duch et al. , 2001 ), course instructors encourage students to seek, interpret, and synthesize their own information to the extent possible. Students have access to a variety of instructional formats, and active-learning experiences are incorporated throughout the unit. These activities are interspersed among minilectures and give the students opportunities to apply new information to their existing base of knowledge. The active-learning activities emphasize the key concepts of the minilectures and directly confront common misconceptions about antibiotic resistance, gene expression, and evolution. Weekly classes include question/answer/discussion sessions to address student misconceptions and 20-min minilectures on such topics as antibiotic resistance, evolution, and the central dogma of molecular biology. Students gather information about antibiotic resistance in N. gonorrhoeae , epidemiology of gonorrhea, and treatment options for the disease, and each team is expected to formulate a plan to address ciprofloxacin resistance in N. gonorrhoeae .

In this project, the authors assessed student gains in terms of content knowledge regarding topics covered such as the role of evolution in antibiotic resistance, mechanisms of gene expression, and the role of oncogenes in human disease. They also measured HOCS as gains in problem solving, according to a rubric that assessed self-reported abilities to communicate ideas logically, solve difficult problems about microbiology, propose hypotheses, analyze data, and draw conclusions. Comparing the pre- and posttests, students reported significant learning of scientific content. Among the thinking skill categories, students demonstrated measurable gains in their ability to solve problems about microbiology but the unit seemed to have little impact on their more general perceived problem-solving skills ( Cloud-Hansen et al. , 2008 ).

What would such a class look like with the addition of explicit creativity-promoting approaches? Would the gains in problem-solving abilities have been greater if during the minilectures and other activities, students had been introduced explicitly to elements of creative thinking from the Sternberg and Williams (1998) list described above? Would the students have reported greater gains if their instructors had encouraged idea generation with weekly brainstorming sessions; if they had reminded students to cross-fertilize ideas by integrating material across subject areas; built self-efficacy by helping students believe in their own capacity to be creative; helped students question their own assumptions; and encouraged students to imagine other viewpoints and possibilities? Of most relevance, could the authors have been more explicit in assessing the originality of the student plans? In an experiment that required college students to develop plans of a different, but comparable, type, Osborn and Mumford (2006) created an originality rubric ( Figure 2 ) that could apply equally to assist instructors in judging student plans in any course. With such modifications, would student gains in problem-solving abilities or other HOCS have been greater? Would their plans have been measurably more imaginative?

Figure 2. Originality rubric (adapted from Osburn and Mumford, 2006 , p. 183).

Answers to these questions can only be obtained when a course like that described by Cloud-Hansen et al. (2008) is taught with explicit instruction in creativity of the type I described above. But, such answers could be based upon more than subjective impressions of the course instructors. For example, students could be pretested with items from the TTCT-Verbal or TTCT-Figural like those shown. If, during minilectures and at every contact with instructors, students were repeatedly reminded and shown how to be as creative as possible, to integrate material across subject areas, to question their own assumptions and imagine other viewpoints and possibilities, would their scores on TTCT posttest items improve? Would the plans they formulated to address ciprofloxacin resistance become more imaginative?

Recall that in their meta-analysis, Scott et al. (2004) found that explicitly informing students about the nature of creativity and offering strategies for creative thinking were the most effective components of instruction. From their careful examination of 70 experimental studies, they concluded that approaches such as social modeling, cooperative learning, and case-based (project-based) techniques that required the application of newly acquired knowledge were positively correlated with high effect sizes. The study was clear in confirming that explicit creativity instruction can be successful in enhancing divergent thinking and problem solving. Would the same strategies work for courses in ecology and environmental biology, as detailed by Ebert-May and Hodder (2008) , or for a unit elaborated by Knight and Wood (2005) that applies classroom response clickers?

Finally, I return to my opening question with the fictional Dr. Dunne. Could a weekly brainstorming “invention session” included in a course like those described here serve as the site where students are introduced to concepts and strategies of creative problem solving? As frequently applied in schools of engineering ( Paulus and Nijstad, 2003 ), brainstorming provides an opportunity for the instructor to pose a problem and to ask the students to suggest as many solutions as possible in a brief period, thus enhancing ideational fluency. Here, students can be encouraged explicitly to build on the ideas of others and to think flexibly. Would brainstorming enhance students' divergent thinking or creative abilities as measured by TTCT items or an originality rubric? Many studies have demonstrated that group interactions such as brainstorming, under the right conditions, can indeed enhance creativity ( Paulus and Nijstad, 2003 ; Scott et al. , 2004 ), but there is little information from an undergraduate science classroom setting. Intellectual Ventures, a firm founded by Nathan Myhrvold, the creator of Microsoft's Research Division, has gathered groups of engineers and scientists around a table for day-long sessions to brainstorm about a prearranged topic. Here, the method seems to work. Since it was founded in 2000, Intellectual Ventures has filed hundreds of patent applications in more than 30 technology areas, applying the “invention session” strategy ( Gladwell, 2008 ). Currently, the company ranks among the top 50 worldwide in number of patent applications filed annually. Whether such a technique could be applied successfully in a college science course will only be revealed by future research.

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Submitted: 31 December 2008 Revised: 14 May 2009 Accepted: 28 May 2009

© 2009 by The American Society for Cell Biology

Ways of thinking in STEM-based problem solving

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• Volume 55 , pages 1219–1230, ( 2023 )

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This article proposes an interconnected framework, Ways of thinking in STEM-based Problem Solving , which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry, systems thinking, and design-based thinking, which collectively contribute to adaptive and innovative thinking. It is argued that the pinnacle of this framework is learning innovation, involving the generation of powerful disciplinary knowledge and thinking processes that can be applied to subsequent problem challenges. Consideration is first given to STEM-based problem solving with a focus on mathematics. Mathematical and STEM-based problems are viewed here as goal-directed, multifaceted experiences that (1) demand core, facilitative ways of thinking, (2) require the development of productive and adaptive ways to navigate complexity, (3) enable multiple approaches and practices, (4) recruit interdisciplinary solution processes, and (5) facilitate the growth of learning innovation. The nature, role, and contributions of each way of thinking in STEM-based problem solving and learning are then explored, with their interactions highlighted. Examples from classroom-based research are presented, together with teaching implications.

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1 Introduction

With the prevailing emphasis on integrated STEM education, the power of mathematical problem solving has been downplayed. Over two decades we have witnessed a decline in research on mathematical problem solving and thinking, with more questions than answers emerging (English & Gainsburg, 2016 ; Lester & Cai, 2016 ). This is of major concern, especially since work and non-work life increasingly call for resources beyond “textbook” problem solving (Chin et al., 2019 ; Krause et al., 2021 ). Such changing demands could not have been more starkly exposed than in the recent COVID 19 crisis, where mathematics played a crucial role in public and personal discourse, in describing and modelling current and potential scenarios, and in explaining and justifying societal regulations and restrictions. As Krause et al. ( 2021 ) highlighted, “No mathematical task we can create could be a richer application of mathematics than this real situation” (p. 88).

Modelling and statistical analyses that led the search for strategies to “flatten the curve” with minimal social or economic detriment were prominent in the media (Rhodes & Lancaster, 2020 ; Rhodes et al., 2020 ). As nations strive to rebuild their economies including grappling with crippling energy costs, advanced modelling again plays a key role (Aviso et al., 2022 ; Oxford Economics, 2022 ; Teng et al., 2022 ). Unfortunately, the gap between the mathematical modelling applied during the pandemic and how the public interpreted the models has been “palpable and evident” (Aguilar & Castaneda, 2021 ). Sadly, as Di Martino (Krause et al., 2021 ) pointed out regarding his nation:

People’s reactions in this pandemic underlined the spread of a widely negative attitude toward mathematics among the adult population in Italy. We have witnessed the proliferation of strange, unscientific, and dangerous theories but also the risk of refusing to approach facts that involve math and the resulting dependence to fully rely on others when mathematics is used to justify decisions. Also, on this occasion many people showed their own fear of math and their rejection of mathematical arguments as relevant factors in justification (p. 93).

This heightened visibility of mathematics in society coupled with a general lack of mathematical literacy sparked major questions about the repercussions for education and research (Bakker & Wagner, 2020 ; Kollosche & Meyerhöfer, 2021 ). One such repercussion is the need to reconsider perspectives on STEM-based problem solving and how different ways of thinking can enhance or hinder solutions. With reference to engineering education, Dalal et al. ( 2021 ) indicated how numerous calls for a focus on ways of thinking have largely been taken for granted or at least treated at a superficial level. As these authors pointed out, while perceived as a theoretical concept, ways of thinking “can and should be used in practice as a structure for solution-oriented outlooks and innovation” (p. 109).

Given the above points, I propose an interconnected framework, Ways of thinking in STEM-based Problem Solving (Fig.  1 ), which addresses cognitive processes that facilitate learning, problem solving, decision-making, and interdisciplinary concept development (cf. Slavit et al., 2021 ). The framework comprises critical thinking (including critical mathematical modelling and philosophical inquiry), systems thinking, and design-based thinking. Collectively, these thinking skills contribute to adaptive and innovative thinking (McKenna, 2014 ) and ultimately lead to the development of learning innovation (Sect.  3.4 ; English, 2018 ).

These thinking skills have been chosen because of their potential to enhance STEM-based problem solving and interdisciplinary concept development (English et al., 2020 ; Park et al., 2018 ; Slavit et al., 2021 ). Highlighting these ways of thinking, however, is not denying the importance of other thinking skills such as creativity, which is incorporated within the adaptive and innovative thinking component of the proposed framework (Fig.  1 ), and is considered multidimensional in nature (OECD, 2022 ). Other key skills such as communication and collaboration (Stehle & Peters-Burton, 2019 ) are acknowledged but not explored here.

In line with Dalal et al. ( 2021 ), I consider the proposed ways of thinking as providing an organisational structure both individually and interactively when enacted in practice—notwithstanding the contextual and instructional influences that can have an impact here (Slavit et al., 2022 ). Prior to exploring these ideas, I consider STEM-based problem solving with a focus on mathematics.

2 STEM-based problem solving: a focus on mathematics

Within our STEM-intensive society, we face significant challenges in promoting STEM education from the earliest grades while also maintaining the integrity of the individual disciplines (Tytler, 2016 ). With the increasing need for STEM skills across multiple workforce domains, contrasted with difficulties in STEM implementation in many schools (e.g., Dong et al., 2020 ), the urgency to advance STEM education has never been greater. With the massive disruption caused by COVID-19, coupled with problematic international relations, our school students’ futures have become even more uncertain—we cannot ignore the rapid changes that will continue to impact their lives. Unlike business and industry, where disruption creates a “force-to-innovate” approach (Crittenden, 2017 , p. 14), much of school education seems oblivious to preparing students for these disruptive forces or at least are restricted in doing so by set curricula.

Preparing our students for an increasingly uncertain and complex future requires rethinking the nature of their learning experiences, in particular, the need for more relevant and innovative problems that are challenging but manageable, and importantly, facilitate adaptive learning and problem solving (McKenna, 2014 ). A failure to provide such opportunities may have detrimental effects on young students’ learning and their future achievements (Engel et al., 2016 ). Despite mathematics being cited as the core of STEM education and foundational to the other disciplines (e.g., Larson, 2017 ; Roberts et al., 2022 ; Shaughnessy, 2013 ), it is frequently ignored in integrated STEM activities (English, 2016 ; Maass et al., 2019 ; Mayes, 2019 ; Shaughnessy, 2013 ). For example, quantitative reasoning, which is critical to integrated STEM problem solving, is frequently “misrepresented, underdeveloped, and ignored in STEM classrooms” (Mayes, 2019, p. 113). Likewise, Tytler ( 2016 ) warned that there needs to be an explicit focus on the mathematical concepts and thinking processes that arise in STEM activities. Without this focus, STEM programs run the risk of reducing the valuable contributions of mathematical thinking. If children fail to see meaningful links between their learning in mathematics and the other STEM domains, they can lose interest not only in mathematics but also in the other disciplines (Kelley & Knowles, 2016 ).

Traditional notions of mathematical problem solving (e.g., Charles, 1985 ) are now quite inadequate when applied to our current world. At a time of increasing creative disruption, it is essential for mathematical problem solvers to be adaptive in dealing with unforeseen local, national, and international problems. Increasingly, STEM-based problems in the real world encompass more than just disciplinary content and practices. While not denying the essential nature of these components, issues pertaining to cultural, social, political, and ethical dimensions (Kollosche & Meyerhöfer, 2021 ; Pheasants, 2020) can also impact the solution process, necessitating the application of appropriate thinking skills. As Pheasants stressed, “If STEM education is to prepare students to grapple with complex problems in the real world, then more attention ought to be given to approaches that are inclusive of the non-STEM dimensions that exist in those problems.”

In light of the above arguments, I view mathematical and STEM-based problems as goal-directed experiences that (1) demand STEM-relevant ways of thinking, (2) require the development of productive and adaptive ways to navigate complexity, (3) enable multiple approaches and practices (Roberts et al., 2022 ), (4) recruit interdisciplinary solution processes, and (5) facilitate growth of learning innovation for all students regardless of their background (English, 2018 ). In contrast to traditional expectations, such problems need to embody affordances that facilitate learning innovation, where all students can move beyond their existing competence in standard problem solving and be challenged to generate new knowledge in solving unanticipated problems. Even students who achieve average results on standardised tests display conceptual understanding and advanced mathematical thinking not normally seen in the classroom—especially when current common practices emphasise number skills at the expense of problem solving and reasoning with numbers (Kazemi, 2020 ).

Limited attention, however, has been paid to how problem experiences can be developed that press beyond basic content knowledge (Anderson, 2014; Li, Schoenfeld et al., 2019), encompass the STEM disciplines, and develop important ways of thinking. In their recent article, Slavit et al. ( 2021 ) argued that STEM education should be “grounded in our knowledge of how students think in STEM-focused learning environments” (p. 1), and that fostering twenty-first-century skills is essential. Yet, as these authors highlighted, there is not much research on STEM ways of thinking, with even fewer theoretical perspectives and frameworks on which to draw. In the next section, I consider these ways of thinking, defined in Table 1 , and provide examples of their applications to STEM-based problem solving.

3 Ways of thinking in STEM-based problem solving

3.1 critical thinking.

Although long recognised as a significant process in a range of fields, research on critical thinking in education, especially in primary education, has been limited (Aktoprak & Hursen, 2022 ). Critical thinking has long been associated with mathematical reasoning and problem solving, but their association remains under-theorized (Jablonka, 2020 ). Likewise, connections between critical thinking and design thinking have had limited attention largely due to their shared conceptual structures not being articulated (Ericson, 2022 ). As a twenty-first century skill, critical thinking is increasingly recognised as essential in STEM and mathematics education (Kollosche & Meyerhöfer, 2021 ) but is sadly lacking in many school curricula (Braund, 2021 ). As applied to STEM-based problem solving, critical thinking builds on inquiry skills (Nichols et al., 2019 ) and entails evaluating and judging problem situations including statements, claims, and propositions made, analysing arguments, inferring, and reflecting on solution approaches and conclusions drawn. Although critical thinking can contribute significantly to each of the other ways of thinking, its application is often neglected. For example, critical thinking is increasingly needed in design and design thinking, which play a key role in product development, environmental projects, and even in forms of social interaction (as discussed in Sect.  3.3 ; Ericson, 2022 ).

3.1.1 Critical mathematical modelling

One rich source of problem experiences that foster critical thinking is that of modelling. The diverse field of mathematical modelling has long been prominent in the secondary years (e.g., Ärlebäck & Doerr, 2018 ) but remains under-researched in the primary years, especially in relation to its everyday applications. Effective engagement with social, political, and environmental issues through modelling and statistics demands critical thinking, yet such aspects are not often considered in school curricula (Jablonka, 2020 ). This is of particular concern, given the pressing need to tackle such issues in today’s world.

As noted in several publications, the interdisciplinary nature of mathematical modelling makes it ideal for STEM-based problem solving (English, 2016 ; Maass et al., 2019 ; Zawojewski et al., 2008 ). Numerous definitions of models and modelling exist in the literature (e.g., Blum & Leiss, 2007 ; Brady et al., 2015 ). For this article, modelling involves developing conceptual innovations in response to real-world needs; effective modelling requires moving beyond the conventional ways of thinking applied in typical school problems (Lesh et al., 2013 ) to include contextual and critical analysis.

Much has been written about the role of modelling during COVID-19. Mathematical models played a major role in grappling with COVID 19, but their projections were a source of controversy (Rhodes & Lancaster, 2020 ). There seems little appreciation of the critical nature of mathematical models in society (Barbosa, 2006 ) and how assumptions in the modelling process can sway decisions. STEM-based problem solving needs to incorporate not just modelling itself, but also critical mathematical modelling. Critiquing what a model yields, and what is learned, is of increasing social importance (Aguilar & Castaneda, 2021 ; Barbosa, 2006 ). Indeed, as Braund ( 2021 ) illustrated, the Covid-19 pandemic has revealed the urgent need for “critical STEM literacy” (p. 339)—an awareness of the complex and problematic interactions of STEM and politics, and a knowledge and understanding of the underlying STEM concepts and representations is essential:

There are two imperatives that emerge: first, that there is sufficient STEM literacy to negotiate the complex COVID-19 information landscape to enable personal decision taking and second, that this is accompanied by a degree of criticality so that politicians and experts are called to account (Braund, 2021 , p. 339).

Kollosche ( 2021 ) shed further light on the lack of critical thinking in the media’s reporting on COVID, with his argument that “most newspaper reports were effective in creating the problems” because of their focus on ideal forms of mathematical concepts and modelling, without discussing the assumptions and methods behind the reported data. Of concern is that “mass media still fail to present scientific models and results in a way that allows for mathematical reflection and a critical evaluation of such information by citizens.”

Modelling experiences that draw on students’ cultural and community contexts (Anhalt et al., 2018 ; English, 2021a , 2021b ; Turner et al., 2009 ) provide rich opportunities for critical thinking from a citizen’s perspective. Such opportunities can also assist students in appreciating that mathematics is not merely a means of calculating answers but is also a vehicle for social justice, where critical thinking plays a key role (Cirillo et al., 2016 ; Greer et al., 2007 ). In their studies of critical thinking in cultural and community contexts, Turner and her colleagues (Turner et al., 2009 , 2021 , 2022 ) explored culturally responsive, community-based approaches to mathematical modelling with elementary teachers and students. Using a range of authentic modelling contexts, Turner and her colleagues illustrated how students’ modelling processes generated a number of issues that required them to think critically about their lives and their lives within their community. In one activity, students were applying design thinking and processes as they redesigned their local park. They generated, for example, mathematical models to estimate how long children would have to wait to use the swings—this informed their decision that the park did not meet the needs of the community. This community-based modelling highlighted “ongoing negotiation between students’ experiences and intentions related to the community park, the constraints of the actual context, and the mathematical issues that arose” (Turner et al., 2009 , p. 148).

Another example of modelling involving critical thinking in cultural and community contexts was implemented in a sixth-grade Cyprus classroom. Students were required to develop a model for their country to purchase water supplies from a choice of nearby nations (English & Mousoulides, 2011 ). Students were to consider travel distances, water price, available supply per week, oil tanker capacity, costs of water and oil, and quality of the port facilities in the neighbouring countries. The targeted model had to select the best option not only for the present but also for the future. Students’ models ranged from a basic form, where port facilities and water supply were ignored, to more sophisticated models, where all factors were integrated, with carbon emissions also considered. One of the student groups who took into account environmental factors commented, “It would be better for the country to spend a little more money and reduce oil consumption. And there are other environmental issues, like pollution of the Mediterranean Sea.” The more sophisticated models reflected systems thinking (Sect.  3.2 ), where the impact of partial factors such as oil consumption on the whole domain (ocean ecosystems and community) was also considered.

