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Problem Solving Beyond the Classroom: Primary 3 Paperback – January 1, 2013

• Print length 160 pages
• Language English
• Publisher Marshall Cavendish Education
• Publication date January 1, 2013
• ISBN-10 9810195923
• ISBN-13 978-9810195922
• See all details

Product details

• Publisher ‏ : ‎ Marshall Cavendish Education (January 1, 2013)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 160 pages
• ISBN-10 ‏ : ‎ 9810195923
• ISBN-13 ‏ : ‎ 978-9810195922
• Item Weight ‏ : ‎ 8 ounces

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• Collaborative Problem Solving in Schools »

Collaborative Problem Solving in Schools

Collaborative Problem Solving ® (CPS) is an evidence-based, trauma-informed practice that helps students meet expectations, reduces concerning behavior, builds students’ skills, and strengthens their relationships with educators.

Collaborative Problem Solving is designed to meet the needs of all children, including those with social, emotional, and behavioral challenges. It promotes the understanding that students who have trouble meeting expectations or managing their behavior lack the skill—not the will—to do so. These students struggle with skills related to problem-solving, flexibility, and frustration tolerance. Collaborative Problem Solving has been shown to help build these skills.

Collaborative Problem Solving avoids using power, control, and motivational procedures. Instead, it focuses on collaborating with students to solve the problems leading to them not meeting expectations and displaying concerning behavior. This trauma-informed approach provides staff with actionable strategies for trauma-sensitive education and aims to mitigate implicit bias’s impact on school discipline . It integrates with MTSS frameworks, PBIS, restorative practices, and SEL approaches, such as RULER. Collaborative Problem Solving reduces challenging behavior and teacher stress while building future-ready skills and relationships between educators and students.

Transform School Discipline

Traditional school discipline is broken, it doesn’t result in improved behavior or improved relationships between educators and students. In addition, it has been shown to be disproportionately applied to students of color. The Collaborative Problem Solving approach is an equitable and effective form of relational discipline that reduces concerning behavior and teacher stress while building skills and relationships between educators and students. Learn more >>

A Client’s Story

Collaborative Problem Solving and SEL

Collaborative Problem Solving aligns with CASEL’s five core competencies by building relationships between teachers and students using everyday situations. Students develop the skills they need to prepare for the real world, including problem-solving, collaboration and communication, flexibility, perspective-taking, and empathy. Collaborative Problem Solving makes social-emotional learning actionable.

Collaborative Problem Solving and MTSS

The Collaborative Problem Solving approach integrates with Multi-Tiered Systems of Support (MTSS) in educational settings. CPS benefits all students and can be implemented across the three tiers of support within an MTSS framework to effectively identify and meet the diverse social emotional and behavioral needs of students in schools. Learn More >>

The Results

Our research has shown that the Collaborative Problem Solving approach helps kids and adults build crucial social-emotional skills and leads to dramatic decreases in behavior problems across various settings. Results in schools include remarkable reductions in time spent out of class, detentions, suspensions, injuries, teacher stress, and alternative placements as well as increases in emotional safety, attendance, academic growth, and family participation.

Educators, join us in this introductory course and develop your behavioral growth mindset!

This 2-hour, self-paced course introduces the principles of Collaborative Problem Solving ®  while outlining how the approach is uniquely suited to the needs of today's educators and students. Tuition: $39 Enroll Now

Bring CPS to Your School

We can help you bring a more accurate, compassionate, and effective approach to working with children to your school or district.

What Our Clients Say

Education insights, corporal punishment ban in new york sparks awareness of practice, to fix students’ bad behavior, stop punishing them, behaviors charts: helpful or harmful, bringing collaborative problem solving to marshalltown, ia community school district, the benefits of changing school discipline, eliminating the school-to-prison pipeline, ending restraint and seclusion in schools: podcast, a skill-building approach to reducing students’ anxiety and challenging behavior, the school discipline fix book club, what can we do about post-pandemic school violence, sos: our schools are in crisis and we need to act now, talking to kids about the tiktok bathroom destruction challenge, north dakota governor’s summit on innovative education 2021, kids of color suffer from both explicit and implicit bias, school discipline is trauma-insensitive and trauma-uninformed, privacy overview.

The Will to Teach

4 Strategies to Build Your Students’ Problem Solving Skills

Every teacher understands the importance of fostering problem-solving skills in their students. These skills not only help students navigate academic challenges, but they also translate into valuable tools for life beyond the classroom. In this article, we’ll delve into the reasons why it’s crucial to develop these skills and provide practical strategies you can implement in your classroom right away.

Why is Developing Problem Solving Skills Important?

Strategies to develop problem solving skills, real-world example, concluding thoughts.

Problem-solving skills are a crucial part of a well-rounded education. They encourage critical thinking, enhance creativity and flexibility, and equip students with the resilience needed to tackle obstacles head-on.

• Real-World Application:  Problem-solving skills aren’t confined to solving math problems or decoding a science experiment. They are applicable in everyday life situations, from resolving conflicts to making important decisions.
• Enhances Creativity and Critical Thinking:  Problem-solving activities often require students to think outside the box and use their critical thinking abilities. This stimulates creativity and fosters innovative thought.
• Boosts Confidence:  As students improve their problem-solving abilities, they gain confidence in their skills. This confidence can positively influence their academic performance and personal life.

