problem solving in schools

Why Every Educator Needs to Teach Problem-Solving Skills

Strong problem-solving skills will help students be more resilient and will increase their academic and career success .

Want to learn more about how to measure and teach students’ higher-order skills, including problem solving, critical thinking, and written communication?

Problem-solving skills are essential in school, careers, and life.

Problem-solving skills are important for every student to master. They help individuals navigate everyday life and find solutions to complex issues and challenges. These skills are especially valuable in the workplace, where employees are often required to solve problems and make decisions quickly and effectively.

Problem-solving skills are also needed for students’ personal growth and development because they help individuals overcome obstacles and achieve their goals. By developing strong problem-solving skills, students can improve their overall quality of life and become more successful in their personal and professional endeavors.

Problem-Solving Skills Help Students…

develop resilience.

Problem-solving skills are an integral part of resilience and the ability to persevere through challenges and adversity. To effectively work through and solve a problem, students must be able to think critically and creatively. Critical and creative thinking help students approach a problem objectively, analyze its components, and determine different ways to go about finding a solution.

This process in turn helps students build self-efficacy . When students are able to analyze and solve a problem, this increases their confidence, and they begin to realize the power they have to advocate for themselves and make meaningful change.

When students gain confidence in their ability to work through problems and attain their goals, they also begin to build a growth mindset . According to leading resilience researcher, Carol Dweck, “in a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment.”

Set and Achieve Goals

Students who possess strong problem-solving skills are better equipped to set and achieve their goals. By learning how to identify problems, think critically, and develop solutions, students can become more self-sufficient and confident in their ability to achieve their goals. Additionally, problem-solving skills are used in virtually all fields, disciplines, and career paths, which makes them important for everyone. Building strong problem-solving skills will help students enhance their academic and career performance and become more competitive as they begin to seek full-time employment after graduation or pursue additional education and training.

Resolve Conflicts

In addition to increased social and emotional skills like self-efficacy and goal-setting, problem-solving skills teach students how to cooperate with others and work through disagreements and conflicts. Problem-solving promotes “thinking outside the box” and approaching a conflict by searching for different solutions. This is a very different (and more effective!) method than a more stagnant approach that focuses on placing blame or getting stuck on elements of a situation that can’t be changed.

While it’s natural to get frustrated or feel stuck when working through a conflict, students with strong problem-solving skills will be able to work through these obstacles, think more rationally, and address the situation with a more solution-oriented approach. These skills will be valuable for students in school, their careers, and throughout their lives.

Achieve Success

We are all faced with problems every day. Problems arise in our personal lives, in school and in our jobs, and in our interactions with others. Employers especially are looking for candidates with strong problem-solving skills. In today’s job market, most jobs require the ability to analyze and effectively resolve complex issues. Students with strong problem-solving skills will stand out from other applicants and will have a more desirable skill set.

In a recent opinion piece published by The Hechinger Report , Virgel Hammonds, Chief Learning Officer at KnowledgeWorks, stated “Our world presents increasingly complex challenges. Education must adapt so that it nurtures problem solvers and critical thinkers.” Yet, the “traditional K–12 education system leaves little room for students to engage in real-world problem-solving scenarios.” This is the reason that a growing number of K–12 school districts and higher education institutions are transforming their instructional approach to personalized and competency-based learning, which encourage students to make decisions, problem solve and think critically as they take ownership of and direct their educational journey.

Problem-Solving Skills Can Be Measured and Taught

Research shows that problem-solving skills can be measured and taught. One effective method is through performance-based assessments which require students to demonstrate or apply their knowledge and higher-order skills to create a response or product or do a task.

What Are Performance-Based Assessments?

With the No Child Left Behind Act (2002), the use of standardized testing became the primary way to measure student learning in the U.S. The legislative requirements of this act shifted the emphasis to standardized testing, and this led to a decline in nontraditional testing methods .