3.1.2 Philosophical Inquiry

One underrepresented means of fostering critical thinking in mathematical and STEM-based problem solving is through philosophical inquiry (Calvert et al., 2017 ; English, 2013 , 2022 ; Kennedy, 2012 ; Mukhopadhyay & Greer, 2007 ). Such inquiry encourages a range of thinking skills in identifying hidden assumptions, determining alternative courses of action, and reflecting on conclusions drawn and claims made. Several studies have shown how engaging children in communities of philosophical inquiry nurtures critical thinking dispositions, which become both a goal and a method (Bezençon, 2020 ; Daniel et al., 2017 ; Lipman, 2003 , 2008 ). At the same time, philosophical inquiry can lead to “conceptual deepening” (Bezençon, 2017), where analysis of mathematical and related STEM concepts as they apply beyond the classroom can be fostered. Given the increased societal awareness of mathematics and STEM in recent years, philosophical inquiry can be a powerful tool in enhancing students’ understanding and appreciation of how these disciplines shape societies. At the same time, philosophical inquiry can stimulate consideration of ethical issues in the applications of these disciplines (Bezençon, 2020 ). For example, Mukhopadhyay and Greer ( 2007 ) indicated how mathematics education should “convey the complexity of mathematical modeling social phenomena and a sense of what demarcates questions that can be answered by empirical evidence from those that depend on value systems and world-views” (p. 186).

A comprehensive review by O’Reilly et al. ( 2022 ) identified pedagogical approaches to scaffolding early critical thinking skills including inquiry-based teaching using classroom dialogue or questioning techniques. Such techniques include philosophical inquiry and encouraging children to construct, share, and justify their ideas regarding a task or investigation. Other opportunities for philosophical inquiry include group problem solving, peer sharing of created models, and facilitating critical and constructive peer feedback. For example, Gallagher and Jones ( 2021 ) reported on integrating mathematical modelling and economics, where beginning teachers were presented with a task involving a problematic community issue following a school shooting. In such cases, numerous courses of action are typically proposed for addressing the problem. Not surprisingly, various community opinions exist on such proposals, giving rise to valuable contexts for philosophical inquiry and critical modelling, where data and their sources are carefully analysed. With the escalation of statistical data from the mass media, it is imperative to commence the foundations of critical and philosophical thinking early. Students’ skills in asking critical questions as they work with data in constructing and improving a model, reflect on what their models convey, consider consequences of their models, and justify and communicate their conclusions require nurturing throughout school (Gibbs & Young Park, 2022 ).

3.2 Systems thinking

Systems thinking cuts across the STEM disciplines as well as many other fields outside education. It is considered a key component of “critical thinking and problem solving” in 21st Century Learning (P21, 2015 ) and is often cited as a “habit of mind” in engineering education (e.g., Lippard et al., 2018 ; Lucas et al., 2014 ). Numerous definitions exist for systems thinking (e.g., Bielik et al., 2022 ; Damelin et al., 2017 ; Jacobson & Wilenski, 2022 ), with Bielik et al. ( 2022 ) identifying such thinking as the ability to “consider the system boundaries, the components of the system, the interactions between system components and between different subsystems, and emergent properties and behaviour of the system” (p. 219). In more basic terms, Shin et al. ( 2022 ) refer to systems thinking as “the ability to understand a problem or phenomenon as a system of interacting elements that produces emergent behavior” (p. 936).

Systems thinking interacts with the other thinking forms including those displayed in Fig.  1 , as well as computational thinking (Shin et al., 2022), critical thinking (Curwin et al., 2018 ) and mathematical thinking more broadly (Baioa & Carreira, 2022 ). Systems thinking is considered especially important in conceptualizing a problematic situation within a larger context and in perceiving problems in new and different ways (Stroh, 2018 ). Of special relevance to today’s world is the realisation that perfect solutions do not exist and the choices one makes in applying systems thinking will impact on other parts of the system (Meadows, 2008 ). What is often not considered in today’s complex societies—at least not to the extent required—is that we live in a world of intrinsically linked systems, where disruption in one part will reverberate in others. We see so many instances where particular courses of action are advocated or mandated in societal systems, while the impact on sub-components is perilously ignored. Examples are evident in many nations’ responses to COVID-19, where escalating lockdowns impacted economies and communities, whose demands had to be balanced against purely epidemiological factors. The reverberations of such actions stretch far and wide over long periods. Likewise, the various impacts of current climate actions are frequently ignored, such as how the construction of vast areas of renewable resources (e.g., wind turbines) can have deleterious effects on the surrounding environments including wildlife.

Despite its centrality across the STEM domains, systems thinking is almost absent from mathematics education (Curwin et al., 2018 ). This is despite claims by many researchers that modelling, systems thinking, and associated thinking processes should be significant components of students’ education (Bielik et al., 2022 ; Jacobson & Wilenski, 2022 ). Indeed, systems thinking is featured prominently in the US A Framework for K-12 Science Education (NRC, 2012 ) and the Next Generation Science Standards (NGSS Lead States, 2013 ), and has received considerable attention in science education (e.g., Borge, 2016 ; Hmelo-Silver et al., 2017 ; York et al., 2019 ) and engineering education (e.g., Lippard & Riley, 2018 ; Litzinger, 2016 ).

Given the complexity of systems thinking in today’s world, and the diverse ways in which it is applied, students require opportunities to experience how systems thinking can interact with other forms such as design thinking and critical thinking (Curwin et al., 2018 ; Shin et al., 2022). Such interactions occur in many popular STEM investigations including one in which fifth-grade students designed, constructed, and experimented with a loaded paper plane (paper clips added) in determining how load impacts on the distance travelled (English, 2021b ). Students observed that changing one design feature (e.g., wingspan or load position) unsettles some other features (e.g., fuselage depth decreases wingspan). The investigation yielded an appreciation of the intricacy of interactions among a system’s components, and their scarcely predictable mutual effects.

Other studies have revealed how very young children can engage in basic systems thinking within STEM contexts. For example, Feriver et al. ( 2019 ) administered a story reading session to individual 4- to 6-year-old children in preschools in Turkey and Germany, and then followed this with individual semi-structured interviews about the story. The reading session was based on the story book, “The Water Hole” (Base, 2001 ), which draws on basic concepts of systems within an ecosystem context. Their study found the young children to have some complex understanding of systems thinking in terms of detecting obvious gradual changes and two-step domino and/or multiple one-way causalities, as well as describing the behaviour of a balancing loop (corrective actions that try to reduce the gap between a desired level or goal and the actual lever, such as temperature and plant growth). However, the children understandably experienced difficulties in several areas, in which even adults have problems. For example, detecting a reinforcing loop, identifying unintended consequences, detecting hidden components and processes, adopting a multi-dimensional perspective, and predicting how a system would behave in the future were problematic for them. In another study, Gillmeister ( 2017 ) showed how preschool children have a more complex understanding of systems thinking than previously claimed. Their ability to utilize simple systems thinking tools, such as stock-flow maps, feedback loops and behaviour over time graphs, was evident.

Although the research has not been extensive, current findings indicate how we might capitalise on the seeds of early systems thinking across the STEM fields. With the pervasive nature of systems thinking, it is argued that its connections to other forms of thinking across STEM should be nurtured (cf., Svensson, 2022 ). This includes links to design-based thinking where designed products, for example, operate “within broader systems and systems of systems” (Buchanan, 2019 ).

3.3 Design-based thinking and STEM-based problem solving

Design-based thinking plays a major role in complex problem solving, yet its contribution to mathematics learning has been largely ignored, especially at the primary levels. Design is central in technology and engineering practice (English et al., 2020 ; Guzey et al., 2019 ), from bridge construction through to the development of medical tools. Design contributes to all phases of problem solving and drives students toward innovative rather than predetermined outcomes (Goldman & Zielezinski, 2016 ). As applied to STEM education, design thinking is generally viewed as a set of iterative processes of understanding a problem and developing an appropriate solution. It includes problem scoping, idea generation, systems thinking, designing and creating, testing and reflecting, redesigning and recreating, and communicating. Both learning about design and learning through design can help students develop more informed analytical approaches to mathematical and STEM-based problem solving (English et al., 2020 ; Strimel et al., 2018 ).

Learning about design in solving complex problems emphasises design thinking processes per se, that is, students learn about design itself. Design thinking as a means for learning about design is not as prevalent in integrated STEM education. Although learning through and about design should not be divorced during problem solving (van Breukelen et al., 2017 ), one learning goal can take precedence over the other. Both require greater attention, especially in today’s design-focused world (Tornroth & Wikberg Nilsson, 2022 ).

A plurality of solutions of varying levels of sophistication is possible in applying design thinking processes, so students from different achievement levels can devise solutions (Goldman & Kabayadondo, 2017 )—and research suggests that lower-achieving students benefit most (Chin et al., 2019 ). The question of how best to develop design learning across grades K-12, however, has not received adequate attention. This is perhaps not surprising given that comparatively few studies have investigated the design thinking of grades 6–12 and even fewer across the elementary years (Kelley & Sung, 2017 ; Strimel et al., 2018 ).

Also overlooked is how design-based thinking can foster concept development, that is, how it can foster “learning while designing”, or generative learning (English et al., 2020 ). Design-based thinking provides natural opportunities to develop understanding of the required STEM concepts (Hjalmarson et al., 2020 ). As these authors pointed out, when students create designs, they represent models of their thinking. When students have to express their conceptual understanding in the form of design, such as an engineering designed product, their knowledge (e.g., of different material properties) is tested. Studies have revealed such learning occurs when elementary and middle school students design and construct various physical artifacts. For example, in a fifth-grade study involving designing and building an optical instrument that enabled one to see around corners, King and English ( 2017 ) observed how students applied and enriched their understanding of scientific concepts of light and how it travels through a system, together with their mathematical knowledge of geometric properties, angles and measurement.

In a study in the secondary grades (Langman et al. ( 2019 ), student groups completed modules that included a model-eliciting activity (Lesh & Zawojewski, 2007 ) involving iterative design thinking processes. Students were to interpret, assess, and compare images of blood vessel networks grown in scaffolds, develop a procedure or tool for measuring (or scoring) this vessel growth, and demonstrate how to apply their procedure to the images, as well as to any image of a blood vessel network. The results showed how students designed a range of mathematical models of varying levels of sophistication to evaluate the quality of blood vessel networks and developed a knowledge of angiogenesis in doing so.

In another study implemented in a 6th-grade classroom, students were involved in both learning about and learning through design in creating a new sustainable town with the goal of at least 50% renewable energy sources. The students were also engaged in systems thinking, as well as critical thinking, as they planned, developed, and critically analysed the layout and interactions of different components of their town system (e.g., where to place renewable energy sources to minimise impact on the residences and recreational areas; where to situate essential services to reach different town components). Students also had to consider the budgetary constraints in their town designs. Their learning about design was apparent in their iterative processes of problem scoping, idea generation and modification, balancing of benefits and trade-offs (dealing with system subcomponents), critical reflections on their designs, and improvements of the overall town design. Learning though design was evident as students displayed content knowledge pertaining to renewable energy and community needs, applied spatial reasoning in positioning town features, and considered budgetary constraints in reaching their “best” design.

Engineering design processes form a significant component of design thinking and learning, with foundational links across the STEM disciplines including mathematical modelling. Engineering design-based problems help students appreciate how they can apply different ideas and approaches from the STEM disciplines, with more than one outcome possible (Guzey et al., 2019 ). Such design thinking engages students in interpreting problems, developing initial design ideas, selecting and testing a promising design, analysing results from their prototype solution, and revising to improve outcomes.

It is of concern that limited attention has been devoted to engineering design-based thinking in mathematics and the other STEM disciplines in the primary grades. This is despite research indicating how very young children can engage in design-based thinking when provided with appropriate opportunities (e.g., Cunningham, 2018 ; Elkin et al., 2018 ). Elkin et al., for example, used robotics in early childhood classrooms to introduce foundational engineering design thinking processes. Their study illustrated how these young learners used engineering design journals and engaged in design thinking as they engineered creative solutions to challenging problems presented to them. It seems somewhat paradoxical that foundational engineering design thinking is a natural part of young children’s inquiry about their world, yet this important component has been largely ignored in these informative years.

In sum, design-based thinking is a powerful and integrative tool for mathematical and STEM-based problem solving and requires greater focus in school curricula. Both learning about and through design have the potential to improve learning and problem solving well beyond the school years (Chin et al., 2019 ). At the same time, design-based thinking, together with the other ways of thinking, can contribute significantly to learning innovation (English, 2018 ).

3.4 Adaptive and innovative thinking for learning innovation

Disruption is rapidly becoming the norm in almost all spheres of life. The recent national and international upheavals have further stimulated disruptive thinking (or disruptive innovation), where perspectives on commonly accepted (and often inefficient) solutions to problems are rejected for more innovative approaches and products. Given the pressing need for problem solvers capable of developing new and adaptable knowledge, rather than applying limited simplistic procedures or strategies, we need to foster what I term, learning innovation (English, 2018 ; Fig.  2 ). Such learning builds on core content to generate more powerful disciplinary knowledge and thinking processes that can, in turn, be adapted and applied to solving subsequent challenging problems.

Learning innovation

Figure  2 (adapted from McKenna, 2014 ) illustrates how learning innovation can be fostered through the growth of mathematical and STEM knowledge, together with STEM ways of thinking. The optimal adaptability corridor represents the growth of mathematical and STEM-based problem solving from novice to adaptable solver . Adaptable problem solvers (Hatano & Oura, 2003 ) have developed the flexibility, curiosity, and creativity to tackle novel problems—skills that are needed in jobs of the future (Denning & Noray, 2020 ; OECD, 2019 ). Without the disciplinary knowledge, ways of thinking, and engagement in challenging but approachable problems, a student risks remaining merely a routine problem solver—one who is skilled solely in applying previously taught procedures to solve sets of familiar well-worn problems, as typically encountered at school. Learning innovation remains a challenging and unresolved issue across curriculum domains and is proposed as central to dealing effectively with disruption.

Particularly rich experiences for developing learning innovation involve interdisciplinary modelling, incorporating critical mathematical modelling (e.g., Hallström and Schönborn, 2019 ; Lesh et al., 2013 ). As noted, a key feature of model-eliciting experiences is the affordances they provide all students to exhibit “extraordinary abilities to remember and transfer their tools to new situations” (Lesh et al., 2013 , p. 54). Modelling enables students to apply more sophisticated STEM concepts and generate solutions that extend beyond their usual classroom problems. Such experiences require different ways of thinking in problem solving as they deal with, for example, conflicting constraints and trade-offs, alternative paths to follow, and various tools and representations to utilise. In essence, interdisciplinary modelling may be regarded as a way of creating STEM concepts, with modeling and concept development being highly interdependent and mutually supportive (cf., Lesh & Caylor, 2007 ).

4 Concluding points

The ill-defined problems of today, coupled with unexpected disruptions across all walks of life, demand advanced problem-solving by all citizens. The need to update outmoded forms of problem solving, which fail to take into account increasing global challenges, has never been greater (Cowin, 2021 ). The ways-of-thinking framework has been proposed as a powerful means of enhancing problem-solving skills for dealing with today’s unprecedented game-changers. Specifically, critical thinking (including critical mathematical modelling and philosophical inquiry), systems thinking, and design-based thinking are advanced as collectively contributing to the adaptive and innovative skills required for problem success. It is argued that the pinnacle of this framework is learning innovation, which can be within reach of all students. Fostering students’ agency for developing learning innovation is paramount if they are to take some control of their own problem solving and learning (English, 2018 ; Gadanidis et al., 2016 ; Roberts et al., 2022 ).

Establishing a culture of empowerment and equity, with an asset-based approach, where the strengths of all students are recognised, can empower students as learners and achievers in an increasingly uncertain world (Celedón-Pattichis et al., 2018 ). Teacher actions that encourage students to express their ideas, together with a program of future-oriented mathematical and STEM-based problems, can nurture students’ problem-solving confidence and dispositions (Goldman & Zielezinski, 2016 ; Roberts et al., 2022 ). In particular, mathematical and STEM-based modelling has been advocated as a rich means of developing multiple ways of thinking that foster adaptive and innovative learners—learners with a propensity for developing new knowledge and skills, together with a willingness to tackle ill-defined problems of today and the future. Such propensity for dealing effectively with STEM-based problem solving is imperative, beginning in the earliest grades. The skills gained can thus be readily transferred across disciplines, and subsequently across career opportunities.

Data availability

The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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English, L.D. Ways of thinking in STEM-based problem solving. ZDM Mathematics Education 55 , 1219–1230 (2023). https://doi.org/10.1007/s11858-023-01474-7

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35 Scientific Thinking and Reasoning

Kevin N. Dunbar, Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD

David Klahr, Department of Psychology, Carnegie Mellon University, Pittsburgh, PA

• Published: 21 November 2012
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Scientific thinking refers to both thinking about the content of science and the set of reasoning processes that permeate the field of science: induction, deduction, experimental design, causal reasoning, concept formation, hypothesis testing, and so on. Here we cover both the history of research on scientific thinking and the different approaches that have been used, highlighting common themes that have emerged over the past 50 years of research. Future research will focus on the collaborative aspects of scientific thinking, on effective methods for teaching science, and on the neural underpinnings of the scientific mind.

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• Review Article
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• Published: 11 January 2023

The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature

• Enwei Xu   ORCID: orcid.org/0000-0001-6424-8169 1 ,
• Wei Wang 1 &
• Qingxia Wang 1  

Humanities and Social Sciences Communications volume  10 , Article number:  16 ( 2023 ) Cite this article

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Collaborative problem-solving has been widely embraced in the classroom instruction of critical thinking, which is regarded as the core of curriculum reform based on key competencies in the field of education as well as a key competence for learners in the 21st century. However, the effectiveness of collaborative problem-solving in promoting students’ critical thinking remains uncertain. This current research presents the major findings of a meta-analysis of 36 pieces of the literature revealed in worldwide educational periodicals during the 21st century to identify the effectiveness of collaborative problem-solving in promoting students’ critical thinking and to determine, based on evidence, whether and to what extent collaborative problem solving can result in a rise or decrease in critical thinking. The findings show that (1) collaborative problem solving is an effective teaching approach to foster students’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]); (2) in respect to the dimensions of critical thinking, collaborative problem solving can significantly and successfully enhance students’ attitudinal tendencies (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI[0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI[0.58, 0.82]); and (3) the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have an impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. On the basis of these results, recommendations are made for further study and instruction to better support students’ critical thinking in the context of collaborative problem-solving.

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Introduction.

Although critical thinking has a long history in research, the concept of critical thinking, which is regarded as an essential competence for learners in the 21st century, has recently attracted more attention from researchers and teaching practitioners (National Research Council, 2012 ). Critical thinking should be the core of curriculum reform based on key competencies in the field of education (Peng and Deng, 2017 ) because students with critical thinking can not only understand the meaning of knowledge but also effectively solve practical problems in real life even after knowledge is forgotten (Kek and Huijser, 2011 ). The definition of critical thinking is not universal (Ennis, 1989 ; Castle, 2009 ; Niu et al., 2013 ). In general, the definition of critical thinking is a self-aware and self-regulated thought process (Facione, 1990 ; Niu et al., 2013 ). It refers to the cognitive skills needed to interpret, analyze, synthesize, reason, and evaluate information as well as the attitudinal tendency to apply these abilities (Halpern, 2001 ). The view that critical thinking can be taught and learned through curriculum teaching has been widely supported by many researchers (e.g., Kuncel, 2011 ; Leng and Lu, 2020 ), leading to educators’ efforts to foster it among students. In the field of teaching practice, there are three types of courses for teaching critical thinking (Ennis, 1989 ). The first is an independent curriculum in which critical thinking is taught and cultivated without involving the knowledge of specific disciplines; the second is an integrated curriculum in which critical thinking is integrated into the teaching of other disciplines as a clear teaching goal; and the third is a mixed curriculum in which critical thinking is taught in parallel to the teaching of other disciplines for mixed teaching training. Furthermore, numerous measuring tools have been developed by researchers and educators to measure critical thinking in the context of teaching practice. These include standardized measurement tools, such as WGCTA, CCTST, CCTT, and CCTDI, which have been verified by repeated experiments and are considered effective and reliable by international scholars (Facione and Facione, 1992 ). In short, descriptions of critical thinking, including its two dimensions of attitudinal tendency and cognitive skills, different types of teaching courses, and standardized measurement tools provide a complex normative framework for understanding, teaching, and evaluating critical thinking.