There are numerous ways to incorporate problem-solving skill development into your classroom. Here are a few effective strategies:

• Project-Based Learning:  Projects that require planning, execution, and evaluation naturally involve problem-solving. For example, a project where students need to build a model bridge within a budget encourages them to solve logistical and financial problems.
• Group Work :  Group work allows students to face and solve problems together. It encourages communication, cooperation, and collective problem-solving. For example, a group assignment on preparing a presentation on an environmental issue can encourage problem-solving related to information gathering, presentation design, and time management.
• Encourage Questions :  Encourage students to ask and answer their own questions. This promotes independent thinking and problem solving. For example, instead of giving the answer to a complicated math problem, guide them towards the solution by prompting them with questions.
• Role-play Scenarios:  Role-play scenarios can help students develop problem-solving skills by putting them in hypothetical situations and asking them to come up with solutions. For example, a role-play scenario where a student has to navigate a disagreement between friends can help them develop conflict resolution skills.

As a school leader, I’ve seen the power of problem-solving skills firsthand. I remember a group of students who were working on a community garden project. They faced numerous challenges, like budget constraints and unpredictable weather. Despite the hurdles, they didn’t give up. Instead, they came up with creative solutions, such as fundraising to cover costs and building a small greenhouse for year-round gardening. This project not only enhanced their problem-solving skills but also their resilience and team collaboration.

Developing problem-solving skills in students is a crucial aspect of education that extends beyond academic success. By incorporating problem-solving activities into your teaching, you’re equipping your students with a tool that will serve them in all facets of life. Remember, the best learning happens when students are actively engaged , so make problem-solving a fun and integral part of your classroom culture.

1. What are problem-solving skills? Problem-solving skills are abilities that help individuals define problems, analyze potential solutions, and implement effective strategies to solve problems.

2. Why are problem-solving skills important for students? Problem-solving skills are important as they foster creativity, critical thinking, and resilience. They are applicable in real-world situations and can boost student confidence.

3. What are some strategies to develop problem-solving skills in students? Strategies can include project-based learning, group work, encouraging questions, and role-play scenarios.

4. How can I make problem-solving activities engaging for students? Making problem-solving part of a larger project or group work can make it more engaging. Also, try to relate problems to real-world situations that students find relevant.

5. How can I assess my students’ problem-solving skills? You can assess problem-solving skills through direct observation, group project participation, and individual assignments that require problem-solving.

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Center for Teaching

Teaching problem solving.

Print Version

Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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Benefits of Problem-Solving in the K-12 Classroom

Posted October 5, 2022 by Miranda Marshall

From solving complex algebra problems to investigating scientific theories, to making inferences about written texts, problem-solving is central to every subject explored in school. Even beyond the classroom, problem-solving is ranked among the most important skills for students to demonstrate on their resumes, with 82.9% of employers considering it a highly valued attribute. On an even broader scale, students who learn how to apply their problem-solving skills to the issues they notice in their communities – or even globally –  have the tools they need to change the future and leave a lasting impact on the world around them.

Problem-solving can be taught in any content area and can even combine cross-curricular concepts to connect learning from all subjects. On top of building transferrable skills for higher education and beyond, read on to learn more about five amazing benefits students will gain from the inclusion of problem-based learning in their education:

• Problem-solving is inherently student-centered.

Student-centered learning refers to methods of teaching that recognize and cater to students’ individual needs. Students learn at varying paces, have their own unique strengths, and even further, have their own interests and motivations – and a student-centered approach recognizes this diversity within classrooms by giving students some degree of control over their learning and making them active participants in the learning process.

Incorporating problem-solving into your curriculum is a great way to make learning more student-centered, as it requires students to engage with topics by asking questions and thinking critically about explanations and solutions, rather than expecting them to absorb information in a lecture format or through wrote memorization.

• Increases confidence and achievement across all school subjects.

As with any skill, the more students practice problem-solving, the more comfortable they become with the type of critical and analytical thinking that will carry over into other areas of their academic careers. By learning how to approach concepts they are unfamiliar with or questions they do not know the answers to, students develop a greater sense of self-confidence in their ability to apply problem-solving techniques to other subject areas, and even outside of school in their day-to-day lives.

The goal in teaching problem-solving is for it to become second nature, and for students to routinely express their curiosity, explore innovative solutions, and analyze the world around them to draw their own conclusions.

• Encourages collaboration and teamwork.

Since problem-solving often involves working cooperatively in teams, students build a number of important interpersonal skills alongside problem-solving skills. Effective teamwork requires clear communication, a sense of personal responsibility, empathy and understanding for teammates, and goal setting and organization – all of which are important throughout higher education and in the workplace as well.

• Increases metacognitive skills.

Metacognition is often described as “thinking about thinking” because it refers to a person’s ability to analyze and understand their own thought processes. When making decisions, metacognition allows problem-solvers to consider the outcomes of multiple plans of action and determine which one will yield the best results.

Higher metacognitive skills have also widely been linked to improved learning outcomes and improved studying strategies. Metacognitive students are able to reflect on their learning experiences to understand themselves and the world around them better.

• Helps with long-term knowledge retention.

Students who learn problem-solving skills may see an improved ability to retain and recall information. Specifically, being asked to explain how they reached their conclusions at the time of learning, by sharing their ideas and facts they have researched, helps reinforce their understanding of the subject matter.