Cultivating critical thinking in curriculum teaching can start with a problem, and one of the most popular critical thinking instructional approaches is problem-based learning (Liu et al., 2020 ). Duch et al. ( 2001 ) noted that problem-based learning in group collaboration is progressive active learning, which can improve students’ critical thinking and problem-solving skills. Collaborative problem-solving is the organic integration of collaborative learning and problem-based learning, which takes learners as the center of the learning process and uses problems with poor structure in real-world situations as the starting point for the learning process (Liang et al., 2017 ). Students learn the knowledge needed to solve problems in a collaborative group, reach a consensus on problems in the field, and form solutions through social cooperation methods, such as dialogue, interpretation, questioning, debate, negotiation, and reflection, thus promoting the development of learners’ domain knowledge and critical thinking (Cindy, 2004 ; Liang et al., 2017 ).

Collaborative problem-solving has been widely used in the teaching practice of critical thinking, and several studies have attempted to conduct a systematic review and meta-analysis of the empirical literature on critical thinking from various perspectives. However, little attention has been paid to the impact of collaborative problem-solving on critical thinking. Therefore, the best approach for developing and enhancing critical thinking throughout collaborative problem-solving is to examine how to implement critical thinking instruction; however, this issue is still unexplored, which means that many teachers are incapable of better instructing critical thinking (Leng and Lu, 2020 ; Niu et al., 2013 ). For example, Huber ( 2016 ) provided the meta-analysis findings of 71 publications on gaining critical thinking over various time frames in college with the aim of determining whether critical thinking was truly teachable. These authors found that learners significantly improve their critical thinking while in college and that critical thinking differs with factors such as teaching strategies, intervention duration, subject area, and teaching type. The usefulness of collaborative problem-solving in fostering students’ critical thinking, however, was not determined by this study, nor did it reveal whether there existed significant variations among the different elements. A meta-analysis of 31 pieces of educational literature was conducted by Liu et al. ( 2020 ) to assess the impact of problem-solving on college students’ critical thinking. These authors found that problem-solving could promote the development of critical thinking among college students and proposed establishing a reasonable group structure for problem-solving in a follow-up study to improve students’ critical thinking. Additionally, previous empirical studies have reached inconclusive and even contradictory conclusions about whether and to what extent collaborative problem-solving increases or decreases critical thinking levels. As an illustration, Yang et al. ( 2008 ) carried out an experiment on the integrated curriculum teaching of college students based on a web bulletin board with the goal of fostering participants’ critical thinking in the context of collaborative problem-solving. These authors’ research revealed that through sharing, debating, examining, and reflecting on various experiences and ideas, collaborative problem-solving can considerably enhance students’ critical thinking in real-life problem situations. In contrast, collaborative problem-solving had a positive impact on learners’ interaction and could improve learning interest and motivation but could not significantly improve students’ critical thinking when compared to traditional classroom teaching, according to research by Naber and Wyatt ( 2014 ) and Sendag and Odabasi ( 2009 ) on undergraduate and high school students, respectively.

The above studies show that there is inconsistency regarding the effectiveness of collaborative problem-solving in promoting students’ critical thinking. Therefore, it is essential to conduct a thorough and trustworthy review to detect and decide whether and to what degree collaborative problem-solving can result in a rise or decrease in critical thinking. Meta-analysis is a quantitative analysis approach that is utilized to examine quantitative data from various separate studies that are all focused on the same research topic. This approach characterizes the effectiveness of its impact by averaging the effect sizes of numerous qualitative studies in an effort to reduce the uncertainty brought on by independent research and produce more conclusive findings (Lipsey and Wilson, 2001 ).

This paper used a meta-analytic approach and carried out a meta-analysis to examine the effectiveness of collaborative problem-solving in promoting students’ critical thinking in order to make a contribution to both research and practice. The following research questions were addressed by this meta-analysis:

What is the overall effect size of collaborative problem-solving in promoting students’ critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills)?

How are the disparities between the study conclusions impacted by various moderating variables if the impacts of various experimental designs in the included studies are heterogeneous?

This research followed the strict procedures (e.g., database searching, identification, screening, eligibility, merging, duplicate removal, and analysis of included studies) of Cooper’s ( 2010 ) proposed meta-analysis approach for examining quantitative data from various separate studies that are all focused on the same research topic. The relevant empirical research that appeared in worldwide educational periodicals within the 21st century was subjected to this meta-analysis using Rev-Man 5.4. The consistency of the data extracted separately by two researchers was tested using Cohen’s kappa coefficient, and a publication bias test and a heterogeneity test were run on the sample data to ascertain the quality of this meta-analysis.

Data sources and search strategies

There were three stages to the data collection process for this meta-analysis, as shown in Fig. 1 , which shows the number of articles included and eliminated during the selection process based on the statement and study eligibility criteria.

This flowchart shows the number of records identified, included and excluded in the article.

First, the databases used to systematically search for relevant articles were the journal papers of the Web of Science Core Collection and the Chinese Core source journal, as well as the Chinese Social Science Citation Index (CSSCI) source journal papers included in CNKI. These databases were selected because they are credible platforms that are sources of scholarly and peer-reviewed information with advanced search tools and contain literature relevant to the subject of our topic from reliable researchers and experts. The search string with the Boolean operator used in the Web of Science was “TS = (((“critical thinking” or “ct” and “pretest” or “posttest”) or (“critical thinking” or “ct” and “control group” or “quasi experiment” or “experiment”)) and (“collaboration” or “collaborative learning” or “CSCL”) and (“problem solving” or “problem-based learning” or “PBL”))”. The research area was “Education Educational Research”, and the search period was “January 1, 2000, to December 30, 2021”. A total of 412 papers were obtained. The search string with the Boolean operator used in the CNKI was “SU = (‘critical thinking’*‘collaboration’ + ‘critical thinking’*‘collaborative learning’ + ‘critical thinking’*‘CSCL’ + ‘critical thinking’*‘problem solving’ + ‘critical thinking’*‘problem-based learning’ + ‘critical thinking’*‘PBL’ + ‘critical thinking’*‘problem oriented’) AND FT = (‘experiment’ + ‘quasi experiment’ + ‘pretest’ + ‘posttest’ + ‘empirical study’)” (translated into Chinese when searching). A total of 56 studies were found throughout the search period of “January 2000 to December 2021”. From the databases, all duplicates and retractions were eliminated before exporting the references into Endnote, a program for managing bibliographic references. In all, 466 studies were found.

Second, the studies that matched the inclusion and exclusion criteria for the meta-analysis were chosen by two researchers after they had reviewed the abstracts and titles of the gathered articles, yielding a total of 126 studies.

Third, two researchers thoroughly reviewed each included article’s whole text in accordance with the inclusion and exclusion criteria. Meanwhile, a snowball search was performed using the references and citations of the included articles to ensure complete coverage of the articles. Ultimately, 36 articles were kept.

Two researchers worked together to carry out this entire process, and a consensus rate of almost 94.7% was reached after discussion and negotiation to clarify any emerging differences.

Eligibility criteria

Since not all the retrieved studies matched the criteria for this meta-analysis, eligibility criteria for both inclusion and exclusion were developed as follows:

The publication language of the included studies was limited to English and Chinese, and the full text could be obtained. Articles that did not meet the publication language and articles not published between 2000 and 2021 were excluded.

The research design of the included studies must be empirical and quantitative studies that can assess the effect of collaborative problem-solving on the development of critical thinking. Articles that could not identify the causal mechanisms by which collaborative problem-solving affects critical thinking, such as review articles and theoretical articles, were excluded.

The research method of the included studies must feature a randomized control experiment or a quasi-experiment, or a natural experiment, which have a higher degree of internal validity with strong experimental designs and can all plausibly provide evidence that critical thinking and collaborative problem-solving are causally related. Articles with non-experimental research methods, such as purely correlational or observational studies, were excluded.

The participants of the included studies were only students in school, including K-12 students and college students. Articles in which the participants were non-school students, such as social workers or adult learners, were excluded.

The research results of the included studies must mention definite signs that may be utilized to gauge critical thinking’s impact (e.g., sample size, mean value, or standard deviation). Articles that lacked specific measurement indicators for critical thinking and could not calculate the effect size were excluded.

Data coding design

In order to perform a meta-analysis, it is necessary to collect the most important information from the articles, codify that information’s properties, and convert descriptive data into quantitative data. Therefore, this study designed a data coding template (see Table 1 ). Ultimately, 16 coding fields were retained.

The designed data-coding template consisted of three pieces of information. Basic information about the papers was included in the descriptive information: the publishing year, author, serial number, and title of the paper.

The variable information for the experimental design had three variables: the independent variable (instruction method), the dependent variable (critical thinking), and the moderating variable (learning stage, teaching type, intervention duration, learning scaffold, group size, measuring tool, and subject area). Depending on the topic of this study, the intervention strategy, as the independent variable, was coded into collaborative and non-collaborative problem-solving. The dependent variable, critical thinking, was coded as a cognitive skill and an attitudinal tendency. And seven moderating variables were created by grouping and combining the experimental design variables discovered within the 36 studies (see Table 1 ), where learning stages were encoded as higher education, high school, middle school, and primary school or lower; teaching types were encoded as mixed courses, integrated courses, and independent courses; intervention durations were encoded as 0–1 weeks, 1–4 weeks, 4–12 weeks, and more than 12 weeks; group sizes were encoded as 2–3 persons, 4–6 persons, 7–10 persons, and more than 10 persons; learning scaffolds were encoded as teacher-supported learning scaffold, technique-supported learning scaffold, and resource-supported learning scaffold; measuring tools were encoded as standardized measurement tools (e.g., WGCTA, CCTT, CCTST, and CCTDI) and self-adapting measurement tools (e.g., modified or made by researchers); and subject areas were encoded according to the specific subjects used in the 36 included studies.

The data information contained three metrics for measuring critical thinking: sample size, average value, and standard deviation. It is vital to remember that studies with various experimental designs frequently adopt various formulas to determine the effect size. And this paper used Morris’ proposed standardized mean difference (SMD) calculation formula ( 2008 , p. 369; see Supplementary Table S3 ).

Procedure for extracting and coding data

According to the data coding template (see Table 1 ), the 36 papers’ information was retrieved by two researchers, who then entered them into Excel (see Supplementary Table S1 ). The results of each study were extracted separately in the data extraction procedure if an article contained numerous studies on critical thinking, or if a study assessed different critical thinking dimensions. For instance, Tiwari et al. ( 2010 ) used four time points, which were viewed as numerous different studies, to examine the outcomes of critical thinking, and Chen ( 2013 ) included the two outcome variables of attitudinal tendency and cognitive skills, which were regarded as two studies. After discussion and negotiation during data extraction, the two researchers’ consistency test coefficients were roughly 93.27%. Supplementary Table S2 details the key characteristics of the 36 included articles with 79 effect quantities, including descriptive information (e.g., the publishing year, author, serial number, and title of the paper), variable information (e.g., independent variables, dependent variables, and moderating variables), and data information (e.g., mean values, standard deviations, and sample size). Following that, testing for publication bias and heterogeneity was done on the sample data using the Rev-Man 5.4 software, and then the test results were used to conduct a meta-analysis.

Publication bias test

When the sample of studies included in a meta-analysis does not accurately reflect the general status of research on the relevant subject, publication bias is said to be exhibited in this research. The reliability and accuracy of the meta-analysis may be impacted by publication bias. Due to this, the meta-analysis needs to check the sample data for publication bias (Stewart et al., 2006 ). A popular method to check for publication bias is the funnel plot; and it is unlikely that there will be publishing bias when the data are equally dispersed on either side of the average effect size and targeted within the higher region. The data are equally dispersed within the higher portion of the efficient zone, consistent with the funnel plot connected with this analysis (see Fig. 2 ), indicating that publication bias is unlikely in this situation.

This funnel plot shows the result of publication bias of 79 effect quantities across 36 studies.

Heterogeneity test

To select the appropriate effect models for the meta-analysis, one might use the results of a heterogeneity test on the data effect sizes. In a meta-analysis, it is common practice to gauge the degree of data heterogeneity using the I 2 value, and I 2  ≥ 50% is typically understood to denote medium-high heterogeneity, which calls for the adoption of a random effect model; if not, a fixed effect model ought to be applied (Lipsey and Wilson, 2001 ). The findings of the heterogeneity test in this paper (see Table 2 ) revealed that I 2 was 86% and displayed significant heterogeneity ( P  < 0.01). To ensure accuracy and reliability, the overall effect size ought to be calculated utilizing the random effect model.

The analysis of the overall effect size

This meta-analysis utilized a random effect model to examine 79 effect quantities from 36 studies after eliminating heterogeneity. In accordance with Cohen’s criterion (Cohen, 1992 ), it is abundantly clear from the analysis results, which are shown in the forest plot of the overall effect (see Fig. 3 ), that the cumulative impact size of cooperative problem-solving is 0.82, which is statistically significant ( z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]), and can encourage learners to practice critical thinking.

This forest plot shows the analysis result of the overall effect size across 36 studies.

In addition, this study examined two distinct dimensions of critical thinking to better understand the precise contributions that collaborative problem-solving makes to the growth of critical thinking. The findings (see Table 3 ) indicate that collaborative problem-solving improves cognitive skills (ES = 0.70) and attitudinal tendency (ES = 1.17), with significant intergroup differences (chi 2  = 7.95, P  < 0.01). Although collaborative problem-solving improves both dimensions of critical thinking, it is essential to point out that the improvements in students’ attitudinal tendency are much more pronounced and have a significant comprehensive effect (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]), whereas gains in learners’ cognitive skill are slightly improved and are just above average. (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

The analysis of moderator effect size

The whole forest plot’s 79 effect quantities underwent a two-tailed test, which revealed significant heterogeneity ( I 2  = 86%, z  = 12.78, P  < 0.01), indicating differences between various effect sizes that may have been influenced by moderating factors other than sampling error. Therefore, exploring possible moderating factors that might produce considerable heterogeneity was done using subgroup analysis, such as the learning stage, learning scaffold, teaching type, group size, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, in order to further explore the key factors that influence critical thinking. The findings (see Table 4 ) indicate that various moderating factors have advantageous effects on critical thinking. In this situation, the subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), learning scaffold (chi 2  = 9.03, P  < 0.01), and teaching type (chi 2  = 7.20, P  < 0.05) are all significant moderators that can be applied to support the cultivation of critical thinking. However, since the learning stage and the measuring tools did not significantly differ among intergroup (chi 2  = 3.15, P  = 0.21 > 0.05, and chi 2  = 0.08, P  = 0.78 > 0.05), we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving. These are the precise outcomes, as follows:

Various learning stages influenced critical thinking positively, without significant intergroup differences (chi 2  = 3.15, P  = 0.21 > 0.05). High school was first on the list of effect sizes (ES = 1.36, P  < 0.01), then higher education (ES = 0.78, P  < 0.01), and middle school (ES = 0.73, P  < 0.01). These results show that, despite the learning stage’s beneficial influence on cultivating learners’ critical thinking, we are unable to explain why it is essential for cultivating critical thinking in the context of collaborative problem-solving.

Different teaching types had varying degrees of positive impact on critical thinking, with significant intergroup differences (chi 2  = 7.20, P  < 0.05). The effect size was ranked as follows: mixed courses (ES = 1.34, P  < 0.01), integrated courses (ES = 0.81, P  < 0.01), and independent courses (ES = 0.27, P  < 0.01). These results indicate that the most effective approach to cultivate critical thinking utilizing collaborative problem solving is through the teaching type of mixed courses.

Various intervention durations significantly improved critical thinking, and there were significant intergroup differences (chi 2  = 12.18, P  < 0.01). The effect sizes related to this variable showed a tendency to increase with longer intervention durations. The improvement in critical thinking reached a significant level (ES = 0.85, P  < 0.01) after more than 12 weeks of training. These findings indicate that the intervention duration and critical thinking’s impact are positively correlated, with a longer intervention duration having a greater effect.

Different learning scaffolds influenced critical thinking positively, with significant intergroup differences (chi 2  = 9.03, P  < 0.01). The resource-supported learning scaffold (ES = 0.69, P  < 0.01) acquired a medium-to-higher level of impact, the technique-supported learning scaffold (ES = 0.63, P  < 0.01) also attained a medium-to-higher level of impact, and the teacher-supported learning scaffold (ES = 0.92, P  < 0.01) displayed a high level of significant impact. These results show that the learning scaffold with teacher support has the greatest impact on cultivating critical thinking.

Various group sizes influenced critical thinking positively, and the intergroup differences were statistically significant (chi 2  = 8.77, P  < 0.05). Critical thinking showed a general declining trend with increasing group size. The overall effect size of 2–3 people in this situation was the biggest (ES = 0.99, P  < 0.01), and when the group size was greater than 7 people, the improvement in critical thinking was at the lower-middle level (ES < 0.5, P  < 0.01). These results show that the impact on critical thinking is positively connected with group size, and as group size grows, so does the overall impact.

Various measuring tools influenced critical thinking positively, with significant intergroup differences (chi 2  = 0.08, P  = 0.78 > 0.05). In this situation, the self-adapting measurement tools obtained an upper-medium level of effect (ES = 0.78), whereas the complete effect size of the standardized measurement tools was the largest, achieving a significant level of effect (ES = 0.84, P  < 0.01). These results show that, despite the beneficial influence of the measuring tool on cultivating critical thinking, we are unable to explain why it is crucial in fostering the growth of critical thinking by utilizing the approach of collaborative problem-solving.

Different subject areas had a greater impact on critical thinking, and the intergroup differences were statistically significant (chi 2  = 13.36, P  < 0.05). Mathematics had the greatest overall impact, achieving a significant level of effect (ES = 1.68, P  < 0.01), followed by science (ES = 1.25, P  < 0.01) and medical science (ES = 0.87, P  < 0.01), both of which also achieved a significant level of effect. Programming technology was the least effective (ES = 0.39, P  < 0.01), only having a medium-low degree of effect compared to education (ES = 0.72, P  < 0.01) and other fields (such as language, art, and social sciences) (ES = 0.58, P  < 0.01). These results suggest that scientific fields (e.g., mathematics, science) may be the most effective subject areas for cultivating critical thinking utilizing the approach of collaborative problem-solving.

The effectiveness of collaborative problem solving with regard to teaching critical thinking

According to this meta-analysis, using collaborative problem-solving as an intervention strategy in critical thinking teaching has a considerable amount of impact on cultivating learners’ critical thinking as a whole and has a favorable promotional effect on the two dimensions of critical thinking. According to certain studies, collaborative problem solving, the most frequently used critical thinking teaching strategy in curriculum instruction can considerably enhance students’ critical thinking (e.g., Liang et al., 2017 ; Liu et al., 2020 ; Cindy, 2004 ). This meta-analysis provides convergent data support for the above research views. Thus, the findings of this meta-analysis not only effectively address the first research query regarding the overall effect of cultivating critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills) utilizing the approach of collaborative problem-solving, but also enhance our confidence in cultivating critical thinking by using collaborative problem-solving intervention approach in the context of classroom teaching.

Furthermore, the associated improvements in attitudinal tendency are much stronger, but the corresponding improvements in cognitive skill are only marginally better. According to certain studies, cognitive skill differs from the attitudinal tendency in classroom instruction; the cultivation and development of the former as a key ability is a process of gradual accumulation, while the latter as an attitude is affected by the context of the teaching situation (e.g., a novel and exciting teaching approach, challenging and rewarding tasks) (Halpern, 2001 ; Wei and Hong, 2022 ). Collaborative problem-solving as a teaching approach is exciting and interesting, as well as rewarding and challenging; because it takes the learners as the focus and examines problems with poor structure in real situations, and it can inspire students to fully realize their potential for problem-solving, which will significantly improve their attitudinal tendency toward solving problems (Liu et al., 2020 ). Similar to how collaborative problem-solving influences attitudinal tendency, attitudinal tendency impacts cognitive skill when attempting to solve a problem (Liu et al., 2020 ; Zhang et al., 2022 ), and stronger attitudinal tendencies are associated with improved learning achievement and cognitive ability in students (Sison, 2008 ; Zhang et al., 2022 ). It can be seen that the two specific dimensions of critical thinking as well as critical thinking as a whole are affected by collaborative problem-solving, and this study illuminates the nuanced links between cognitive skills and attitudinal tendencies with regard to these two dimensions of critical thinking. To fully develop students’ capacity for critical thinking, future empirical research should pay closer attention to cognitive skills.

The moderating effects of collaborative problem solving with regard to teaching critical thinking

In order to further explore the key factors that influence critical thinking, exploring possible moderating effects that might produce considerable heterogeneity was done using subgroup analysis. The findings show that the moderating factors, such as the teaching type, learning stage, group size, learning scaffold, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, could all support the cultivation of collaborative problem-solving in critical thinking. Among them, the effect size differences between the learning stage and measuring tool are not significant, which does not explain why these two factors are crucial in supporting the cultivation of critical thinking utilizing the approach of collaborative problem-solving.

In terms of the learning stage, various learning stages influenced critical thinking positively without significant intergroup differences, indicating that we are unable to explain why it is crucial in fostering the growth of critical thinking.

Although high education accounts for 70.89% of all empirical studies performed by researchers, high school may be the appropriate learning stage to foster students’ critical thinking by utilizing the approach of collaborative problem-solving since it has the largest overall effect size. This phenomenon may be related to student’s cognitive development, which needs to be further studied in follow-up research.

With regard to teaching type, mixed course teaching may be the best teaching method to cultivate students’ critical thinking. Relevant studies have shown that in the actual teaching process if students are trained in thinking methods alone, the methods they learn are isolated and divorced from subject knowledge, which is not conducive to their transfer of thinking methods; therefore, if students’ thinking is trained only in subject teaching without systematic method training, it is challenging to apply to real-world circumstances (Ruggiero, 2012 ; Hu and Liu, 2015 ). Teaching critical thinking as mixed course teaching in parallel to other subject teachings can achieve the best effect on learners’ critical thinking, and explicit critical thinking instruction is more effective than less explicit critical thinking instruction (Bensley and Spero, 2014 ).

In terms of the intervention duration, with longer intervention times, the overall effect size shows an upward tendency. Thus, the intervention duration and critical thinking’s impact are positively correlated. Critical thinking, as a key competency for students in the 21st century, is difficult to get a meaningful improvement in a brief intervention duration. Instead, it could be developed over a lengthy period of time through consistent teaching and the progressive accumulation of knowledge (Halpern, 2001 ; Hu and Liu, 2015 ). Therefore, future empirical studies ought to take these restrictions into account throughout a longer period of critical thinking instruction.

With regard to group size, a group size of 2–3 persons has the highest effect size, and the comprehensive effect size decreases with increasing group size in general. This outcome is in line with some research findings; as an example, a group composed of two to four members is most appropriate for collaborative learning (Schellens and Valcke, 2006 ). However, the meta-analysis results also indicate that once the group size exceeds 7 people, small groups cannot produce better interaction and performance than large groups. This may be because the learning scaffolds of technique support, resource support, and teacher support improve the frequency and effectiveness of interaction among group members, and a collaborative group with more members may increase the diversity of views, which is helpful to cultivate critical thinking utilizing the approach of collaborative problem-solving.

With regard to the learning scaffold, the three different kinds of learning scaffolds can all enhance critical thinking. Among them, the teacher-supported learning scaffold has the largest overall effect size, demonstrating the interdependence of effective learning scaffolds and collaborative problem-solving. This outcome is in line with some research findings; as an example, a successful strategy is to encourage learners to collaborate, come up with solutions, and develop critical thinking skills by using learning scaffolds (Reiser, 2004 ; Xu et al., 2022 ); learning scaffolds can lower task complexity and unpleasant feelings while also enticing students to engage in learning activities (Wood et al., 2006 ); learning scaffolds are designed to assist students in using learning approaches more successfully to adapt the collaborative problem-solving process, and the teacher-supported learning scaffolds have the greatest influence on critical thinking in this process because they are more targeted, informative, and timely (Xu et al., 2022 ).

With respect to the measuring tool, despite the fact that standardized measurement tools (such as the WGCTA, CCTT, and CCTST) have been acknowledged as trustworthy and effective by worldwide experts, only 54.43% of the research included in this meta-analysis adopted them for assessment, and the results indicated no intergroup differences. These results suggest that not all teaching circumstances are appropriate for measuring critical thinking using standardized measurement tools. “The measuring tools for measuring thinking ability have limits in assessing learners in educational situations and should be adapted appropriately to accurately assess the changes in learners’ critical thinking.”, according to Simpson and Courtney ( 2002 , p. 91). As a result, in order to more fully and precisely gauge how learners’ critical thinking has evolved, we must properly modify standardized measuring tools based on collaborative problem-solving learning contexts.

With regard to the subject area, the comprehensive effect size of science departments (e.g., mathematics, science, medical science) is larger than that of language arts and social sciences. Some recent international education reforms have noted that critical thinking is a basic part of scientific literacy. Students with scientific literacy can prove the rationality of their judgment according to accurate evidence and reasonable standards when they face challenges or poorly structured problems (Kyndt et al., 2013 ), which makes critical thinking crucial for developing scientific understanding and applying this understanding to practical problem solving for problems related to science, technology, and society (Yore et al., 2007 ).

Suggestions for critical thinking teaching

Other than those stated in the discussion above, the following suggestions are offered for critical thinking instruction utilizing the approach of collaborative problem-solving.

First, teachers should put a special emphasis on the two core elements, which are collaboration and problem-solving, to design real problems based on collaborative situations. This meta-analysis provides evidence to support the view that collaborative problem-solving has a strong synergistic effect on promoting students’ critical thinking. Asking questions about real situations and allowing learners to take part in critical discussions on real problems during class instruction are key ways to teach critical thinking rather than simply reading speculative articles without practice (Mulnix, 2012 ). Furthermore, the improvement of students’ critical thinking is realized through cognitive conflict with other learners in the problem situation (Yang et al., 2008 ). Consequently, it is essential for teachers to put a special emphasis on the two core elements, which are collaboration and problem-solving, and design real problems and encourage students to discuss, negotiate, and argue based on collaborative problem-solving situations.

Second, teachers should design and implement mixed courses to cultivate learners’ critical thinking, utilizing the approach of collaborative problem-solving. Critical thinking can be taught through curriculum instruction (Kuncel, 2011 ; Leng and Lu, 2020 ), with the goal of cultivating learners’ critical thinking for flexible transfer and application in real problem-solving situations. This meta-analysis shows that mixed course teaching has a highly substantial impact on the cultivation and promotion of learners’ critical thinking. Therefore, teachers should design and implement mixed course teaching with real collaborative problem-solving situations in combination with the knowledge content of specific disciplines in conventional teaching, teach methods and strategies of critical thinking based on poorly structured problems to help students master critical thinking, and provide practical activities in which students can interact with each other to develop knowledge construction and critical thinking utilizing the approach of collaborative problem-solving.

Third, teachers should be more trained in critical thinking, particularly preservice teachers, and they also should be conscious of the ways in which teachers’ support for learning scaffolds can promote critical thinking. The learning scaffold supported by teachers had the greatest impact on learners’ critical thinking, in addition to being more directive, targeted, and timely (Wood et al., 2006 ). Critical thinking can only be effectively taught when teachers recognize the significance of critical thinking for students’ growth and use the proper approaches while designing instructional activities (Forawi, 2016 ). Therefore, with the intention of enabling teachers to create learning scaffolds to cultivate learners’ critical thinking utilizing the approach of collaborative problem solving, it is essential to concentrate on the teacher-supported learning scaffolds and enhance the instruction for teaching critical thinking to teachers, especially preservice teachers.

Implications and limitations

There are certain limitations in this meta-analysis, but future research can correct them. First, the search languages were restricted to English and Chinese, so it is possible that pertinent studies that were written in other languages were overlooked, resulting in an inadequate number of articles for review. Second, these data provided by the included studies are partially missing, such as whether teachers were trained in the theory and practice of critical thinking, the average age and gender of learners, and the differences in critical thinking among learners of various ages and genders. Third, as is typical for review articles, more studies were released while this meta-analysis was being done; therefore, it had a time limit. With the development of relevant research, future studies focusing on these issues are highly relevant and needed.

Conclusions

The subject of the magnitude of collaborative problem-solving’s impact on fostering students’ critical thinking, which received scant attention from other studies, was successfully addressed by this study. The question of the effectiveness of collaborative problem-solving in promoting students’ critical thinking was addressed in this study, which addressed a topic that had gotten little attention in earlier research. The following conclusions can be made:

Regarding the results obtained, collaborative problem solving is an effective teaching approach to foster learners’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]). With respect to the dimensions of critical thinking, collaborative problem-solving can significantly and effectively improve students’ attitudinal tendency, and the comprehensive effect is significant (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

As demonstrated by both the results and the discussion, there are varying degrees of beneficial effects on students’ critical thinking from all seven moderating factors, which were found across 36 studies. In this context, the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have a positive impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. Since the learning stage (chi 2  = 3.15, P  = 0.21 > 0.05) and measuring tools (chi 2  = 0.08, P  = 0.78 > 0.05) did not demonstrate any significant intergroup differences, we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving.

Data availability

All data generated or analyzed during this study are included within the article and its supplementary information files, and the supplementary information files are available in the Dataverse repository: https://doi.org/10.7910/DVN/IPFJO6 .

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Acknowledgements

This research was supported by the graduate scientific research and innovation project of Xinjiang Uygur Autonomous Region named “Research on in-depth learning of high school information technology courses for the cultivation of computing thinking” (No. XJ2022G190) and the independent innovation fund project for doctoral students of the College of Educational Science of Xinjiang Normal University named “Research on project-based teaching of high school information technology courses from the perspective of discipline core literacy” (No. XJNUJKYA2003).

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Xu, E., Wang, W. & Wang, Q. The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature. Humanit Soc Sci Commun 10 , 16 (2023). https://doi.org/10.1057/s41599-023-01508-1

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Critical Thinking: A Model of Intelligence for Solving Real-World Problems

Diane f. halpern.

1 Department of Psychology, Claremont McKenna College, Emerita, Altadena, CA 91001, USA

Dana S. Dunn

2 Department of Psychology, Moravian College, Bethlehem, PA 18018, USA; ude.naivarom@nnud

Most theories of intelligence do not directly address the question of whether people with high intelligence can successfully solve real world problems. A high IQ is correlated with many important outcomes (e.g., academic prominence, reduced crime), but it does not protect against cognitive biases, partisan thinking, reactance, or confirmation bias, among others. There are several newer theories that directly address the question about solving real-world problems. Prominent among them is Sternberg’s adaptive intelligence with “adaptation to the environment” as the central premise, a construct that does not exist on standardized IQ tests. Similarly, some scholars argue that standardized tests of intelligence are not measures of rational thought—the sort of skill/ability that would be needed to address complex real-world problems. Other investigators advocate for critical thinking as a model of intelligence specifically designed for addressing real-world problems. Yes, intelligence (i.e., critical thinking) can be enhanced and used for solving a real-world problem such as COVID-19, which we use as an example of contemporary problems that need a new approach.

1. Introduction

The editors of this Special Issue asked authors to respond to a deceptively simple statement: “How Intelligence Can Be a Solution to Consequential World Problems.” This statement holds many complexities, including how intelligence is defined and which theories are designed to address real-world problems.

2. The Problem with Using Standardized IQ Measures for Real-World Problems

For the most part, we identify high intelligence as having a high score on a standardized test of intelligence. Like any test score, IQ can only reflect what is on the given test. Most contemporary standardized measures of intelligence include vocabulary, working memory, spatial skills, analogies, processing speed, and puzzle-like elements (e.g., Wechsler Adult Intelligence Scale Fourth Edition; see ( Drozdick et al. 2012 )). Measures of IQ correlate with many important outcomes, including academic performance ( Kretzschmar et al. 2016 ), job-related skills ( Hunter and Schmidt 1996 ), reduced likelihood of criminal behavior ( Burhan et al. 2014 ), and for those with exceptionally high IQs, obtaining a doctorate and publishing scholarly articles ( McCabe et al. 2020 ). Gottfredson ( 1997, p. 81 ) summarized these effects when she said the “predictive validity of g is ubiquitous.” More recent research using longitudinal data, found that general mental abilities and specific abilities are good predictors of several work variables including job prestige, and income ( Lang and Kell 2020 ). Although assessments of IQ are useful in many contexts, having a high IQ does not protect against falling for common cognitive fallacies (e.g., blind spot bias, reactance, anecdotal reasoning), relying on biased and blatantly one-sided information sources, failing to consider information that does not conform to one’s preferred view of reality (confirmation bias), resisting pressure to think and act in a certain way, among others. This point was clearly articulated by Stanovich ( 2009, p. 3 ) when he stated that,” IQ tests measure only a small set of the thinking abilities that people need.”

3. Which Theories of Intelligence Are Relevant to the Question?

Most theories of intelligence do not directly address the question of whether people with high intelligence can successfully solve real world problems. For example, Grossmann et al. ( 2013 ) cite many studies in which IQ scores have not predicted well-being, including life satisfaction and longevity. Using a stratified random sample of Americans, these investigators found that wise reasoning is associated with life satisfaction, and that “there was no association between intelligence and well-being” (p. 944). (critical thinking [CT] is often referred to as “wise reasoning” or “rational thinking,”). Similar results were reported by Wirthwein and Rost ( 2011 ) who compared life satisfaction in several domains for gifted adults and adults of average intelligence. There were no differences in any of the measures of subjective well-being, except for leisure, which was significantly lower for the gifted adults. Additional research in a series of experiments by Stanovich and West ( 2008 ) found that participants with high cognitive ability were as likely as others to endorse positions that are consistent with their biases, and they were equally likely to prefer one-sided arguments over those that provided a balanced argument. There are several newer theories that directly address the question about solving real-world problems. Prominent among them is Sternberg’s adaptive intelligence with “adaptation to the environment” as the central premise, a construct that does not exist on standardized IQ tests (e.g., Sternberg 2019 ). Similarly, Stanovich and West ( 2014 ) argue that standardized tests of intelligence are not measures of rational thought—the sort of skill/ability that would be needed to address complex real-world problems. Halpern and Butler ( 2020 ) advocate for CT as a useful model of intelligence for addressing real-world problems because it was designed for this purpose. Although there is much overlap among these more recent theories, often using different terms for similar concepts, we use Halpern and Butler’s conceptualization to make our point: Yes, intelligence (i.e., CT) can be enhanced and used for solving a real-world problem like COVID-19.

4. Critical Thinking as an Applied Model for Intelligence

One definition of intelligence that directly addresses the question about intelligence and real-world problem solving comes from Nickerson ( 2020, p. 205 ): “the ability to learn, to reason well, to solve novel problems, and to deal effectively with novel problems—often unpredictable—that confront one in daily life.” Using this definition, the question of whether intelligent thinking can solve a world problem like the novel coronavirus is a resounding “yes” because solutions to real-world novel problems are part of his definition. This is a popular idea in the general public. For example, over 1000 business managers and hiring executives said that they want employees who can think critically based on the belief that CT skills will help them solve work-related problems ( Hart Research Associates 2018 ).

We define CT as the use of those cognitive skills or strategies that increase the probability of a desirable outcome. It is used to describe thinking that is purposeful, reasoned, and goal directed--the kind of thinking involved in solving problems, formulating inferences, calculating likelihoods, and making decisions, when the thinker is using skills that are thoughtful and effective for the particular context and type of thinking task. International surveys conducted by the OECD ( 2019, p. 16 ) established “key information-processing competencies” that are “highly transferable, in that they are relevant to many social contexts and work situations; and ‘learnable’ and therefore subject to the influence of policy.” One of these skills is problem solving, which is one subset of CT skills.

The CT model of intelligence is comprised of two components: (1) understanding information at a deep, meaningful level and (2) appropriate use of CT skills. The underlying idea is that CT skills can be identified, taught, and learned, and when they are recognized and applied in novel settings, the individual is demonstrating intelligent thought. CT skills include judging the credibility of an information source, making cost–benefit calculations, recognizing regression to the mean, understanding the limits of extrapolation, muting reactance responses, using analogical reasoning, rating the strength of reasons that support and fail to support a conclusion, and recognizing hindsight bias or confirmation bias, among others. Critical thinkers use these skills appropriately, without prompting, and usually with conscious intent in a variety of settings.

One of the key concepts in this model is that CT skills transfer in appropriate situations. Thus, assessments using situational judgments are needed to assess whether particular skills have transferred to a novel situation where it is appropriate. In an assessment created by the first author ( Halpern 2018 ), short paragraphs provide information about 20 different everyday scenarios (e.g., A speaker at the meeting of your local school board reported that when drug use rises, grades decline; so schools need to enforce a “war on drugs” to improve student grades); participants provide two response formats for every scenario: (a) constructed responses where they respond with short written responses, followed by (b) forced choice responses (e.g., multiple choice, rating or ranking of alternatives) for the same situations.

There is a large and growing empirical literature to support the assertion that CT skills can be learned and will transfer (when taught for transfer). See for example, Holmes et al. ( 2015 ), who wrote in the prestigious Proceedings of the National Academy of Sciences , that there was “significant and sustained improvement in students’ critical thinking behavior” (p. 11,199) for students who received CT instruction. Abrami et al. ( 2015, para. 1 ) concluded from a meta-analysis that “there are effective strategies for teaching CT skills, both generic and content specific, and CT dispositions, at all educational levels and across all disciplinary areas.” Abrami et al. ( 2008, para. 1 ), included 341 effect sizes in a meta-analysis. They wrote: “findings make it clear that improvement in students’ CT skills and dispositions cannot be a matter of implicit expectation.” A strong test of whether CT skills can be used for real-word problems comes from research by Butler et al. ( 2017 ). Community adults and college students (N = 244) completed several scales including an assessment of CT, an intelligence test, and an inventory of real-life events. Both CT scores and intelligence scores predicted individual outcomes on the inventory of real-life events, but CT was a stronger predictor.

Heijltjes et al. ( 2015, p. 487 ) randomly assigned participants to either a CT instruction group or one of six other control conditions. They found that “only participants assigned to CT instruction improved their reasoning skills.” Similarly, when Halpern et al. ( 2012 ) used random assignment of participants to either a learning group where they were taught scientific reasoning skills using a game format or a control condition (which also used computerized learning and was similar in length), participants in the scientific skills learning group showed higher proportional learning gains than students who did not play the game. As the body of additional supportive research is too large to report here, interested readers can find additional lists of CT skills and support for the assertion that these skills can be learned and will transfer in Halpern and Dunn ( Forthcoming ). There is a clear need for more high-quality research on the application and transfer of CT and its relationship to IQ.

5. Pandemics: COVID-19 as a Consequential Real-World Problem

A pandemic occurs when a disease runs rampant over an entire country or even the world. Pandemics have occurred throughout history: At the time of writing this article, COVID-19 is a world-wide pandemic whose actual death rate is unknown but estimated with projections of several million over the course of 2021 and beyond ( Mega 2020 ). Although vaccines are available, it will take some time to inoculate most or much of the world’s population. Since March 2020, national and international health agencies have created a list of actions that can slow and hopefully stop the spread of COVID (e.g., wearing face masks, practicing social distancing, avoiding group gatherings), yet many people in the United States and other countries have resisted their advice.

Could instruction in CT encourage more people to accept and comply with simple life-saving measures? There are many possible reasons to believe that by increasing citizens’ CT abilities, this problematic trend can be reversed for, at least, some unknown percentage of the population. We recognize the long history of social and cognitive research showing that changing attitudes and behaviors is difficult, and it would be unrealistic to expect that individuals with extreme beliefs supported by their social group and consistent with their political ideologies are likely to change. For example, an Iranian cleric and an orthodox rabbi both claimed (separately) that the COVID-19 vaccine can make people gay ( Marr 2021 ). These unfounded opinions are based on deeply held prejudicial beliefs that we expect to be resistant to CT. We are targeting those individuals who beliefs are less extreme and may be based on reasonable reservations, such as concern about the hasty development of the vaccine and the lack of long-term data on its effects. There should be some unknown proportion of individuals who can change their COVID-19-related beliefs and actions with appropriate instruction in CT. CT can be a (partial) antidote for the chaos of the modern world with armies of bots creating content on social media, political and other forces deliberately attempting to confuse issues, and almost all media labeled “fake news” by social influencers (i.e., people with followers that sometimes run to millions on various social media). Here, are some CT skills that could be helpful in getting more people to think more critically about pandemic-related issues.