Problem-solving scenarios in which students participate in small-group discussions can be especially beneficial, as this discussion gives students the opportunity to both ask and answer questions about the new concepts they’re exploring.

At all grade levels, students can see tremendous gains in their academic performance and emotional intelligence when problem-solving is thoughtfully planned into their learning.

Interested in helping your students build problem-solving skills, but aren’t sure where to start? Future Problem Solving Problem International (FPSPI) is an amazing academic competition for students of all ages, all around the world, that includes helpful resources for educators to implement in their own classrooms!

Learn more about this year’s competition season from this recorded webinar:    https://youtu.be/AbeKQ8_Sm8U and/or email [email protected] to get started!

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Using an Inquiry Process to Solve Persistent Classroom Problems

Teachers can resolve challenges that come up over and over by using data to keep testing strategies until they find what works.

The start of a new school year is always filled with anticipation. Teachers hope for engaged students who want to attain success. Students set personal goals and often hope that this year will be better than last year. Parents want their children to try hard, do well, and they want their children’s teachers to be supportive and offer a safe learning space. The new school year is often filled with hope.

However, despite all the best intentions, at some point, the teacher will encounter a problem. Many problems can be resolved with the knowledge acquired through a teacher’s experience. Students may forget to bring a pencil to class, so you just keep a jar of sharpened pencils on your desk. Students who are English language learners struggle to read Shakespeare, so you provide them and all the other students with a link to the audio version of the play that they can listen to. These impromptu decisions have the potential to swiftly address the problem, thereby eliminating the need for further investigation.

What is Teacher Inquiry?

But what is a teacher supposed to do if a problem persists over time? Some students are always late to class right after lunch. Some students never raise their hand to participate in a class discussion. Some students don’t effectively edit their work prior to handing it in. How can a teacher work to identify strategies that can solve these persistent classroom problems? This is where teacher inquiry becomes a valuable tool.

As Marilyn Cochran-Smith and Susan L. Lytle discuss in their book Inquiry as Stance: Practitioner Research for the Next Generation , teacher inquiry is a process of questioning, exploring, and implementing strategies to address persistent classroom challenges. It mirrors the active learning process we encourage in students and can transform recurring problems into opportunities for growth. Most important, it also creates space for students to share their voices and perspectives—allowing them to play a role in guiding the changes that are implemented in the classroom.

How to Start the Inquiry Process

Identify the problem. Begin by clearly defining the issue. For example, if students are frequently late after lunch, consider this as your inquiry focus.

Gather action information. Before rushing to solutions, gather insights from blogs, research, books, or colleagues. For instance, if the problem is tardiness, you might explore strategies like greeting students at the door or starting the class with a high-energy, collaborative activity that is engaging for students .

Frame your inquiry question. Craft a focused question using the format: What impact does X have on Y? Here X is the planned intervention, and Y is the behavior.

• What impact does greeting students at the classroom door have on their punctuality?
• What impact does a sharing circle have on students’ presentation anxiety?

This approach shifts the perspective from seeing students as the problem to exploring solutions to unwanted behaviors. Rather than saying, “Students are always late to class right after lunch,” we can ask, “What impact does an engaging collaborative activity at the start of class have on students’ punctuality?” 

Implementing and Assessing the Strategy

Plan data collection. Before implementing your strategy, decide how you’ll measure its effectiveness. This could involve the following:

Quantitative data: Use attendance records, test scores, or quick surveys—whether digital or paper-based—to track student engagement. For example, monitor the number of students arriving on time before and after you start greeting them. Choose the survey method that best fits your classroom’s needs, whether it’s a digital link or QR code for students with technology, or a paper survey for those without.

Qualitative data: Collect student feedback through informal interviews or reflective journals to understand their experiences.

Mixed methods: You can collect a combination of quantitative and qualitative data to allow for quick, easy-to-read facts (quantitative) with an understanding of the why (qualitative) for the data.

Tip: To avoid overwhelming yourself, use data that you’re already collecting and analyze it with your inquiry question in mind.

Implement the strategy. Start with a small, manageable change. If you’re trying to improve punctuality, greet students at the door for a week and note any changes.

Evaluating the Results

Analyze the data . Review your collected data to see if there’s a noticeable effect. Did more students arrive on time? If you used a survey, what do the results indicate about students’ attitudes?

Reflect on the outcome. If the strategy worked, consider how it can be sustained or adapted for other challenges. If it didn’t, reflect on why. Did the strategy need more time, or should a different approach be tried?

Example: If greeting students didn’t improve punctuality, consider if greeting needs to be combined with another intervention, like a change in seating arrangements or communicating with students’ families to remind them about the importance of punctuality.

What if the Strategy Doesn’t Work?

Not all inquiries lead to success, and that’s OK. If your initial strategy doesn’t yield the desired results, reflect on the process.

• What could be adjusted? Perhaps the data collection method wasn’t effective, or the strategy needs more time to show results.
• What did you learn? Even if the strategy didn’t solve the problem, what insights did you gain that could inform future inquiries?

Adopt the same growth mindset you encourage in your students in order to view setbacks as learning opportunities . Inquiry is a cycle of continuous improvement, not a onetime fix.