Reasoning by Analogy and Judging the Credibility of the Source of Information

Early communications about the ability of masks to prevent the spread of COVID from national health agencies were not consistent. In many regions of the world, the benefits of wearing masks incited prolonged and acrimonious debates ( Tang 2020 ). However, after the initial confusion, virtually all of the global and national health organizations (e.g., WHO, National Health Service in the U. K., U. S. Centers for Disease Control and Prevention) endorse masks as a way to slow the spread of COVID ( Cheng et al. 2020 ; Chu et al. 2020 ). However, as we know, some people do not trust governmental agencies and often cite the conflicting information that was originally given as a reason for not wearing a mask. There are varied reasons for refusing to wear a mask, but the one most often cited is that it is against civil liberties ( Smith 2020 ). Reasoning by analogy is an appropriate CT skill for evaluating this belief (and a key skill in legal thinking). It might be useful to cite some of the many laws that already regulate our behavior such as, requiring health inspections for restaurants, setting speed limits, mandating seat belts when riding in a car, and establishing the age at which someone can consume alcohol. Individuals would be asked to consider how the mandate to wear a mask compares to these and other regulatory laws.

Another reason why some people resist the measures suggested by virtually every health agency concerns questions about whom to believe. Could training in CT change the beliefs and actions of even a small percentage of those opposed to wearing masks? Such training would include considering the following questions with practice across a wide domain of knowledge: (a) Does the source have sufficient expertise? (b) Is the expertise recent and relevant? (c) Is there a potential for gain by the information source, such as financial gain? (d) What would the ideal information source be and how close is the current source to the ideal? (e) Does the information source offer evidence that what they are recommending is likely to be correct? (f) Have you traced URLs to determine if the information in front of you really came from the alleged source?, etc. Of course, not everyone will respond in the same way to each question, so there is little likelihood that we would all think alike, but these questions provide a framework for evaluating credibility. Donovan et al. ( 2015 ) were successful using a similar approach to improve dynamic decision-making by asking participants to reflect on questions that relate to the decision. Imagine the effect of rigorous large-scale education in CT from elementary through secondary schools, as well as at the university-level. As stated above, empirical evidence has shown that people can become better thinkers with appropriate instruction in CT. With training, could we encourage some portion of the population to become more astute at judging the credibility of a source of information? It is an experiment worth trying.

6. Making Cost—Benefit Assessments for Actions That Would Slow the Spread of COVID-19

Historical records show that refusal to wear a mask during a pandemic is not a new reaction. The epidemic of 1918 also included mandates to wear masks, which drew public backlash. Then, as now, many people refused, even when they were told that it was a symbol of “wartime patriotism” because the 1918 pandemic occurred during World War I ( Lovelace 2020 ). CT instruction would include instruction in why and how to compute cost–benefit analyses. Estimates of “lives saved” by wearing a mask can be made meaningful with graphical displays that allow more people to understand large numbers. Gigerenzer ( 2020 ) found that people can understand risk ratios in medicine when the numbers are presented as frequencies instead of probabilities. If this information were used when presenting the likelihood of illness and death from COVID-19, could we increase the numbers of people who understand the severity of this disease? Small scale studies by Gigerenzer have shown that it is possible.

Analyzing Arguments to Determine Degree of Support for a Conclusion

The process of analyzing arguments requires that individuals rate the strength of support for and against a conclusion. By engaging in this practice, they must consider evidence and reasoning that may run counter to a preferred outcome. Kozyreva et al. ( 2020 ) call the deliberate failure to consider both supporting and conflicting data “deliberate ignorance”—avoiding or failing to consider information that could be useful in decision-making because it may collide with an existing belief. When applied to COVID-19, people would have to decide if the evidence for and against wearing a face mask is a reasonable way to stop the spread of this disease, and if they conclude that it is not, what are the costs and benefits of not wearing masks at a time when governmental health organizations are making them mandatory in public spaces? Again, we wonder if rigorous and systematic instruction in argument analysis would result in more positive attitudes and behaviors that relate to wearing a mask or other real-world problems. We believe that it is an experiment worth doing.

7. Conclusions

We believe that teaching CT is a worthwhile approach for educating the general public in order to improve reasoning and motivate actions to address, avert, or ameliorate real-world problems like the COVID-19 pandemic. Evidence suggests that CT can guide intelligent responses to societal and global problems. We are NOT claiming that CT skills will be a universal solution for the many real-world problems that we confront in contemporary society, or that everyone will substitute CT for other decision-making practices, but we do believe that systematic education in CT can help many people become better thinkers, and we believe that this is an important step toward creating a society that values and practices routine CT. The challenges are great, but the tools to tackle them are available, if we are willing to use them.

Author Contributions

Conceptualization, D.F.H. and D.S.D.; resources, D.F.H.; data curation, writing—original draft preparation, D.F.H.; writing—review and editing, D.F.H. and D.S.D. All authors have read and agreed to the published version of the manuscript.

This research received no external funding.

Institutional Review Board Statement

No IRB Review.

Informed Consent Statement

No Informed Consent.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Scientific Literacy and Critical Thinking Skills: Nurturing a Better Future

Scientific literacy and critical thinking are essential components of a well-rounded education, preparing students to better understand the world we live in and make informed decisions. As science and technology continue to advance and impact various aspects of our lives, it is increasingly important for individuals to develop the ability to think critically about scientific information, fostering a deeper understanding of the implications and consequences of such advancements. By fostering scientific literacy, students become equipped with the knowledge and skills to actively engage with science-related issues in a responsible and informed manner.

Focusing on scientific literacy and critical thinking in education prepares students for a world where science and technology play a pivotal role across numerous fields. By cultivating these capacities, students will be better prepared to face complex issues and tasks, contribute positively to society, and pave the way for continued advancements and innovations.

Key Concepts and Principles

Science education foundations, metacognition and reflection.

Metacognition, or the process of thinking about one’s own thinking, plays a crucial role in fostering critical thinking skills in science education. Cambridge highlights key steps in the critical thinking process, which include:

In summary, a well-rounded science education places emphasis on the development of scientific literacy and critical thinking skills, based on a strong foundation in core concepts and knowledge. Incorporating metacognitive strategies and promoting reflection throughout the learning process further enhances these skills, equipping students for success in their future scientific endeavors. Remember to maintain a confident, knowledgeable, neutral, and clear tone of voice when discussing these topics.

Curriculum and Pedagogy

Teaching and learning approaches, incorporating argumentation and experimentation.

By incorporating these teaching and learning approaches, as well as focusing on argumentation and experimentation, educators can effectively promote scientific literacy and critical thinking skills in their curriculum and pedagogy.

Assessing Scientific Literacy and Critical Thinking Skills

Test instruments and procedures.

The TOSLS is a multiple-choice test that allows educators to evaluate students’ understanding of scientific reasoning and their ability to apply scientific concepts in real-life situations.

International Comparisons

Factors influencing performance and motivation, role of gender in physics education.

Research indicates that gender plays a significant role in students’ performance and motivation in physics education. Male and female students exhibit different levels of interest and confidence in the subject, which impact their academic achievements. A correlational study found a positive relationship between critical thinking skills and scientific literacy in both genders but did not identify any significant correlation between gender and these skills.

Decision Making and Problem-Solving

Scientific literacy in everyday life, interpreting news reports.

For example, when encountering a news report about a new health study, it is essential to consider sample size, research methodology, and potential conflicts of interest among the researchers. A clear understanding of these factors can help prevent the spread of misinformation and promote informed decision-making.

Understanding and Evaluating Scientific Facts

For instance, the recognition that the Earth revolves around the Sun is a fact, while the theory of evolution provides a comprehensive explanation of the origin and development of species. Developing the ability to analyze and contextualize scientific information is crucial for forming well-grounded opinions and engaging in informed discussions.

Future Research Agenda

One of the key issues to address within this agenda is the relationship between science knowledge and attitudes toward science. This includes assessing whether a significant correlation exists between improved scientific understanding and more positive attitudes towards the scientific method and scientific discovery. Gaining insights into this aspect will help guide the development of educational resources and methodologies to foster a more science-minded society.

Furthermore, emphasizing the role of scientific literacy for citizens as decision-makers is crucial. It is important to examine how improved scientific literacy influences students’ capacities to evaluate information, engage in public discourse, and make informed choices on matters that involve scientific data or principles.

Frequently Asked Questions

What are the benefits of having scientific literacy and critical thinking skills.

Scientific literacy and critical thinking skills are essential for individuals to understand the world around them and make informed decisions. These skills enable people to differentiate science from pseudoscience and evaluate the credibility of information. Moreover, scientifically literate citizens are better equipped to participate in important societal discussions and contribute to policy-making processes.

How can educators effectively teach scientific literacy and critical thinking skills?

What role does digital literacy play in promoting scientific literacy and critical thinking, how do life and career skills relate to scientific literacy and critical thinking.

Life and career skills, such as communication, problem solving, and adaptability, are intertwined with scientific literacy and critical thinking. These abilities are crucial in equipping individuals to face real-world challenges and make informed decisions in various fields, from science and technology to business and government. An understanding of scientific principles and the ability to think critically foster the development of crucial life and career skills that are increasingly sought-after in today’s world.

What’s the connection between problem-solving skills and scientific literacy?

How can reflective practice enhance critical thinking in science, you may also like, elements of scientific thinking: a guide to effective inquiry.

Scientific Thinking and Research: Essential Guide to Methodological Approaches

Scientific thinking examples: a comprehensive guide for practical application, best books on the scientific thinking method: your ultimate guide, download this free ebook.

How to use scientific thinking to demystify complexity

Transforming assumptions into solutions, using data and evidence

Written by Working Voices • 9 February 2023

Future Skills

Scientific thinking is a secret card up your sleeve, it worked for Einstein, Curie and Hawking, and it can help you too. You don’t have to be a scientist but sometimes it helps to think like one. How do scientists think? By making an assumption, testing it against data and evidence, updating their opinion and coming to a conclusion. A cornerstone of future skills , scientific thinking is about thoughtful decision-making, it’s a step-by-step process and it’s easy to learn. 

What is scientific thinking?

Scientific thinking is the ability – or actually the habit – of thinking like a scientist. It’s what distinguishes the genuine expert on any subject from someone with only a shallow familiarity based on a couple of data points and some jargon.

Flawed assumptions made too quickly can have long-lasting effects. It’s important to keep an open mind so that when you find new data you can revise your assumption. This process of updating your beliefs based on new information is key to scientific thinking. Conclusions supported by evidence lead to rational decisions that encourage other people to trust your opinion. Scientific thinking strengthens your credibility, trustworthiness, and authority.

Deanna Kuhn, of the Teachers College at Columbia University, connects scientific thinking to argumentative thinking , where evidence is relied on in persuading others of the validity of your argument.

Kuhn defines scientific thinking as a “specific reasoning strategy”, in other words purposeful thinking that can be best thought of as “knowledge seeking”. It’s not about science itself, or even scientific aptitude. Scientific thinking is something people do , not something they have . It relies on the kind of rigorous, evidence-based thinking that is essential to science, but not specific to it. For these reasons, scientific thinking is engaged in by most people rather than a rarefied few.

Key elements of scientific thinking

Sometimes, you can face a situation that might seem like a rush of complexity and frenzy. For example – your sales may show an unexpected dip that can’t be immediately explained. Early assumptions might point to a downturn in internal performance, but perhaps there’s more to it than that. To manage complexity, it helps to build solid points of understanding, each refining your assumption and leading you through the problem, like stepping-stones across a river.

Stepping from one point to the next, you start with an assumption, then challenge this with early information. This helps you revise your assumption. Additional data takes you a step further – transforming your assumption into a stronger conclusion. Getting through complexity by taking one careful step at a time is a better bet than leaping to a wobbly assumption that might strand you in deep water.

Scientific thinking skills

Astronomer Moiya McTier offers three simple steps, which we’ve paraphrased here:

1) Learn to distinguish between observables and assumptions

The brain uses automatic assumptions (heuristics) to get from observation to action as quickly as possible. When we look out of the window and see blue sky and sunshine, we assume it’s warm. On questioning this assumption, by stepping outside, we actually find it’s cold. That’s why in business we need to verify our natural assumptions: Do you know the client is happy with your product, or are you assuming so based on their buying record? Avoid mistakes, by asking good questions.

2) Be guided by your questions, rather than your task

Scientists take things slowly, only moving to the next step when they’re sure of the last. The rest of us tend to gallop towards achieving the task. If the numbers are down on last year, and the task is to improve them, then maybe we need to sell more products? Better, however, to ask questions each step of the way. Why were the numbers down? Let’s answer that before racing towards a remedy.

3) For every question, create a working hypothesis

Having focused on a question, how will you know when you’ve answered it? Scientists form assumptions (hypotheses), giving them a direction to go in. If their findings match their hypothesis, they’re on the right track. If not, they need to revise their ideas, and ask new questions. In everyday life, we also use hypotheses all the time, but rarely voice them. They lie hidden in a lot of discussions. For example, someone asserts that sales are up 20% but profits only up 5%, indicating that we need to cut costs. Maybe. But the hidden hypothesis is that the disappointing profitability is caused by inefficiency. It may be. Or maybe the increased sales are of products with a lower profit margin. In that case, the problem – if there is one – is more complex.  Finding efficiencies might be the way forward but it’s not the whole story.

Scientific thinking examples

Beware – the brain craves clarity and will try to interpret something as 100% likely or 0% likely. And in the same way, it rather primitively divides scenarios into two groups: complex = no meaningful action possible; simple = let’s fix it now! We are biased to seek out simplistic explanations that open the gates to action. This urge is best restrained by asking more questions and reshaping your hypothesis. By rigorously and accurately finding causes, you’re more likely to adopt appropriate reactions.

Being cautious is less fun than getting excited about a promising idea. So we can be too quick to latch on to something that sounds good. Likewise, we can be too slow to let go of what we’re attached to. When new evidence contradicts existing beliefs, a defensive reaction is triggered in the brain. Think of it like an immune system: the brain rejects and attacks information that would disrupt our model of the world.

In the example earlier, the concerns about sales led to early assumptions about internal performance. If however the data shows that your sales team are meeting KPIs, the problem may need more investigation. New evidence may point to the fact that clients’ budgets are shrinking in the face of uncertain economic data.

The objective of a scientific approach is to develop interpretations of information that are accurate enough for leaders to rely on when deciding on a course of action. Pursuing the process in search of definitive proof is likely to be an impossible task, nor is it necessary. Instead, what leaders principally need is reasonable grounds for action.

Types of scientific thinking

We’ve seen that scientific thinking is a useful skill in managing specific complex questions. Once mastered as a habit however, scientific thinking can continuously play a background role in helping us manage routine aspects of daily life.

In particular, the deluge of content and data we experience in our digital lives, at home and at work, can be overwhelming. It’s deliberately attention-grabbing, seeking to persuade us to buy into its messaging, often literally.

Similarly, in the relentless pace of modern work, decisions are made at full tilt with the picture changing in real time. An ability to swiftly assess the evidence, data and analysis we’re served up is pivotal.

We don’t always have the time and space needed to step back and think, but going with the flow leaves us open to influence. Did you know, for example, that when Facebook switched its message alert (the tiny circle at the corner of the icon that tells you how many messages are waiting for you) from blue to red, engagement rocketed: the colour change triggered a decision to check the messages?

Marketing, media and PR professionals know how to influence our thoughts and behaviour in a thousand tiny ways. And every designer of websites and pitch books uses multiple micro-prompts to smooth the reader’s path towards a decision.

Even if you are not in those influencing professions, you yourself probably do your best to use those methods. The reports and presentations you put together are designed to persuade – not just inform. It would be a great compliment to be told that you’d delivered a ‘compelling’ presentation, but let’s stop and think what that means: to ‘compel’ is to force, to give someone no choice but to believe.

So, there is a lot more compelling data around than there used to be and to resist its appeal – and keep as objective as possible – we need to activate our critical faculties. That’s what scientific thinking can do for us.

How to develop scientific thinking?

With practice. The first few times we put the brakes on, step back, and review our thinking process, it will feel ponderous and pedantic. After all, the way we were thinking was probably fine; our intuition about the solution was probably as good as any other problem-solving process. But once scientific thinking becomes habitual, we can do it on the run, which is how we have to do most things these days.

At Working Voices, our range of courses in future skills will help you keep a competitive edge in the uncertain years ahead. In particular, our course on scientific thinking focuses on keeping an open mind in using new data to revise early assumptions. We don’t all need to be scientists. But by habitually relying on the ability to revise interpretations, we can make the informed decisions that will demystify complexity and give us a direction to go in.

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7 Module 7: Thinking, Reasoning, and Problem-Solving

This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure out the solution to many problems, because you feel capable of using logic to argue a point, because you can evaluate whether the things you read and hear make sense—you do not need any special training in thinking. But this, of course, is one of the key barriers to helping people think better. If you do not believe that there is anything wrong, why try to fix it?

The human brain is indeed a remarkable thinking machine, capable of amazing, complex, creative, logical thoughts. Why, then, are we telling you that you need to learn how to think? Mainly because one major lesson from cognitive psychology is that these capabilities of the human brain are relatively infrequently realized. Many psychologists believe that people are essentially “cognitive misers.” It is not that we are lazy, but that we have a tendency to expend the least amount of mental effort necessary. Although you may not realize it, it actually takes a great deal of energy to think. Careful, deliberative reasoning and critical thinking are very difficult. Because we seem to be successful without going to the trouble of using these skills well, it feels unnecessary to develop them. As you shall see, however, there are many pitfalls in the cognitive processes described in this module. When people do not devote extra effort to learning and improving reasoning, problem solving, and critical thinking skills, they make many errors.

As is true for memory, if you develop the cognitive skills presented in this module, you will be more successful in school. It is important that you realize, however, that these skills will help you far beyond school, even more so than a good memory will. Although it is somewhat useful to have a good memory, ten years from now no potential employer will care how many questions you got right on multiple choice exams during college. All of them will, however, recognize whether you are a logical, analytical, critical thinker. With these thinking skills, you will be an effective, persuasive communicator and an excellent problem solver.

The module begins by describing different kinds of thought and knowledge, especially conceptual knowledge and critical thinking. An understanding of these differences will be valuable as you progress through school and encounter different assignments that require you to tap into different kinds of knowledge. The second section covers deductive and inductive reasoning, which are processes we use to construct and evaluate strong arguments. They are essential skills to have whenever you are trying to persuade someone (including yourself) of some point, or to respond to someone’s efforts to persuade you. The module ends with a section about problem solving. A solid understanding of the key processes involved in problem solving will help you to handle many daily challenges.

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

By reading and studying Module 7, you should be able to remember and describe:

• Concepts and inferences (7.1)
• Procedural knowledge (7.1)
• Metacognition (7.1)
• Characteristics of critical thinking:  skepticism; identify biases, distortions, omissions, and assumptions; reasoning and problem solving skills  (7.1)
• Reasoning:  deductive reasoning, deductively valid argument, inductive reasoning, inductively strong argument, availability heuristic, representativeness heuristic  (7.2)
• Fixation:  functional fixedness, mental set  (7.3)
• Algorithms, heuristics, and the role of confirmation bias (7.3)
• Effective problem solving sequence (7.3)

By reading and thinking about how the concepts in Module 6 apply to real life, you should be able to:

• Identify which type of knowledge a piece of information is (7.1)
• Recognize examples of deductive and inductive reasoning (7.2)
• Recognize judgments that have probably been influenced by the availability heuristic (7.2)
• Recognize examples of problem solving heuristics and algorithms (7.3)

Analyze, Evaluate, and Create

By reading and thinking about Module 6, participating in classroom activities, and completing out-of-class assignments, you should be able to:

• Use the principles of critical thinking to evaluate information (7.1)
• Explain whether examples of reasoning arguments are deductively valid or inductively strong (7.2)
• Outline how you could try to solve a problem from your life using the effective problem solving sequence (7.3)

7.1. Different kinds of thought and knowledge

• Take a few minutes to write down everything that you know about dogs.
• Do you believe that:
• Psychic ability exists?
• Hypnosis is an altered state of consciousness?
• Magnet therapy is effective for relieving pain?
• Aerobic exercise is an effective treatment for depression?
• UFO’s from outer space have visited earth?

On what do you base your belief or disbelief for the questions above?

Of course, we all know what is meant by the words  think  and  knowledge . You probably also realize that they are not unitary concepts; there are different kinds of thought and knowledge. In this section, let us look at some of these differences. If you are familiar with these different kinds of thought and pay attention to them in your classes, it will help you to focus on the right goals, learn more effectively, and succeed in school. Different assignments and requirements in school call on you to use different kinds of knowledge or thought, so it will be very helpful for you to learn to recognize them (Anderson, et al. 2001).

Factual and conceptual knowledge

Module 5 introduced the idea of declarative memory, which is composed of facts and episodes. If you have ever played a trivia game or watched Jeopardy on TV, you realize that the human brain is able to hold an extraordinary number of facts. Likewise, you realize that each of us has an enormous store of episodes, essentially facts about events that happened in our own lives. It may be difficult to keep that in mind when we are struggling to retrieve one of those facts while taking an exam, however. Part of the problem is that, in contradiction to the advice from Module 5, many students continue to try to memorize course material as a series of unrelated facts (picture a history student simply trying to memorize history as a set of unrelated dates without any coherent story tying them together). Facts in the real world are not random and unorganized, however. It is the way that they are organized that constitutes a second key kind of knowledge, conceptual.

Concepts are nothing more than our mental representations of categories of things in the world. For example, think about dogs. When you do this, you might remember specific facts about dogs, such as they have fur and they bark. You may also recall dogs that you have encountered and picture them in your mind. All of this information (and more) makes up your concept of dog. You can have concepts of simple categories (e.g., triangle), complex categories (e.g., small dogs that sleep all day, eat out of the garbage, and bark at leaves), kinds of people (e.g., psychology professors), events (e.g., birthday parties), and abstract ideas (e.g., justice). Gregory Murphy (2002) refers to concepts as the “glue that holds our mental life together” (p. 1). Very simply, summarizing the world by using concepts is one of the most important cognitive tasks that we do. Our conceptual knowledge  is  our knowledge about the world. Individual concepts are related to each other to form a rich interconnected network of knowledge. For example, think about how the following concepts might be related to each other: dog, pet, play, Frisbee, chew toy, shoe. Or, of more obvious use to you now, how these concepts are related: working memory, long-term memory, declarative memory, procedural memory, and rehearsal? Because our minds have a natural tendency to organize information conceptually, when students try to remember course material as isolated facts, they are working against their strengths.

One last important point about concepts is that they allow you to instantly know a great deal of information about something. For example, if someone hands you a small red object and says, “here is an apple,” they do not have to tell you, “it is something you can eat.” You already know that you can eat it because it is true by virtue of the fact that the object is an apple; this is called drawing an  inference , assuming that something is true on the basis of your previous knowledge (for example, of category membership or of how the world works) or logical reasoning.

Procedural knowledge

Physical skills, such as tying your shoes, doing a cartwheel, and driving a car (or doing all three at the same time, but don’t try this at home) are certainly a kind of knowledge. They are procedural knowledge, the same idea as procedural memory that you saw in Module 5. Mental skills, such as reading, debating, and planning a psychology experiment, are procedural knowledge, as well. In short, procedural knowledge is the knowledge how to do something (Cohen & Eichenbaum, 1993).

Metacognitive knowledge

Floyd used to think that he had a great memory. Now, he has a better memory. Why? Because he finally realized that his memory was not as great as he once thought it was. Because Floyd eventually learned that he often forgets where he put things, he finally developed the habit of putting things in the same place. (Unfortunately, he did not learn this lesson before losing at least 5 watches and a wedding ring.) Because he finally realized that he often forgets to do things, he finally started using the To Do list app on his phone. And so on. Floyd’s insights about the real limitations of his memory have allowed him to remember things that he used to forget.

All of us have knowledge about the way our own minds work. You may know that you have a good memory for people’s names and a poor memory for math formulas. Someone else might realize that they have difficulty remembering to do things, like stopping at the store on the way home. Others still know that they tend to overlook details. This knowledge about our own thinking is actually quite important; it is called metacognitive knowledge, or  metacognition . Like other kinds of thinking skills, it is subject to error. For example, in unpublished research, one of the authors surveyed about 120 General Psychology students on the first day of the term. Among other questions, the students were asked them to predict their grade in the class and report their current Grade Point Average. Two-thirds of the students predicted that their grade in the course would be higher than their GPA. (The reality is that at our college, students tend to earn lower grades in psychology than their overall GPA.) Another example: Students routinely report that they thought they had done well on an exam, only to discover, to their dismay, that they were wrong (more on that important problem in a moment). Both errors reveal a breakdown in metacognition.

The Dunning-Kruger Effect

In general, most college students probably do not study enough. For example, using data from the National Survey of Student Engagement, Fosnacht, McCormack, and Lerma (2018) reported that first-year students at 4-year colleges in the U.S. averaged less than 14 hours per week preparing for classes. The typical suggestion is that you should spend two hours outside of class for every hour in class, or 24 – 30 hours per week for a full-time student. Clearly, students in general are nowhere near that recommended mark. Many observers, including some faculty, believe that this shortfall is a result of students being too busy or lazy. Now, it may be true that many students are too busy, with work and family obligations, for example. Others, are not particularly motivated in school, and therefore might correctly be labeled lazy. A third possible explanation, however, is that some students might not think they need to spend this much time. And this is a matter of metacognition. Consider the scenario that we mentioned above, students thinking they had done well on an exam only to discover that they did not. Justin Kruger and David Dunning examined scenarios very much like this in 1999. Kruger and Dunning gave research participants tests measuring humor, logic, and grammar. Then, they asked the participants to assess their own abilities and test performance in these areas. They found that participants in general tended to overestimate their abilities, already a problem with metacognition. Importantly, the participants who scored the lowest overestimated their abilities the most. Specifically, students who scored in the bottom quarter (averaging in the 12th percentile) thought they had scored in the 62nd percentile. This has become known as the  Dunning-Kruger effect . Many individual faculty members have replicated these results with their own student on their course exams, including the authors of this book. Think about it. Some students who just took an exam and performed poorly believe that they did well before seeing their score. It seems very likely that these are the very same students who stopped studying the night before because they thought they were “done.” Quite simply, it is not just that they did not know the material. They did not know that they did not know the material. That is poor metacognition.

In order to develop good metacognitive skills, you should continually monitor your thinking and seek frequent feedback on the accuracy of your thinking (Medina, Castleberry, & Persky 2017). For example, in classes get in the habit of predicting your exam grades. As soon as possible after taking an exam, try to find out which questions you missed and try to figure out why. If you do this soon enough, you may be able to recall the way it felt when you originally answered the question. Did you feel confident that you had answered the question correctly? Then you have just discovered an opportunity to improve your metacognition. Be on the lookout for that feeling and respond with caution.

concept :  a mental representation of a category of things in the world

Dunning-Kruger effect : individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

inference : an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

metacognition :  knowledge about one’s own cognitive processes; thinking about your thinking

Critical thinking

One particular kind of knowledge or thinking skill that is related to metacognition is  critical thinking (Chew, 2020). You may have noticed that critical thinking is an objective in many college courses, and thus it could be a legitimate topic to cover in nearly any college course. It is particularly appropriate in psychology, however. As the science of (behavior and) mental processes, psychology is obviously well suited to be the discipline through which you should be introduced to this important way of thinking.

More importantly, there is a particular need to use critical thinking in psychology. We are all, in a way, experts in human behavior and mental processes, having engaged in them literally since birth. Thus, perhaps more than in any other class, students typically approach psychology with very clear ideas and opinions about its subject matter. That is, students already “know” a lot about psychology. The problem is, “it ain’t so much the things we don’t know that get us into trouble. It’s the things we know that just ain’t so” (Ward, quoted in Gilovich 1991). Indeed, many of students’ preconceptions about psychology are just plain wrong. Randolph Smith (2002) wrote a book about critical thinking in psychology called  Challenging Your Preconceptions,  highlighting this fact. On the other hand, many of students’ preconceptions about psychology are just plain right! But wait, how do you know which of your preconceptions are right and which are wrong? And when you come across a research finding or theory in this class that contradicts your preconceptions, what will you do? Will you stick to your original idea, discounting the information from the class? Will you immediately change your mind? Critical thinking can help us sort through this confusing mess.

But what is critical thinking? The goal of critical thinking is simple to state (but extraordinarily difficult to achieve): it is to be right, to draw the correct conclusions, to believe in things that are true and to disbelieve things that are false. We will provide two definitions of critical thinking (or, if you like, one large definition with two distinct parts). First, a more conceptual one: Critical thinking is thinking like a scientist in your everyday life (Schmaltz, Jansen, & Wenckowski, 2017).  Our second definition is more operational; it is simply a list of skills that are essential to be a critical thinker. Critical thinking entails solid reasoning and problem solving skills; skepticism; and an ability to identify biases, distortions, omissions, and assumptions. Excellent deductive and inductive reasoning, and problem solving skills contribute to critical thinking. So, you can consider the subject matter of sections 7.2 and 7.3 to be part of critical thinking. Because we will be devoting considerable time to these concepts in the rest of the module, let us begin with a discussion about the other aspects of critical thinking.

Let’s address that first part of the definition. Scientists form hypotheses, or predictions about some possible future observations. Then, they collect data, or information (think of this as making those future observations). They do their best to make unbiased observations using reliable techniques that have been verified by others. Then, and only then, they draw a conclusion about what those observations mean. Oh, and do not forget the most important part. “Conclusion” is probably not the most appropriate word because this conclusion is only tentative. A scientist is always prepared that someone else might come along and produce new observations that would require a new conclusion be drawn. Wow! If you like to be right, you could do a lot worse than using a process like this.

A Critical Thinker’s Toolkit 

Now for the second part of the definition. Good critical thinkers (and scientists) rely on a variety of tools to evaluate information. Perhaps the most recognizable tool for critical thinking is  skepticism (and this term provides the clearest link to the thinking like a scientist definition, as you are about to see). Some people intend it as an insult when they call someone a skeptic. But if someone calls you a skeptic, if they are using the term correctly, you should consider it a great compliment. Simply put, skepticism is a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided. People from Missouri should recognize this principle, as Missouri is known as the Show-Me State. As a skeptic, you are not inclined to believe something just because someone said so, because someone else believes it, or because it sounds reasonable. You must be persuaded by high quality evidence.

Of course, if that evidence is produced, you have a responsibility as a skeptic to change your belief. Failure to change a belief in the face of good evidence is not skepticism; skepticism has open mindedness at its core. M. Neil Browne and Stuart Keeley (2018) use the term weak sense critical thinking to describe critical thinking behaviors that are used only to strengthen a prior belief. Strong sense critical thinking, on the other hand, has as its goal reaching the best conclusion. Sometimes that means strengthening your prior belief, but sometimes it means changing your belief to accommodate the better evidence.

Many times, a failure to think critically or weak sense critical thinking is related to a  bias , an inclination, tendency, leaning, or prejudice. Everybody has biases, but many people are unaware of them. Awareness of your own biases gives you the opportunity to control or counteract them. Unfortunately, however, many people are happy to let their biases creep into their attempts to persuade others; indeed, it is a key part of their persuasive strategy. To see how these biases influence messages, just look at the different descriptions and explanations of the same events given by people of different ages or income brackets, or conservative versus liberal commentators, or by commentators from different parts of the world. Of course, to be successful, these people who are consciously using their biases must disguise them. Even undisguised biases can be difficult to identify, so disguised ones can be nearly impossible.

Here are some common sources of biases:

• Personal values and beliefs.  Some people believe that human beings are basically driven to seek power and that they are typically in competition with one another over scarce resources. These beliefs are similar to the world-view that political scientists call “realism.” Other people believe that human beings prefer to cooperate and that, given the chance, they will do so. These beliefs are similar to the world-view known as “idealism.” For many people, these deeply held beliefs can influence, or bias, their interpretations of such wide ranging situations as the behavior of nations and their leaders or the behavior of the driver in the car ahead of you. For example, if your worldview is that people are typically in competition and someone cuts you off on the highway, you may assume that the driver did it purposely to get ahead of you. Other types of beliefs about the way the world is or the way the world should be, for example, political beliefs, can similarly become a significant source of bias.
• Racism, sexism, ageism and other forms of prejudice and bigotry.  These are, sadly, a common source of bias in many people. They are essentially a special kind of “belief about the way the world is.” These beliefs—for example, that women do not make effective leaders—lead people to ignore contradictory evidence (examples of effective women leaders, or research that disputes the belief) and to interpret ambiguous evidence in a way consistent with the belief.
• Self-interest.  When particular people benefit from things turning out a certain way, they can sometimes be very susceptible to letting that interest bias them. For example, a company that will earn a profit if they sell their product may have a bias in the way that they give information about their product. A union that will benefit if its members get a generous contract might have a bias in the way it presents information about salaries at competing organizations. (Note that our inclusion of examples describing both companies and unions is an explicit attempt to control for our own personal biases). Home buyers are often dismayed to discover that they purchased their dream house from someone whose self-interest led them to lie about flooding problems in the basement or back yard. This principle, the biasing power of self-interest, is likely what led to the famous phrase  Caveat Emptor  (let the buyer beware) .  

Knowing that these types of biases exist will help you evaluate evidence more critically. Do not forget, though, that people are not always keen to let you discover the sources of biases in their arguments. For example, companies or political organizations can sometimes disguise their support of a research study by contracting with a university professor, who comes complete with a seemingly unbiased institutional affiliation, to conduct the study.

People’s biases, conscious or unconscious, can lead them to make omissions, distortions, and assumptions that undermine our ability to correctly evaluate evidence. It is essential that you look for these elements. Always ask, what is missing, what is not as it appears, and what is being assumed here? For example, consider this (fictional) chart from an ad reporting customer satisfaction at 4 local health clubs.

Clearly, from the results of the chart, one would be tempted to give Club C a try, as customer satisfaction is much higher than for the other 3 clubs.

There are so many distortions and omissions in this chart, however, that it is actually quite meaningless. First, how was satisfaction measured? Do the bars represent responses to a survey? If so, how were the questions asked? Most importantly, where is the missing scale for the chart? Although the differences look quite large, are they really?

Well, here is the same chart, with a different scale, this time labeled:

Club C is not so impressive any more, is it? In fact, all of the health clubs have customer satisfaction ratings (whatever that means) between 85% and 88%. In the first chart, the entire scale of the graph included only the percentages between 83 and 89. This “judicious” choice of scale—some would call it a distortion—and omission of that scale from the chart make the tiny differences among the clubs seem important, however.

Also, in order to be a critical thinker, you need to learn to pay attention to the assumptions that underlie a message. Let us briefly illustrate the role of assumptions by touching on some people’s beliefs about the criminal justice system in the US. Some believe that a major problem with our judicial system is that many criminals go free because of legal technicalities. Others believe that a major problem is that many innocent people are convicted of crimes. The simple fact is, both types of errors occur. A person’s conclusion about which flaw in our judicial system is the greater tragedy is based on an assumption about which of these is the more serious error (letting the guilty go free or convicting the innocent). This type of assumption is called a value assumption (Browne and Keeley, 2018). It reflects the differences in values that people develop, differences that may lead us to disregard valid evidence that does not fit in with our particular values.

Oh, by the way, some students probably noticed this, but the seven tips for evaluating information that we shared in Module 1 are related to this. Actually, they are part of this section. The tips are, to a very large degree, set of ideas you can use to help you identify biases, distortions, omissions, and assumptions. If you do not remember this section, we strongly recommend you take a few minutes to review it.

skepticism :  a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

bias : an inclination, tendency, leaning, or prejudice

• Which of your beliefs (or disbeliefs) from the Activate exercise for this section were derived from a process of critical thinking? If some of your beliefs were not based on critical thinking, are you willing to reassess these beliefs? If the answer is no, why do you think that is? If the answer is yes, what concrete steps will you take?

7.2 Reasoning and Judgment

• What percentage of kidnappings are committed by strangers?
• Which area of the house is riskiest: kitchen, bathroom, or stairs?
• What is the most common cancer in the US?
• What percentage of workplace homicides are committed by co-workers?

An essential set of procedural thinking skills is  reasoning , the ability to generate and evaluate solid conclusions from a set of statements or evidence. You should note that these conclusions (when they are generated instead of being evaluated) are one key type of inference that we described in Section 7.1. There are two main types of reasoning, deductive and inductive.

Deductive reasoning

Suppose your teacher tells you that if you get an A on the final exam in a course, you will get an A for the whole course. Then, you get an A on the final exam. What will your final course grade be? Most people can see instantly that you can conclude with certainty that you will get an A for the course. This is a type of reasoning called  deductive reasoning , which is defined as reasoning in which a conclusion is guaranteed to be true as long as the statements leading to it are true. The three statements can be listed as an  argument , with two beginning statements and a conclusion:

Statement 1: If you get an A on the final exam, you will get an A for the course

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

This particular arrangement, in which true beginning statements lead to a guaranteed true conclusion, is known as a  deductively valid argument . Although deductive reasoning is often the subject of abstract, brain-teasing, puzzle-like word problems, it is actually an extremely important type of everyday reasoning. It is just hard to recognize sometimes. For example, imagine that you are looking for your car keys and you realize that they are either in the kitchen drawer or in your book bag. After looking in the kitchen drawer, you instantly know that they must be in your book bag. That conclusion results from a simple deductive reasoning argument. In addition, solid deductive reasoning skills are necessary for you to succeed in the sciences, philosophy, math, computer programming, and any endeavor involving the use of logic to persuade others to your point of view or to evaluate others’ arguments.

Cognitive psychologists, and before them philosophers, have been quite interested in deductive reasoning, not so much for its practical applications, but for the insights it can offer them about the ways that human beings think. One of the early ideas to emerge from the examination of deductive reasoning is that people learn (or develop) mental versions of rules that allow them to solve these types of reasoning problems (Braine, 1978; Braine, Reiser, & Rumain, 1984). The best way to see this point of view is to realize that there are different possible rules, and some of them are very simple. For example, consider this rule of logic:

therefore q

Logical rules are often presented abstractly, as letters, in order to imply that they can be used in very many specific situations. Here is a concrete version of the of the same rule:

I’ll either have pizza or a hamburger for dinner tonight (p or q)

I won’t have pizza (not p)

Therefore, I’ll have a hamburger (therefore q)

This kind of reasoning seems so natural, so easy, that it is quite plausible that we would use a version of this rule in our daily lives. At least, it seems more plausible than some of the alternative possibilities—for example, that we need to have experience with the specific situation (pizza or hamburger, in this case) in order to solve this type of problem easily. So perhaps there is a form of natural logic (Rips, 1990) that contains very simple versions of logical rules. When we are faced with a reasoning problem that maps onto one of these rules, we use the rule.

But be very careful; things are not always as easy as they seem. Even these simple rules are not so simple. For example, consider the following rule. Many people fail to realize that this rule is just as valid as the pizza or hamburger rule above.

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

The simple fact is, it can be very difficult for people to apply rules of deductive logic correctly; as a result, they make many errors when trying to do so. Is this a deductively valid argument or not?

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

Many people are surprised to discover that this is not a logically valid argument; the conclusion is not guaranteed to be true from the beginning statements. Although the first statement says that students who like school study a lot, it does NOT say that students who do not like school do not study a lot. In other words, it may very well be possible to study a lot without liking school. Even people who sometimes get problems like this right might not be using the rules of deductive reasoning. Instead, they might just be making judgments for examples they know, in this case, remembering instances of people who get good grades despite not liking school.