Embracing the Inquiry Mindset

Inquiry empowers teachers to approach challenges with curiosity and adaptability. By framing problems as opportunities to learn, gathering and analyzing data, and reflecting on outcomes, teachers model the persistence and growth mindset we aim to instill in our students. Even when results aren’t immediate, the process fosters a culture of continuous learning and improvement, benefiting teachers and students alike.

THE PROJECT APPROACH

Managed by the Educators Institute at Duke School

ENGAGING CHILDREN'S MINDS

Building on natural curiosity to engage, problem-solve, and connect

Authentic Discovery

Problem-Solving

Extending beyond the classroom to each student's community

Shaping the next generation of problem-solvers

Natural Curiosity

Building on natural curiosity to enable interaction and connection

The Project Approach

Children have a strong disposition to explore and discover. The Project Approach builds on natural curiosity, enabling children to interact, question, connect, problem-solve, communicate, reflect, and more. This kind of authentic learning extends beyond the classroom to each student’s home, community, nation, and world. It essentially makes learning the stuff of real life and children active participants in and shapers of their worlds.

The Project Approach Study Guide

The study guide offers educators an overview of the Project Approach and guides them through the process of developing and implementing a project in the classroom. Readings provide both practical knowledge and a theoretical framework, while assignments offer a flexible, step-by-step approach that allows teachers to learn in the process of trying out their first (or second or third) project in the classroom.

The Guide is an adaptation of the online course as taught by Project Approach founder, Sylvia Chard. It is still a little like a course but designed for a teacher to study for him or herself.

Journal prompts with each of the seven sections offer opportunities for teachers to reflect on and refine their strategies, ideas, and practices. Establishing a regular journal writing routine is a fundamental part of project-based teaching as this is a process that evolves with reflection and experience.

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Problem Solving Beyond the Classroom 1

Problem-solving Beyond the Classroom is written based on the Singapore Ministry of Education 2014 Mathematics syllabus.

Aligned with the successful My Pals are Here! Maths series, this book is packed with cross-referencing links to help reinforce the concepts and strategies learnt. Numerous teaching tips are incorporated to guide pupils through more advanced sums. 

Problem-solving heuristics methods are structured in a systematic way to stimulate critical thinking and boost the pupils’ ability and confidence through exposures to various types of problem sums. ‘The 4-Step Thinking Process’ approach breaks down the heuristic methods in a way that is easy to digest and understand for pupils who are building up their Mathematical foundations.

Unit 1: Addition and Subtraction within 10 (Heuristics: Systematic Listening) Unit 2: Shapes and Patterns (Heuristics: Mathematical Investigation with Shapes) Unit 3: Addition and Subtraction within 20 (Heuristics: Look for A Pattern/ Numbers) Unit 4: Addition and Subtraction within 40 (Heuristics: Look for A Pattern/Numbers) Unit 5: Multiplication(Heuristics: Working Backwards) Unit 6: Division (Heuristics: Make a Table) Unit 7: Addition and Subtraction within 100 (Heuristics: Mathematical Investigation with Numbers) Unit 8: Money (Heuristics: Guess and Check)

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9 Beyond Behavioral Objectives: Problem Solving and Constructivism 

“There are many ways to learn and many ways of encouraging different forms of learning with different ends in view. At the heart of the decision process, there must be a value judgment about how the mind should be cultivated to what end.” –Jerome Bruner

Introduction

Most experts agree that behavioral objectives have a place in the curriculum, but most experts agree that it is important to include other kinds of objectives that encourage critical and creative thinking (White, 2018). When engaging in problem-solving, constructivist, and experiential learning, it is important to go beyond behavioral objectives.

According to the Center for Teaching Excellence at the University of Waterloo, “True problem-solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem-solver has not seen before, to obtain a satisfactory solution.”

Wilson (2020) states that:

There are two alternate forms of writing objectives beyond behavioral ones – they are problems-solving objectives and expressive activities that lead to expressive outcomes [such as in the fine or visual arts, drama, etc.]. Teachers should know how to use these because they extend the artistry of the profession. More importantly, they can be crafted to provide students with powerful types of learning activities that encourage higher-level thinking skills and that are closely aligned to learning experiences in the real world.

In simpler terms, behavioral objectives refer to objectives that are measurable and observable as determined and stated prior to the lesson, and problem-solving objectives refer to objectives that are revealed as a result of student inquiry and self-directed learning. For more details about problem-solving and expressive objectives, access Wilson’s slide show at Beyond Behavioral Objectives .

Essential Questions

• Behavioral objectives have a place in curriculum, but it is also important to have non-behavioral objectives. Why?
• What are two alternative ways of writing objectives?
• What skills do students need to have to do problem-solving?
• What challenge is posed when working with both expert and novice problem-solvers?

Insight 9.1

Problem-solving can be an exciting and engaging way to teach because the students become more invested in learning that is creative, “hands-on” with a teacher as a “guide-on-the-side” and not just the “sage-on-the-stage.” As a classroom teacher, I discovered that students who were bored with the traditional read-and-answer-the-questions format became motivated and excited about learning when they were able to identify a problem, apply strategies to solve the problem, and work together for a solution. Students do not necessarily have the strategies initially, so sometimes there is a trial-and-error period that involves important learning about what does not work and why . One of the benefits of problem-solving is that the skills and strategies can be transferred to other subjects and even to the real world.