Making deductive reasoning even more difficult is the fact that there are two important properties that an argument may have. One, it can be valid or invalid (meaning that the conclusion does or does not follow logically from the statements leading up to it). Two, an argument (or more correctly, its conclusion) can be true or false. Here is an example of an argument that is logically valid, but has a false conclusion (at least we think it is false).

Either you are eleven feet tall or the Grand Canyon was created by a spaceship crashing into the earth.

You are not eleven feet tall

Therefore the Grand Canyon was created by a spaceship crashing into the earth

This argument has the exact same form as the pizza or hamburger argument above, making it is deductively valid. The conclusion is so false, however, that it is absurd (of course, the reason the conclusion is false is that the first statement is false). When people are judging arguments, they tend to not observe the difference between deductive validity and the empirical truth of statements or conclusions. If the elements of an argument happen to be true, people are likely to judge the argument logically valid; if the elements are false, they will very likely judge it invalid (Markovits & Bouffard-Bouchard, 1992; Moshman & Franks, 1986). Thus, it seems a stretch to say that people are using these logical rules to judge the validity of arguments. Many psychologists believe that most people actually have very limited deductive reasoning skills (Johnson-Laird, 1999). They argue that when faced with a problem for which deductive logic is required, people resort to some simpler technique, such as matching terms that appear in the statements and the conclusion (Evans, 1982). This might not seem like a problem, but what if reasoners believe that the elements are true and they happen to be wrong; they will would believe that they are using a form of reasoning that guarantees they are correct and yet be wrong.

deductive reasoning :  a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

argument :  a set of statements in which the beginning statements lead to a conclusion

deductively valid argument :  an argument for which true beginning statements guarantee that the conclusion is true

Inductive reasoning and judgment

Every day, you make many judgments about the likelihood of one thing or another. Whether you realize it or not, you are practicing  inductive reasoning   on a daily basis. In inductive reasoning arguments, a conclusion is likely whenever the statements preceding it are true. The first thing to notice about inductive reasoning is that, by definition, you can never be sure about your conclusion; you can only estimate how likely the conclusion is. Inductive reasoning may lead you to focus on Memory Encoding and Recoding when you study for the exam, but it is possible the instructor will ask more questions about Memory Retrieval instead. Unlike deductive reasoning, the conclusions you reach through inductive reasoning are only probable, not certain. That is why scientists consider inductive reasoning weaker than deductive reasoning. But imagine how hard it would be for us to function if we could not act unless we were certain about the outcome.

Inductive reasoning can be represented as logical arguments consisting of statements and a conclusion, just as deductive reasoning can be. In an inductive argument, you are given some statements and a conclusion (or you are given some statements and must draw a conclusion). An argument is  inductively strong   if the conclusion would be very probable whenever the statements are true. So, for example, here is an inductively strong argument:

• Statement #1: The forecaster on Channel 2 said it is going to rain today.
• Statement #2: The forecaster on Channel 5 said it is going to rain today.
• Statement #3: It is very cloudy and humid.
• Statement #4: You just heard thunder.
• Conclusion (or judgment): It is going to rain today.

Think of the statements as evidence, on the basis of which you will draw a conclusion. So, based on the evidence presented in the four statements, it is very likely that it will rain today. Will it definitely rain today? Certainly not. We can all think of times that the weather forecaster was wrong.

A true story: Some years ago psychology student was watching a baseball playoff game between the St. Louis Cardinals and the Los Angeles Dodgers. A graphic on the screen had just informed the audience that the Cardinal at bat, (Hall of Fame shortstop) Ozzie Smith, a switch hitter batting left-handed for this plate appearance, had never, in nearly 3000 career at-bats, hit a home run left-handed. The student, who had just learned about inductive reasoning in his psychology class, turned to his companion (a Cardinals fan) and smugly said, “It is an inductively strong argument that Ozzie Smith will not hit a home run.” He turned back to face the television just in time to watch the ball sail over the right field fence for a home run. Although the student felt foolish at the time, he was not wrong. It was an inductively strong argument; 3000 at-bats is an awful lot of evidence suggesting that the Wizard of Ozz (as he was known) would not be hitting one out of the park (think of each at-bat without a home run as a statement in an inductive argument). Sadly (for the die-hard Cubs fan and Cardinals-hating student), despite the strength of the argument, the conclusion was wrong.

Given the possibility that we might draw an incorrect conclusion even with an inductively strong argument, we really want to be sure that we do, in fact, make inductively strong arguments. If we judge something probable, it had better be probable. If we judge something nearly impossible, it had better not happen. Think of inductive reasoning, then, as making reasonably accurate judgments of the probability of some conclusion given a set of evidence.

We base many decisions in our lives on inductive reasoning. For example:

Statement #1: Psychology is not my best subject

Statement #2: My psychology instructor has a reputation for giving difficult exams

Statement #3: My first psychology exam was much harder than I expected

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

Some other examples of judgments that people commonly make in a school context include judgments of the likelihood that:

• A particular class will be interesting/useful/difficult
• You will be able to finish writing a paper by next week if you go out tonight
• Your laptop’s battery will last through the next trip to the library
• You will not miss anything important if you skip class tomorrow
• Your instructor will not notice if you skip class tomorrow
• You will be able to find a book that you will need for a paper
• There will be an essay question about Memory Encoding on the next exam

Tversky and Kahneman (1983) recognized that there are two general ways that we might make these judgments; they termed them extensional (i.e., following the laws of probability) and intuitive (i.e., using shortcuts or heuristics, see below). We will use a similar distinction between Type 1 and Type 2 thinking, as described by Keith Stanovich and his colleagues (Evans and Stanovich, 2013; Stanovich and West, 2000). Type 1 thinking is fast, automatic, effortful, and emotional. In fact, it is hardly fair to call it reasoning at all, as judgments just seem to pop into one’s head. Type 2 thinking , on the other hand, is slow, effortful, and logical. So obviously, it is more likely to lead to a correct judgment, or an optimal decision. The problem is, we tend to over-rely on Type 1. Now, we are not saying that Type 2 is the right way to go for every decision or judgment we make. It seems a bit much, for example, to engage in a step-by-step logical reasoning procedure to decide whether we will have chicken or fish for dinner tonight.

Many bad decisions in some very important contexts, however, can be traced back to poor judgments of the likelihood of certain risks or outcomes that result from the use of Type 1 when a more logical reasoning process would have been more appropriate. For example:

Statement #1: It is late at night.

Statement #2: Albert has been drinking beer for the past five hours at a party.

Statement #3: Albert is not exactly sure where he is or how far away home is.

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

As you can see in this example, the three statements backing up the judgment do not really support it. In other words, this argument is not inductively strong because it is based on judgments that ignore the laws of probability. What are the chances that someone facing these conditions will be able to walk home alone easily? And one need not be drunk to make poor decisions based on judgments that just pop into our heads.

The truth is that many of our probability judgments do not come very close to what the laws of probability say they should be. Think about it. In order for us to reason in accordance with these laws, we would need to know the laws of probability, which would allow us to calculate the relationship between particular pieces of evidence and the probability of some outcome (i.e., how much likelihood should change given a piece of evidence), and we would have to do these heavy math calculations in our heads. After all, that is what Type 2 requires. Needless to say, even if we were motivated, we often do not even know how to apply Type 2 reasoning in many cases.

So what do we do when we don’t have the knowledge, skills, or time required to make the correct mathematical judgment? Do we hold off and wait until we can get better evidence? Do we read up on probability and fire up our calculator app so we can compute the correct probability? Of course not. We rely on Type 1 thinking. We “wing it.” That is, we come up with a likelihood estimate using some means at our disposal. Psychologists use the term heuristic to describe the type of “winging it” we are talking about. A  heuristic   is a shortcut strategy that we use to make some judgment or solve some problem (see Section 7.3). Heuristics are easy and quick, think of them as the basic procedures that are characteristic of Type 1.  They can absolutely lead to reasonably good judgments and decisions in some situations (like choosing between chicken and fish for dinner). They are, however, far from foolproof. There are, in fact, quite a lot of situations in which heuristics can lead us to make incorrect judgments, and in many cases the decisions based on those judgments can have serious consequences.

Let us return to the activity that begins this section. You were asked to judge the likelihood (or frequency) of certain events and risks. You were free to come up with your own evidence (or statements) to make these judgments. This is where a heuristic crops up. As a judgment shortcut, we tend to generate specific examples of those very events to help us decide their likelihood or frequency. For example, if we are asked to judge how common, frequent, or likely a particular type of cancer is, many of our statements would be examples of specific cancer cases:

Statement #1: Andy Kaufman (comedian) had lung cancer.

Statement #2: Colin Powell (US Secretary of State) had prostate cancer.

Statement #3: Bob Marley (musician) had skin and brain cancer

Statement #4: Sandra Day O’Connor (Supreme Court Justice) had breast cancer.

Statement #5: Fred Rogers (children’s entertainer) had stomach cancer.

Statement #6: Robin Roberts (news anchor) had breast cancer.

Statement #7: Bette Davis (actress) had breast cancer.

Judgment: Breast cancer is the most common type.

Your own experience or memory may also tell you that breast cancer is the most common type. But it is not (although it is common). Actually, skin cancer is the most common type in the US. We make the same types of misjudgments all the time because we do not generate the examples or evidence according to their actual frequencies or probabilities. Instead, we have a tendency (or bias) to search for the examples in memory; if they are easy to retrieve, we assume that they are common. To rephrase this in the language of the heuristic, events seem more likely to the extent that they are available to memory. This bias has been termed the  availability heuristic   (Kahneman and Tversky, 1974).

The fact that we use the availability heuristic does not automatically mean that our judgment is wrong. The reason we use heuristics in the first place is that they work fairly well in many cases (and, of course that they are easy to use). So, the easiest examples to think of sometimes are the most common ones. Is it more likely that a member of the U.S. Senate is a man or a woman? Most people have a much easier time generating examples of male senators. And as it turns out, the U.S. Senate has many more men than women (74 to 26 in 2020). In this case, then, the availability heuristic would lead you to make the correct judgment; it is far more likely that a senator would be a man.

In many other cases, however, the availability heuristic will lead us astray. This is because events can be memorable for many reasons other than their frequency. Section 5.2, Encoding Meaning, suggested that one good way to encode the meaning of some information is to form a mental image of it. Thus, information that has been pictured mentally will be more available to memory. Indeed, an event that is vivid and easily pictured will trick many people into supposing that type of event is more common than it actually is. Repetition of information will also make it more memorable. So, if the same event is described to you in a magazine, on the evening news, on a podcast that you listen to, and in your Facebook feed; it will be very available to memory. Again, the availability heuristic will cause you to misperceive the frequency of these types of events.

Most interestingly, information that is unusual is more memorable. Suppose we give you the following list of words to remember: box, flower, letter, platypus, oven, boat, newspaper, purse, drum, car. Very likely, the easiest word to remember would be platypus, the unusual one. The same thing occurs with memories of events. An event may be available to memory because it is unusual, yet the availability heuristic leads us to judge that the event is common. Did you catch that? In these cases, the availability heuristic makes us think the exact opposite of the true frequency. We end up thinking something is common because it is unusual (and therefore memorable). Yikes.

The misapplication of the availability heuristic sometimes has unfortunate results. For example, if you went to K-12 school in the US over the past 10 years, it is extremely likely that you have participated in lockdown and active shooter drills. Of course, everyone is trying to prevent the tragedy of another school shooting. And believe us, we are not trying to minimize how terrible the tragedy is. But the truth of the matter is, school shootings are extremely rare. Because the federal government does not keep a database of school shootings, the Washington Post has maintained their own running tally. Between 1999 and January 2020 (the date of the most recent school shooting with a death in the US at of the time this paragraph was written), the Post reported a total of 254 people died in school shootings in the US. Not 254 per year, 254 total. That is an average of 12 per year. Of course, that is 254 people who should not have died (particularly because many were children), but in a country with approximately 60,000,000 students and teachers, this is a very small risk.

But many students and teachers are terrified that they will be victims of school shootings because of the availability heuristic. It is so easy to think of examples (they are very available to memory) that people believe the event is very common. It is not. And there is a downside to this. We happen to believe that there is an enormous gun violence problem in the United States. According the the Centers for Disease Control and Prevention, there were 39,773 firearm deaths in the US in 2017. Fifteen of those deaths were in school shootings, according to the Post. 60% of those deaths were suicides. When people pay attention to the school shooting risk (low), they often fail to notice the much larger risk.

And examples like this are by no means unique. The authors of this book have been teaching psychology since the 1990’s. We have been able to make the exact same arguments about the misapplication of the availability heuristics and keep them current by simply swapping out for the “fear of the day.” In the 1990’s it was children being kidnapped by strangers (it was known as “stranger danger”) despite the facts that kidnappings accounted for only 2% of the violent crimes committed against children, and only 24% of kidnappings are committed by strangers (US Department of Justice, 2007). This fear overlapped with the fear of terrorism that gripped the country after the 2001 terrorist attacks on the World Trade Center and US Pentagon and still plagues the population of the US somewhat in 2020. After a well-publicized, sensational act of violence, people are extremely likely to increase their estimates of the chances that they, too, will be victims of terror. Think about the reality, however. In October of 2001, a terrorist mailed anthrax spores to members of the US government and a number of media companies. A total of five people died as a result of this attack. The nation was nearly paralyzed by the fear of dying from the attack; in reality the probability of an individual person dying was 0.00000002.

The availability heuristic can lead you to make incorrect judgments in a school setting as well. For example, suppose you are trying to decide if you should take a class from a particular math professor. You might try to make a judgment of how good a teacher she is by recalling instances of friends and acquaintances making comments about her teaching skill. You may have some examples that suggest that she is a poor teacher very available to memory, so on the basis of the availability heuristic you judge her a poor teacher and decide to take the class from someone else. What if, however, the instances you recalled were all from the same person, and this person happens to be a very colorful storyteller? The subsequent ease of remembering the instances might not indicate that the professor is a poor teacher after all.

Although the availability heuristic is obviously important, it is not the only judgment heuristic we use. Amos Tversky and Daniel Kahneman examined the role of heuristics in inductive reasoning in a long series of studies. Kahneman received a Nobel Prize in Economics for this research in 2002, and Tversky would have certainly received one as well if he had not died of melanoma at age 59 in 1996 (Nobel Prizes are not awarded posthumously). Kahneman and Tversky demonstrated repeatedly that people do not reason in ways that are consistent with the laws of probability. They identified several heuristic strategies that people use instead to make judgments about likelihood. The importance of this work for economics (and the reason that Kahneman was awarded the Nobel Prize) is that earlier economic theories had assumed that people do make judgments rationally, that is, in agreement with the laws of probability.

Another common heuristic that people use for making judgments is the  representativeness heuristic (Kahneman & Tversky 1973). Suppose we describe a person to you. He is quiet and shy, has an unassuming personality, and likes to work with numbers. Is this person more likely to be an accountant or an attorney? If you said accountant, you were probably using the representativeness heuristic. Our imaginary person is judged likely to be an accountant because he resembles, or is representative of the concept of, an accountant. When research participants are asked to make judgments such as these, the only thing that seems to matter is the representativeness of the description. For example, if told that the person described is in a room that contains 70 attorneys and 30 accountants, participants will still assume that he is an accountant.

inductive reasoning :  a type of reasoning in which we make judgments about likelihood from sets of evidence

inductively strong argument :  an inductive argument in which the beginning statements lead to a conclusion that is probably true

heuristic :  a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

availability heuristic :  judging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

representativeness heuristic:   judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

Type 1 thinking : fast, automatic, and emotional thinking.

Type 2 thinking : slow, effortful, and logical thinking.

• What percentage of workplace homicides are co-worker violence?

Many people get these questions wrong. The answers are 10%; stairs; skin; 6%. How close were your answers? Explain how the availability heuristic might have led you to make the incorrect judgments.

• Can you think of some other judgments that you have made (or beliefs that you have) that might have been influenced by the availability heuristic?

7.3 Problem Solving

• Please take a few minutes to list a number of problems that you are facing right now.
• Now write about a problem that you recently solved.
• What is your definition of a problem?

Mary has a problem. Her daughter, ordinarily quite eager to please, appears to delight in being the last person to do anything. Whether getting ready for school, going to piano lessons or karate class, or even going out with her friends, she seems unwilling or unable to get ready on time. Other people have different kinds of problems. For example, many students work at jobs, have numerous family commitments, and are facing a course schedule full of difficult exams, assignments, papers, and speeches. How can they find enough time to devote to their studies and still fulfill their other obligations? Speaking of students and their problems: Show that a ball thrown vertically upward with initial velocity v0 takes twice as much time to return as to reach the highest point (from Spiegel, 1981).

These are three very different situations, but we have called them all problems. What makes them all the same, despite the differences? A psychologist might define a  problem   as a situation with an initial state, a goal state, and a set of possible intermediate states. Somewhat more meaningfully, we might consider a problem a situation in which you are in here one state (e.g., daughter is always late), you want to be there in another state (e.g., daughter is not always late), and with no obvious way to get from here to there. Defined this way, each of the three situations we outlined can now be seen as an example of the same general concept, a problem. At this point, you might begin to wonder what is not a problem, given such a general definition. It seems that nearly every non-routine task we engage in could qualify as a problem. As long as you realize that problems are not necessarily bad (it can be quite fun and satisfying to rise to the challenge and solve a problem), this may be a useful way to think about it.

Can we identify a set of problem-solving skills that would apply to these very different kinds of situations? That task, in a nutshell, is a major goal of this section. Let us try to begin to make sense of the wide variety of ways that problems can be solved with an important observation: the process of solving problems can be divided into two key parts. First, people have to notice, comprehend, and represent the problem properly in their minds (called  problem representation ). Second, they have to apply some kind of solution strategy to the problem. Psychologists have studied both of these key parts of the process in detail.

When you first think about the problem-solving process, you might guess that most of our difficulties would occur because we are failing in the second step, the application of strategies. Although this can be a significant difficulty much of the time, the more important source of difficulty is probably problem representation. In short, we often fail to solve a problem because we are looking at it, or thinking about it, the wrong way.

problem :  a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

problem representation :  noticing, comprehending and forming a mental conception of a problem

Defining and Mentally Representing Problems in Order to Solve Them

So, the main obstacle to solving a problem is that we do not clearly understand exactly what the problem is. Recall the problem with Mary’s daughter always being late. One way to represent, or to think about, this problem is that she is being defiant. She refuses to get ready in time. This type of representation or definition suggests a particular type of solution. Another way to think about the problem, however, is to consider the possibility that she is simply being sidetracked by interesting diversions. This different conception of what the problem is (i.e., different representation) suggests a very different solution strategy. For example, if Mary defines the problem as defiance, she may be tempted to solve the problem using some kind of coercive tactics, that is, to assert her authority as her mother and force her to listen. On the other hand, if Mary defines the problem as distraction, she may try to solve it by simply removing the distracting objects.

As you might guess, when a problem is represented one way, the solution may seem very difficult, or even impossible. Seen another way, the solution might be very easy. For example, consider the following problem (from Nasar, 1998):

Two bicyclists start 20 miles apart and head toward each other, each going at a steady rate of 10 miles per hour. At the same time, a fly that travels at a steady 15 miles per hour starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner until he is crushed between the two front wheels. Question: what total distance did the fly cover?

Please take a few minutes to try to solve this problem.

Most people represent this problem as a question about a fly because, well, that is how the question is asked. The solution, using this representation, is to figure out how far the fly travels on the first leg of its journey, then add this total to how far it travels on the second leg of its journey (when it turns around and returns to the first bicycle), then continue to add the smaller distance from each leg of the journey until you converge on the correct answer. You would have to be quite skilled at math to solve this problem, and you would probably need some time and pencil and paper to do it.