In one instance during a math lesson, the students were having difficulty with division, and they did not understand what 20 divided by five meant. In a small group, we counted out 20 beans, and I asked the students to pretend that there were five mice who each wanted beans, but they had to be divided evenly.  The students decided that they could use five small paper plates, one for each mouse. The students divided the 20 beans, one at a time, and placed them onto the five plates. Voila! Each plate had four beans! It was a fair way to divide the 20 beans. I then showed the students how to write the equation: 20/5. Later, we looked at the inverse process: 4 x 5 = 20. That made sense to them, too. They then came up with their own problems and worked them out with beans and plates and their newly acquired problem-solving skills.

It would be very simple to write a behavioral objective for the first part of the lesson:

“The students will use 20 beans and five paper plates to solve the equation 20/ 5= 4,” but there would not be a way to write discrete behavioral objectives for the problems the students posed later. Creative thinking and problem-solving go beyond discrete objectives because the students are provided with a “window of opportunity” to pose and solve their own problems.

However, the complicating factor is that the objective was written prior to the lesson. Because there are multiple ways of solving the problem, several students might be able to get the correct answer using different methods: paper and pencil computation, separating the beans, etc.  This would make an excellent discussion after the students shared their answers so they could see that problems can be solved in different ways. This concept fits the larger goal of problem-solving.

Problem-solving Through Constructivist Learning

In many traditional classrooms, teachers present the behavioral objectives and information to the students at the beginning of the lesson. This process is often effective and can be very appropriate because the teacher can present much information in a short period of time. It can be an efficient way of teaching although the students must absorb the information “upfront.” In constructivist teaching, the process becomes more meaningful because the students are more fully engaged in solving the problem, so there is a higher probability that they will retain the concepts.

When teaching focuses on students and challenging their perceptions, students report a deeper involvement with learning the subject (Trigwell, Prosser & Waterhouse, 2004). Proponents of constructivism believe that if teachers shift their teaching practices, especially in math and science, it will increase student achievement (Nyagah, 2017). The following insight illustrates how problem-solving and inquiry can be powerful learning models.

Insight 9.2

On September 11, 2001, Vicky, one of my teaching colleagues, had planned to teach a literacy lesson on Colorado history using multiple texts. When the news from New York was broadcast, everything in the 4th-grade classroom stopped.

“Why were the buildings in New York brought down?” one student asked.

“What happened to the people?” asked another.

The teacher answered the questions as best she could then promised the children they would learn more the next day. Vicky spent time that evening developing a unit on the events of September 11, and she chose books that would help 4th-grade students understand what had happened in the context of other accidental and purposeful events with tragic results, as well as books on New York as a center of trade, and the bravery of first responders and citizens in other situations. One group that she deemed most mature read screened articles about the causes of the September 11th tragedy.

The children were motivated to read about their topics. They asked and answered questions and discussed the new concepts they had learned. At the end of the unit, they shared what they learned from different sources and came up with five conclusions, beginning with “Sometimes things happen that we don’t understand, and we want to learn more about them.”

Vicky’s unit required the students to find out why the September 11th event, as well as events such as fires and collapsing bridges, had occurred, and what they learned as a result of reading about these topics. She said that at the end of the unit, the students had gained knowledge about what happened on September 11, as well as tragedies that had happened in other places, how brave people responded, and what they learned from the events. The problem-solving objectives were not stated at the beginning of the unit because it was uncertain at that time what the students would learn. Their discussions and critical thinking defined what was learned. I should note here that Vicky was a veteran teacher who was in communication with parents and had experience in guiding children in constructivist lessons.

For this experience, Vicky was guided by the following principles suggested by Honebein (1996), which summarize the seven pedagogical goals of constructivist learning environments:

Teaching Problem Solving

The Vanderbilt Center For Teaching offers these additional “ Tips and Techniques ” for teaching problem-solving.

Communicate

• Have students  identify specific problems, difficulties, or confusion . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work their problem out loud . This slows down the thinking process, making it more accurate and allowing them to access understanding of the process.
• Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column.
• This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems.
• Two-Column Solution (Math)
• Two-Column Solution (Physics)

Encourage Independence

• Model the problem-solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts, and make your thinking clear.
• Have students work through problems on their own. Ask directing questions or give helpful suggestions but  provide only minimal assistance and only when needed to overcome obstacles.
• Students can frequently help each other and talking about a problem helps them think more critically about the steps needed to solve the problem.
• Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others.

Be Sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning.
• It is important to recognize this when students come to us for help and to give each student some feeling of mastery.
• Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK not to have an instant solution.
• This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem-solving through a step-by-step process.

Interactive Learning Activity (ILA) 9.0

Which problem-solving technique resonated with you? Was it something that “worked” for you or your students? Use the ILA Responses Group for your responses.

Expert vs. Novice Problem-Solvers

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem-solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem-solving skills,  a teacher should be aware of the principles and strategies of good problem-solving in his or her discipline .

The mathematician George Polya captured the problem-solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes a summary of Polya’s problem-solving heuristic as well as advice on the teaching of problem-solving.

Novices in a particular field typically have not yet developed effective problem-solving principles and strategies. Helping students identify their own problem-solving errors is part of helping them develop effective problem-solving skills. Beverly Black and Elizabeth Axelson’s  list of common problem-solving errors , adapted from Arthur Whimbey and Jack Lochhead’s book Problem Solving and Comprehension (Lawrence Erlbaum, 1999), provides useful insight into the mindset of a novice problem solver.

The Vanderbilt Center for Teaching has an Open Educational Resource at their Center for Teaching Guide that offers Tips and Techniques for Teaching Problem Solving .

An excellent video by Michael Arnold describes some very innovative ways to teach children how to solve problems, and how we can find the “Lost Einsteins.”

Insight 9.3

Lessons with objectives provide a solid structure for curriculum planning and lessons, but inquiry and problem-solving provide a different dimension for student learning that can motivate and engage student learning at a deep level.

Problem-solving and creative thinking can be an exciting way to teach and an engaging way for students to learn because it is connected to the real world.

While traditional learning holds to single answers, problem-solving can lead to multiple solutions and even new problems. Since the process is more important than the product, teachers function best if they have collaborative learning and a supportive classroom atmosphere that encourages risk-taking.

Curriculum Essentials: A Journey Copyright © 2021 by Linda J. Button, Ed.D. is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

Inviting Uncertainty into the Classroom

1. View (Good) Uncertainty as an Opportunity

2. try lesson unplanning, 3. assign complex challenges, 4. explore the backstory of famous solutions, 5. launch never-ending projects, the beautiful risk.

Premium Resource

• What is the problem? Identifying a problem that's relevant to students is the first step. Potential challenges or problems can emerge from what students are learning in class or what they're experiencing in their lives, schools, homes, or neighborhoods.
• Why does it matter? Once students have identified a challenge, they need to understand why it needs to be addressed. This includes learning more about the challenge, obtaining feedback and perspectives from various stakeholders, and becoming able to articulate to others the importance of addressing this problem.
• What are we going to do about it? Students must start developing a plan for addressing the problem by drawing on their existing relevant knowledge, identifying areas where they need additional information, establishing external partnerships, and identifying initial steps to take.
• What lasting legacy will our work addressing this problem leave? This question distinguishes legacy challenges from other kinds of problem-solving efforts. It requires students to take a long view of the challenge and identify how their work will be sustained, curated, and passed on from one generation of students and project partners to the next.

Beghetto, R. A. (forthcoming). What if? Unleashing the power of complex challenges in teaching and learning . Alexandria, VA: ASCD.

Beghetto, R. A. (2017). Legacy projects: Helping young people respond productively to the challenges of a changing world. Roeper Review , 39 , 1–4.

Beghetto, R. A. (2016a). Big wins, small steps: How to lead for and with creativity . Thousand Oaks, CA: Corwin.

Beghetto, R. A. (2016b). Leveraging micro-opportunities to address macroproblems: Toward an unshakeable sense of possibility thinking. In D. Ambrose & R. J. Sternberg (Eds.) Creative intelligence in the 21st Century: Grappling with enormous problems and huge opportunities (pp. 159–174). Rotterdam: Sense.

Lee, H. S., & Anderson, J. R. (2013). Student learning: What has instruction got to do with it? Annual Review of Psychology , 64 , 445–469.

Niu, W., & Zhou, Z. (2010). Creativity in mathematics teaching: A Chinese perspective. In R. A. Beghetto and J. C. Kaufman (Eds.) Creativity in the classroom (pp. 270–288). New York: Cambridge University Press.

Root-Bernstein, R., & Root-Bernstein, M. (2017). People, passions, problems: The role of creative exemplars in teaching for creativity. In R. A. Beghetto & B. Sriraman (Eds.), Creative Contradictions in Education (pp. 143–164). Switzerland: Springer.

Stone, A. (April, 2016). Science Fair 2016: Meet the next generation of America's innovators. Retrieved from https://obamawhitehouse.archives.gov/blog/2016/04/08/science-fair-2016-meet-next-generation-americas-innovators

Ronald A. Beghetto is an internationally recognized expert on creativity in educational settings. He is professor of educational psychology in the Neag School of Education and director of the Innovation House at the University of Connecticut. He is editor-in-chief of the  Journal of Creative Behavior  and a fellow of the American Psychological Association and the Society for the Psychology of Aesthetics, Creativity and the Arts.

Beghetto has published seven books and more than 100 articles and scholarly book chapters on creative and innovative approaches to teaching, learning, and leadership in schools and classrooms. He speaks and provides workshops around the world on issues related to helping teachers and instructional leaders develop new and transformative possibilities for classroom teaching, learning, and leadership in K–12 and higher education settings.

ASCD is a community dedicated to educators' professional growth and well-being.

Let us help you put your vision into action., related articles.

Teaching for Total Participation

Adapting Discussions to Unpredictable Attendance

Taking Risks with Rough Draft Teaching

Been to a Good Lecture?

Creating Autonomy Within Fidelity

From our issue.

Why Schools Need to Change Purpose and Problem-Solving: Developing Leaders in the Classroom

Taiwo A. Togun (he, him, his) Faculty, Pierrepont School, and Co-Founder & Executive Director, InclusionBridge, Inc. in Connecticut

Today’s learners face an uncertain present and a rapidly changing future that demand far different skills and knowledge than were needed in the 20th century. We also know so much more about enabling deep, powerful learning than we ever did before. Our collective future depends on how well young people prepare for the challenges and opportunities of 21st-century life.

As educators transform learning in their classrooms, they can develop their students ’ talent and their own leadership while also making a difference for their community.