If you consider a different representation, however, you can solve this problem in your head. Instead of thinking about it as a question about a fly, think about it as a question about the bicycles. They are 20 miles apart, and each is traveling 10 miles per hour. How long will it take for the bicycles to reach each other? Right, one hour. The fly is traveling 15 miles per hour; therefore, it will travel a total of 15 miles back and forth in the hour before the bicycles meet. Represented one way (as a problem about a fly), the problem is quite difficult. Represented another way (as a problem about two bicycles), it is easy. Changing your representation of a problem is sometimes the best—sometimes the only—way to solve it.

Unfortunately, however, changing a problem’s representation is not the easiest thing in the world to do. Often, problem solvers get stuck looking at a problem one way. This is called  fixation . Most people who represent the preceding problem as a problem about a fly probably do not pause to reconsider, and consequently change, their representation. A parent who thinks her daughter is being defiant is unlikely to consider the possibility that her behavior is far less purposeful.

Problem-solving fixation was examined by a group of German psychologists called Gestalt psychologists during the 1930’s and 1940’s. Karl Dunker, for example, discovered an important type of failure to take a different perspective called  functional fixedness . Imagine being a participant in one of his experiments. You are asked to figure out how to mount two candles on a door and are given an assortment of odds and ends, including a small empty cardboard box and some thumbtacks. Perhaps you have already figured out a solution: tack the box to the door so it forms a platform, then put the candles on top of the box. Most people are able to arrive at this solution. Imagine a slight variation of the procedure, however. What if, instead of being empty, the box had matches in it? Most people given this version of the problem do not arrive at the solution given above. Why? Because it seems to people that when the box contains matches, it already has a function; it is a matchbox. People are unlikely to consider a new function for an object that already has a function. This is functional fixedness.

Mental set is a type of fixation in which the problem solver gets stuck using the same solution strategy that has been successful in the past, even though the solution may no longer be useful. It is commonly seen when students do math problems for homework. Often, several problems in a row require the reapplication of the same solution strategy. Then, without warning, the next problem in the set requires a new strategy. Many students attempt to apply the formerly successful strategy on the new problem and therefore cannot come up with a correct answer.

The thing to remember is that you cannot solve a problem unless you correctly identify what it is to begin with (initial state) and what you want the end result to be (goal state). That may mean looking at the problem from a different angle and representing it in a new way. The correct representation does not guarantee a successful solution, but it certainly puts you on the right track.

A bit more optimistically, the Gestalt psychologists discovered what may be considered the opposite of fixation, namely  insight . Sometimes the solution to a problem just seems to pop into your head. Wolfgang Kohler examined insight by posing many different problems to chimpanzees, principally problems pertaining to their acquisition of out-of-reach food. In one version, a banana was placed outside of a chimpanzee’s cage and a short stick inside the cage. The stick was too short to retrieve the banana, but was long enough to retrieve a longer stick also located outside of the cage. This second stick was long enough to retrieve the banana. After trying, and failing, to reach the banana with the shorter stick, the chimpanzee would try a couple of random-seeming attempts, react with some apparent frustration or anger, then suddenly rush to the longer stick, the correct solution fully realized at this point. This sudden appearance of the solution, observed many times with many different problems, was termed insight by Kohler.

Lest you think it pertains to chimpanzees only, Karl Dunker demonstrated that children also solve problems through insight in the 1930s. More importantly, you have probably experienced insight yourself. Think back to a time when you were trying to solve a difficult problem. After struggling for a while, you gave up. Hours later, the solution just popped into your head, perhaps when you were taking a walk, eating dinner, or lying in bed.

fixation :  when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

functional fixedness :  a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

mental set :  a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

Correctly identifying the problem and your goal for a solution is a good start, but recall the psychologist’s definition of a problem: it includes a set of possible intermediate states. Viewed this way, a problem can be solved satisfactorily only if one can find a path through some of these intermediate states to the goal. Imagine a fairly routine problem, finding a new route to school when your ordinary route is blocked (by road construction, for example). At each intersection, you may turn left, turn right, or go straight. A satisfactory solution to the problem (of getting to school) is a sequence of selections at each intersection that allows you to wind up at school.

If you had all the time in the world to get to school, you might try choosing intermediate states randomly. At one corner you turn left, the next you go straight, then you go left again, then right, then right, then straight. Unfortunately, trial and error will not necessarily get you where you want to go, and even if it does, it is not the fastest way to get there. For example, when a friend of ours was in college, he got lost on the way to a concert and attempted to find the venue by choosing streets to turn onto randomly (this was long before the use of GPS). Amazingly enough, the strategy worked, although he did end up missing two out of the three bands who played that night.

Trial and error is not all bad, however. B.F. Skinner, a prominent behaviorist psychologist, suggested that people often behave randomly in order to see what effect the behavior has on the environment and what subsequent effect this environmental change has on them. This seems particularly true for the very young person. Picture a child filling a household’s fish tank with toilet paper, for example. To a child trying to develop a repertoire of creative problem-solving strategies, an odd and random behavior might be just the ticket. Eventually, the exasperated parent hopes, the child will discover that many of these random behaviors do not successfully solve problems; in fact, in many cases they create problems. Thus, one would expect a decrease in this random behavior as a child matures. You should realize, however, that the opposite extreme is equally counterproductive. If the children become too rigid, never trying something unexpected and new, their problem solving skills can become too limited.

Effective problem solving seems to call for a happy medium that strikes a balance between using well-founded old strategies and trying new ground and territory. The individual who recognizes a situation in which an old problem-solving strategy would work best, and who can also recognize a situation in which a new untested strategy is necessary is halfway to success.

Solving Problems with Algorithms and Heuristics

For many problems there is a possible strategy available that will guarantee a correct solution. For example, think about math problems. Math lessons often consist of step-by-step procedures that can be used to solve the problems. If you apply the strategy without error, you are guaranteed to arrive at the correct solution to the problem. This approach is called using an  algorithm , a term that denotes the step-by-step procedure that guarantees a correct solution. Because algorithms are sometimes available and come with a guarantee, you might think that most people use them frequently. Unfortunately, however, they do not. As the experience of many students who have struggled through math classes can attest, algorithms can be extremely difficult to use, even when the problem solver knows which algorithm is supposed to work in solving the problem. In problems outside of math class, we often do not even know if an algorithm is available. It is probably fair to say, then, that algorithms are rarely used when people try to solve problems.

Because algorithms are so difficult to use, people often pass up the opportunity to guarantee a correct solution in favor of a strategy that is much easier to use and yields a reasonable chance of coming up with a correct solution. These strategies are called  problem solving heuristics . Similar to what you saw in section 6.2 with reasoning heuristics, a problem solving heuristic is a shortcut strategy that people use when trying to solve problems. It usually works pretty well, but does not guarantee a correct solution to the problem. For example, one problem solving heuristic might be “always move toward the goal” (so when trying to get to school when your regular route is blocked, you would always turn in the direction you think the school is). A heuristic that people might use when doing math homework is “use the same solution strategy that you just used for the previous problem.”

By the way, we hope these last two paragraphs feel familiar to you. They seem to parallel a distinction that you recently learned. Indeed, algorithms and problem-solving heuristics are another example of the distinction between Type 1 thinking and Type 2 thinking.

Although it is probably not worth describing a large number of specific heuristics, two observations about heuristics are worth mentioning. First, heuristics can be very general or they can be very specific, pertaining to a particular type of problem only. For example, “always move toward the goal” is a general strategy that you can apply to countless problem situations. On the other hand, “when you are lost without a functioning gps, pick the most expensive car you can see and follow it” is specific to the problem of being lost. Second, all heuristics are not equally useful. One heuristic that many students know is “when in doubt, choose c for a question on a multiple-choice exam.” This is a dreadful strategy because many instructors intentionally randomize the order of answer choices. Another test-taking heuristic, somewhat more useful, is “look for the answer to one question somewhere else on the exam.”

You really should pay attention to the application of heuristics to test taking. Imagine that while reviewing your answers for a multiple-choice exam before turning it in, you come across a question for which you originally thought the answer was c. Upon reflection, you now think that the answer might be b. Should you change the answer to b, or should you stick with your first impression? Most people will apply the heuristic strategy to “stick with your first impression.” What they do not realize, of course, is that this is a very poor strategy (Lilienfeld et al, 2009). Most of the errors on exams come on questions that were answered wrong originally and were not changed (so they remain wrong). There are many fewer errors where we change a correct answer to an incorrect answer. And, of course, sometimes we change an incorrect answer to a correct answer. In fact, research has shown that it is more common to change a wrong answer to a right answer than vice versa (Bruno, 2001).

The belief in this poor test-taking strategy (stick with your first impression) is based on the  confirmation bias   (Nickerson, 1998; Wason, 1960). You first saw the confirmation bias in Module 1, but because it is so important, we will repeat the information here. People have a bias, or tendency, to notice information that confirms what they already believe. Somebody at one time told you to stick with your first impression, so when you look at the results of an exam you have taken, you will tend to notice the cases that are consistent with that belief. That is, you will notice the cases in which you originally had an answer correct and changed it to the wrong answer. You tend not to notice the other two important (and more common) cases, changing an answer from wrong to right, and leaving a wrong answer unchanged.

Because heuristics by definition do not guarantee a correct solution to a problem, mistakes are bound to occur when we employ them. A poor choice of a specific heuristic will lead to an even higher likelihood of making an error.

algorithm :  a step-by-step procedure that guarantees a correct solution to a problem

problem solving heuristic :  a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

confirmation bias :  people’s tendency to notice information that confirms what they already believe

An Effective Problem-Solving Sequence

You may be left with a big question: If algorithms are hard to use and heuristics often don’t work, how am I supposed to solve problems? Robert Sternberg (1996), as part of his theory of what makes people successfully intelligent (Module 8) described a problem-solving sequence that has been shown to work rather well:

• Identify the existence of a problem.  In school, problem identification is often easy; problems that you encounter in math classes, for example, are conveniently labeled as problems for you. Outside of school, however, realizing that you have a problem is a key difficulty that you must get past in order to begin solving it. You must be very sensitive to the symptoms that indicate a problem.
• Define the problem.  Suppose you realize that you have been having many headaches recently. Very likely, you would identify this as a problem. If you define the problem as “headaches,” the solution would probably be to take aspirin or ibuprofen or some other anti-inflammatory medication. If the headaches keep returning, however, you have not really solved the problem—likely because you have mistaken a symptom for the problem itself. Instead, you must find the root cause of the headaches. Stress might be the real problem. For you to successfully solve many problems it may be necessary for you to overcome your fixations and represent the problems differently. One specific strategy that you might find useful is to try to define the problem from someone else’s perspective. How would your parents, spouse, significant other, doctor, etc. define the problem? Somewhere in these different perspectives may lurk the key definition that will allow you to find an easier and permanent solution.
• Formulate strategy.  Now it is time to begin planning exactly how the problem will be solved. Is there an algorithm or heuristic available for you to use? Remember, heuristics by their very nature guarantee that occasionally you will not be able to solve the problem. One point to keep in mind is that you should look for long-range solutions, which are more likely to address the root cause of a problem than short-range solutions.
• Represent and organize information.  Similar to the way that the problem itself can be defined, or represented in multiple ways, information within the problem is open to different interpretations. Suppose you are studying for a big exam. You have chapters from a textbook and from a supplemental reader, along with lecture notes that all need to be studied. How should you (represent and) organize these materials? Should you separate them by type of material (text versus reader versus lecture notes), or should you separate them by topic? To solve problems effectively, you must learn to find the most useful representation and organization of information.
• Allocate resources.  This is perhaps the simplest principle of the problem solving sequence, but it is extremely difficult for many people. First, you must decide whether time, money, skills, effort, goodwill, or some other resource would help to solve the problem Then, you must make the hard choice of deciding which resources to use, realizing that you cannot devote maximum resources to every problem. Very often, the solution to problem is simply to change how resources are allocated (for example, spending more time studying in order to improve grades).
• Monitor and evaluate solutions.  Pay attention to the solution strategy while you are applying it. If it is not working, you may be able to select another strategy. Another fact you should realize about problem solving is that it never does end. Solving one problem frequently brings up new ones. Good monitoring and evaluation of your problem solutions can help you to anticipate and get a jump on solving the inevitable new problems that will arise.

Please note that this as  an  effective problem-solving sequence, not  the  effective problem solving sequence. Just as you can become fixated and end up representing the problem incorrectly or trying an inefficient solution, you can become stuck applying the problem-solving sequence in an inflexible way. Clearly there are problem situations that can be solved without using these skills in this order.

Additionally, many real-world problems may require that you go back and redefine a problem several times as the situation changes (Sternberg et al. 2000). For example, consider the problem with Mary’s daughter one last time. At first, Mary did represent the problem as one of defiance. When her early strategy of pleading and threatening punishment was unsuccessful, Mary began to observe her daughter more carefully. She noticed that, indeed, her daughter’s attention would be drawn by an irresistible distraction or book. Fresh with a re-representation of the problem, she began a new solution strategy. She began to remind her daughter every few minutes to stay on task and remind her that if she is ready before it is time to leave, she may return to the book or other distracting object at that time. Fortunately, this strategy was successful, so Mary did not have to go back and redefine the problem again.

Pick one or two of the problems that you listed when you first started studying this section and try to work out the steps of Sternberg’s problem solving sequence for each one.

a mental representation of a category of things in the world

an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

knowledge about one’s own cognitive processes; thinking about your thinking

individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

Thinking like a scientist in your everyday life for the purpose of drawing correct conclusions. It entails skepticism; an ability to identify biases, distortions, omissions, and assumptions; and excellent deductive and inductive reasoning, and problem solving skills.

a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

an inclination, tendency, leaning, or prejudice

a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

a set of statements in which the beginning statements lead to a conclusion

an argument for which true beginning statements guarantee that the conclusion is true

a type of reasoning in which we make judgments about likelihood from sets of evidence

an inductive argument in which the beginning statements lead to a conclusion that is probably true

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

udging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

noticing, comprehending and forming a mental conception of a problem

when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

a sudden realization of a solution to a problem

a step-by-step procedure that guarantees a correct solution to a problem

The tendency to notice and pay attention to information that confirms your prior beliefs and to ignore information that disconfirms them.

a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

Introduction to Psychology Copyright © 2020 by Ken Gray; Elizabeth Arnott-Hill; and Or'Shaundra Benson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Master of Business Administration (MBA)

The Reinhardt MBA program develops in each graduate the skills necessary to analyze and interpret complex business situations, to seek and employ innovative methods for solving business problems, and to lead diverse groups of individuals effectively and ethically .  Furthermore, the Reinhardt MBA teaches students to recognize strategic and   operational advantages and to use analytical and critical thinking skills necessary for effective   strategic and tactical decision-making. Reinhardt MBA students learn to utilize interpersonal skills to foster team consensus ,  leadership, business ethics,   and individual as well as social responsibility.

Program Coordinator

Tony   Daniel,   Ph.D.,   SHRM-SCP  Professor of Business 770-720-5638 [email protected]

Accreditation

Reinhardt University is accredited by the Southern Association of Colleges and Schools Commission on Colleges (SACSCOC) to award associate, baccalaureate, and masters. Questions about the accreditation of Reinhardt University may be directed in writing to the Southern Association of Colleges and Schools Commission on Colleges at 1866 Southern Lane, Decatur, GA 30033-4097, by calling(404) 679-4500, or by using information available on SACSCOC’s website ( www.sacscoc.org).

Reinhardt University's overall educational program emphasizes the study of liberal arts, sciences and professional studies within the University's historic commitment to the United Methodist faith and tradition. The University affirms that learning is best facilitated through a partnership between faculty members and students where the integration of faith and   learning   is   essential.   The   University   is   committed to students who desire a small, caring community dedicated to personalized attention.

The MBA program shares the same commitments of the University's overall mission, but with a focus on the graduate student community. The MBA program challenges students academically and “puts them in the chair” of the decision maker in actual business situations. This is done by personal interaction and case   study   assignments with   other   students   and   with   a unique faculty that is academically qualified and seasoned with of business experience.

MBA   Student   Learning Outcomes

MBA students demonstrate the following qualities, abilities, and skills upon completion of the program:

M1 Critical Thinking, Analytical and Problem- Solving Skills -  analyze business situations using information and logic to make recommendations for problem solving and decision making.

M2 Interpersonal, Teamwork, Leadership, and Communications Skills -  use team building and collaborative behaviors in the accomplishment of group tasks and will communicate effectively the problem alternatives considered, a recommended solution, and an implementation strategy in oral, written and electronic form.

M3 Ethical Issues and Responsibilities -  recognize and analyze ethical dilemmas and propose resolutions for practical business solutions.

M4 Business Skills and Knowledge -  apply best practices, established theories, and managerial skills to business situations and problems.

M5 Awareness of Global and Multicultural Issues -  demonstrate awareness of, and analyze, global and multicultural issues as they relate to  business.

M6 Knowledge of Research Methodologies  - derive business decision-making applications based upon sound research practices and procedures.

Admission  Requirements

All admission documents should be sent to the following address:

Office of Admissions  Reinhardt University  7300 Reinhardt Circle Waleska, GA 30183 PHONE: 770-720-5526 e-mail:   [email protected]

General admission to Reinhardt University graduate studies:

• The Graduate Admission Application form—complete and submit the Online Application for Admission
• Submit official transcripts from all institutions attended; proof of a baccalaureate degree from a regionally accredited institution should be on one transcript. If a transcript includes any graduate classes, the applicant should have left the graduate program in good standing.

Official transcripts must be mailed from the granting institution, or delivered in   a   sealed envelope from   the institution, or sent via a professional electronic transcript sending service.

Additional admission requirements for the Reinhardt MBA:

• A professional résumé.
• A 300-word essay on how an online MBA fits with the applicant’s career goals
• Three letters of reference addressing the applicant’s ability to carry out graduate course work, with one letter addressing the applicant’s two (2) years of full-time, post- baccalaureate career experience.

And, either

A Bachelor’s Degree in Business from a regionally accredited university with a minimum 2.75 GPA (alternate discretion criteria: a greater than 3.0 GPA in the last 60 credits)

• An online interview with the MBA Program Coordinator or his/her designee may be required.

Note:  If the applicant’s undergraduate degree is not in Business, then, the candidate must have a Bachelor's Degree from a regionally accredited university with at least a 2.75 GPA.

Admission for Current Reinhardt  University Undergraduate Students

Applicants   who   complete   an   a   bachelor’s   degree   at Reinhardt University with a 3.0 GPA or higher-

• Submit the graduate school application
• Students in this category can automatically be accepted without references, interviews, and/or essays by the admissions department

Applicants   who   complete   a   bachelor’s   degree   at   Reinhardt University with less than a 3.0 GPA-

• Submit graduate application
• Students in this category can be accepted without references, interviews, and/or essays but must be approved by the program coordinator
• Other documents may be required at the discretion of the program coordinator

Transfer  Credit

No transfer courses are accepted for credit.

Credit   hour   policy  (Online)

Over seven (7) weeks, students will spend a variable number of minutes per week in online lectures, class discussions, and in preparation of class projects and research papers. Instructional time includes a 3-hour final exam. Out-of-class work includes homework and preparation for exams and quizzes and is a variable number of minutes per week (6750 minutes for the semester).

Graduate Students are expected to participate each week in required assignments as scheduled by the instructor. This may require collaboration among classmates and outside research .

Academic Performance

MBA students are expected to earn grades of “A” or “B” in their course work. Only one (1) course grade of   “C”   may   be   included   in   the   computation   for   degree completion.   A   second   course grade   of   “C”   will   result in   Academic   Probation. The   course   must   be retaken to count toward degree completion.   A third course   grade   of   “C”   or   a   first   course   grade   of “F” will result in Academic Dismissal.

A student may appeal a dismissal by submitting a letter to the vice President for Academic Affairs describing the condition and identifying the reasons for seeking a positive decision of the appeal.

See also Grade Appeals  and Enrollment Related Appeals  under Appeals and Petitions .

Graduation Requirements:

• A cumulative GPA of at least 3.0, and
• No more than (1) one “C” in the program, counted toward degree completion, regardless of the GPA.
• A maximum of 5 years for completion

See Academic Performance and Degree Completion Requirements .

Degrees and Certificates

Master of Business Administration (MBA), Master of Business Administration (MBA)