“Purpose is a stable and generalized intention to accomplish something that is at once meaningful to the self and consequential to the world beyond the self” –Bill Damon, Professor of Education, Stanford University

As an educator, my purpose is to nurture and develop young talents. While I have been teaching for over a decade, I only articulated my purpose as an educator last year during my master’s program in technology leadership while learning to integrate technology, strategy, and leadership. Coincidentally, I became a Project Invent fellow at the same time, which only served to embolden my sense of purpose. Clarity of purpose is a vital leadership quality that shapes my experience and something I believe ought to begin every teacher’s leadership journey. While one’s articulation of purpose may change over time, there’s something quite powerful and differently effective about writing down and reading out loud your purpose statement. In the following reflection, my goal is to share how I approach my development as an educator and a leader as one and the same and how my experience with Project Invent’s design thinking curriculum represents a continuing education in leadership.

Developing a Leadership Identity

As I work toward establishing my leadership identity and persona as an educator, I find myself reflecting on Sun Tzu’s Art Of War in which he described “ Leadership [as] a matter of intelligence, trustworthiness, humaneness, courage, and discipline. ” Additional discourses from the likes of Thomas Carlyle , Tolstoy , and Plato have all helped me arrive at an understanding of leadership as a function of nature, nurture, and situation . In addition to clarity of purpose, other leadership qualities must be deliberately nurtured through training and cultivated through practicing acts of leadership. I believe an effective leader empowers others and recognizes situations when the act of leadership is, in fact, letting others lead. This summarizes the core takeaway of my “teacher as a leader” philosophy.

In 2021, I applied to Project Invent’s educator fellowship , hoping to reinforce my leadership identity as an educator. Project Invent is a nonprofit organization that trains educators in six key teacher practices, each aimed at empowering students with the mindsets to become fearless, compassionate, and creative problem solvers. As a Project Invent Fellow, I have made significant progress in mastering these six teacher practices:

• Make failure okay
• Push to the next level
• Be a co-learner
• Let students take the wheel
• Leave room for exploration
• Challenge assumptions

Courtesy of Project Invent

Leadership in Practice

Each of these teacher practices can occur independently but are often interrelated. Deliberately committing to one can undoubtedly lead to others. For example, being comfortable with being a co-learner allows space for leaving room for exploration of alternatives. Openness to the possibility of new alternatives begets making failure okay and also encourages letting students take the wheel and drive the process, while the teacher-leader nudges them to push to the next level. Of course, the order of these is not fixed.

I teach computer science at Pierrepont School in Westport, Connecticut. My Project Invent student teams come from two classes of juniors and seniors, who originally signed up for an Applied Data Science course. We began our journey in the second semester in January, after which the students were informed that their course name had changed from “Applied Data Science” to “Essential Skills of the Emerging Economy” which has two parts: “Critical Reasoning & Storytelling with Data” and “Human-centered Problem-solving.” These are the only details my brave students had to work with. Needless to say, students had to be open-minded about how the journey would shape up. After all, it is not the first time that I would modify course requirements to marry interests and new opportunities that would benefit my students. I enjoy such flexibility and reasonable autonomy at my school; I also enjoy the flexibility and reasonable autonomy of learning as I teach. I am comfortable admitting to my students that I have absolutely no idea how to solve a challenge that I assign them, but assure them we can figure it out together… and we always do.

In January, the challenge was dauntingly ambiguous: We were going to invent a new technology intended to positively impact members of our community. Given their awareness of how little I knew about what we might need, or how to invent anything for that matter, students had to buy into taking a journey with an uncertain destination together. My job as a co-learner was to make sure to emphasize that it was all about the journey, the lessons, and the fun we have; and not necessarily the end. The humility and willingness to be a co-learner with students in the driver's seat have served me very well throughout my journey as a teacher, and I can not begin to describe the gratification of learning with and from students and seeing them rise to the challenge. This time, however, we had access to a community of resources, fellows, and mentors through the extended Project Invent team, who made it even more reassuring despite the many unknowns. From the onset of our journey, my students demonstrated creative confidence and trust in one another (most of the time) and our system as a class. Together as a team, we were ready and excited for the journey.

“Coming into this class with a limited computer science background, I was a little intimidated to embark on a project that had the potential to create such a big and meaningful improvement in our community. However, as I grew more comfortable with my team, my fears eased. I was able to develop from a quiet listener to a confident doer, not only for the duration of this project but also in my longer-term data science pursuits.” –Alexis Bienstock, Pierrepont School Junior

Project Invent as Context for Leadership Development

Human-centeredness brings a new dimension to problem-solving. It helps to establish and define a worthy purpose. My students and I began our journey on our Project Invent experience by getting to know our “client” Roderick Sewell , a Paralympic athlete and swimmer, as a person—what he enjoys doing, how he got to become a serious athlete, and what his goals and aspirations are. We focused on his abilities, accomplishments, and strengths. This set the stage for helping us—students and teachers alike—cultivate mindsets of empathy and curiosity. It is this empathic curiosity that would eventually lead to two Project Invent teams of ambitious students, who set out to address Roderick’s expressed challenges of lower back pain and efficient switch from running to walking legs:

“Because there’s nothing to absorb the load except for my lower back…If there was a little more cushioning on the soles to absorb the impact, then everything would be even more doable.” “ I can’t really run with my walking leg. One question that I always have is if something happened, how fast would I be able to get up and get away? ” –Roderick Sewell

Team SNAILS, a team of one senior and five juniors, proposed and prototyped an invention they called Quick Switch Support Shoe (“QS-cubed”), a multifunctional prosthetic foot support with adjustable springs to minimize back pain and maximize run-walk efficiency for their community partner.

Team Pierrepont Innovators with three seniors and four juniors had the ambitious goal of completely redesigning Roderick’s prosthetic ankle with a dashpot or snubber mechanism and incorporating more effective shock-absorbing materials. They wrestled with disappointments as they came to terms with reality and time constraints, and the team eventually demonstrated resilience and agency as they made a pivot to capitalize on their research of Shock-absorbing materials. They developed a pitch to prosthetic companies which can incorporate their research insights to further possible impact.

The larger purpose of our 10-week journey into design thinking was our connection with Roderick’s expressed discomfort. This purpose shaped our introduction to need-finding, synthesizing and ideation, idea selection and prototyping, prototype refinement, and pitching. Students persevered through their fears, disagreements, and disappointments; they made it work because they did not think it was about them but rather about what they could contribute to support Roderick.

“Our community partner Roderick Sewell is the first bilateral above-the-knee amputee to finish the IRONMAN World Championship. As a serious athlete, he needs to feel his best to perform his best—and that’s our charge!” –Team Pierrepont Innovators

“Working on Project Invent provided me with an appreciation for Roderick Sewell and the time I spend with my classmates. The opportunity to learn Roderick’s story as we worked with him to develop solutions to his lower back pain proved to be the most rewarding part of the process.” –Hagen Feeney, Pierrepont School Senior

Understanding the Journey

“He who has a why to live for can bear almost any how.” –Friedrich Nietzsche

By default, as educators we teach process; learning to solve problems in several different ways is central to our training, and sometimes that dominates our lessons to students. The Project Invent experience helps educators and students alike to prioritize the “why” and “what” of our learning over the “how.” The Project Invent experience added the very essential element of “purpose” which helped my students and me push the boundaries of the typical project-based, creative problem-solving classroom experience. Indeed, such an experience only thrives in and helps to foster a culture of caring, purpose, learning, and enjoyment (all in the dimension of flexibility to respond to change)—the kind of culture espoused by our school, Pierrepont culture ! Through our experience with human-centered problem-solving, students and teachers alike have cultivated practices and mindsets that are necessary to become leaders.

Every Leader Needs a Community and a Support System

“Leadership without support is like trying to make bricks without enough straw. True leaders reinforce their ideas and plan with strategic partnerships, alliances, and supportive audiences.” –Reed Markham, Ph.D.

In addition to the Pierrepont culture that presented a fertile soil for the teacher practices and students’ mindsets we needed, the Project Invent community and support system were so important for us. I recall the confidence boost and reassurance from our first session with a volunteer expert, Valerie Peng, an engineer who builds robots for a living. Not only did my team get to soak invaluable information that was relevant for advancing our project, but we were also all inspired by the passion with which she shared her work with us. Similarly, I found renewed strength and motivation with each conversation with Project Invent staff members and other fellows. In our shared space as educator-leaders, my co-fellows and I were able to explore possible solutions to shared challenges like keeping students motivated through their fears and disappointments, navigating operational logistics and schedule challenges, etc. I am indeed grateful for such a community as it helps to know you are not alone.

Beyond the Classroom

The teacher as leader practices cultivated during my Project Invent experience has affected my work beyond Pierrepont. With clarity of purpose and the necessary focus on impact and human-centeredness, my data science consulting company has embarked on a renewed mission to diversify the data science workforce and bridge the gap to full and equal participation in the emerging digital economy through InclusionBridge . Indeed, the Project Invent experience provided a complementary lens for me to refine my purpose—my journey—of nurturing and developing young talents through problem-solving and meaningful learning experiences. I enjoy creating and facilitating opportunities to help students become fearless, compassionate young leaders.

Image at top is a slide from the student project presentation by Team SNAILS, Pierrepont School.

Taiwo A. Togun (he, him, his)

Faculty, pierrepont school, and co-founder & executive director, inclusionbridge, inc..

Taiwo is an educator, a data scientist, and a social entrepreneur who is passionate about nurturing and developing young talent. He is the architect and director of the Computer Science program and Innovation Lab at Pierrepont School , a private K-12 where he enjoys the challenge of making computer programming and problem-solving skills accessible to students at all levels. Dr. Togun is a visiting scientist at the Boykin Lab at the Department of Cognitive, Linguistic, and Psychological Sciences at Brown University, supporting research to elucidate perceptions of fairness in machine learning algorithms. With a Ph.D. in computational biology & bioinformatics from Yale and a master's in technology leadership from Brown, he combines data science, technology, strategy, and leadership as co-founder and executive director of InclusionBridge . Through InclusionBridge, Taiwo and his team are on a mission to increase diversity in the data science workforce through internships and training programs for underrepresented talent. Follow Taiwo on LinkedIn .

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Problem Solving in and Beyond the Classroom: Perspectives and Products from Participants in a Web-Based Mathematical Competition

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Helia Jacinto

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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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A meta-analysis to gauge the impact of pedagogies employed in mixed-ability high school biology classrooms

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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Received : 07 August 2022

Accepted : 04 January 2023

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DOI : https://doi.org/10.1057/s41599-023-01508-1

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