But many educators, policy makers, and parents have concerns with standardized tests. Some of the top issues include that they don’t provide feedback on how students can perform better, they don’t value creativity, they are not representative of diverse populations, and they can be disadvantageous to lower-income students.

While standardized tests are still the norm, U.S. Secretary of Education Miguel Cardona is encouraging states and districts to move away from traditional multiple choice and short response tests and instead use performance-based assessment, competency-based assessments, and other more authentic methods of measuring students abilities and skills rather than rote learning.

Performance-based assessments measure whether students can apply the skills and knowledge learned from a unit of study. Typically, a performance task challenges students to use their higher-order skills to complete a project or process. Tasks can range from an essay to a complex proposal or design.

Preview a Performance-Based Assessment

Want a closer look at how performance-based assessments work? Preview CAE’s K–12 and Higher Education assessments and see how CAE’s tools help students develop critical thinking, problem-solving, and written communication skills.

Performance-Based Assessments Help Students Build and Practice Problem-Solving Skills

In addition to effectively measuring students’ higher-order skills, including their problem-solving skills, performance-based assessments can help students practice and build these skills. Through the assessment process, students are given opportunities to practically apply their knowledge in real-world situations. By demonstrating their understanding of a topic, students are required to put what they’ve learned into practice through activities such as presentations, experiments, and simulations.

This type of problem-solving assessment tool requires students to analyze information and choose how to approach the presented problems. This process enhances their critical thinking skills and creativity, as well as their problem-solving skills. Unlike traditional assessments based on memorization or reciting facts, performance-based assessments focus on the students’ decisions and solutions, and through these tasks students learn to bridge the gap between theory and practice.

Performance-based assessments like CAE’s College and Career Readiness Assessment (CRA+) and Collegiate Learning Assessment (CLA+) provide students with in-depth reports that show them which higher-order skills they are strongest in and which they should continue to develop. This feedback helps students and their teachers plan instruction and supports to deepen their learning and improve their mastery of critical skills.

Explore CAE’s Problem-Solving Assessments

CAE offers performance-based assessments that measure student proficiency in higher-order skills including problem solving, critical thinking, and written communication.

College and Career Readiness Assessment (CCRA+) for secondary education and
Collegiate Learning Assessment (CLA+) for higher education.

Our solution also includes instructional materials, practice models, and professional development.

We can help you create a program to build students’ problem-solving skills that includes:

Measuring students’ problem-solving skills through a performance-based assessment
Using the problem-solving assessment data to inform instruction and tailor interventions
Teaching students problem-solving skills and providing practice opportunities in real-life scenarios
Supporting educators with quality professional development

Get started with our problem-solving assessment tools to measure and build students’ problem-solving skills today! These skills will be invaluable to students now and in the future.

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Teaching problem solving: Let students get ‘stuck’ and ‘unstuck’

Subscribe to the center for universal education bulletin, kate mills and km kate mills literacy interventionist - red bank primary school helyn kim helyn kim former brookings expert @helyn_kim.

October 31, 2017

This is the second in a six-part blog series on teaching 21st century skills , including problem solving , metacognition , critical thinking , and collaboration , in classrooms.

In the real world, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts.

Here’s what Kate Mills, who taught 4 th grade for 10 years at Knollwood School in New Jersey and is now a Literacy Interventionist at Red Bank Primary School, has to say about creating a classroom culture of problem solvers:

Helping my students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum. From the first day of school, I intentionally choose language and activities that help to create a classroom culture of problem solvers. I want to produce students who are able to think about achieving a particular goal and manage their mental processes . This is known as metacognition , and research shows that metacognitive skills help students become better problem solvers.

I begin by “normalizing trouble” in the classroom. Peter H. Johnston teaches the importance of normalizing struggle , of naming it, acknowledging it, and calling it what it is: a sign that we’re growing. The goal is for the students to accept challenge and failure as a chance to grow and do better.

I look for every chance to share problems and highlight how the students— not the teachers— worked through those problems. There is, of course, coaching along the way. For example, a science class that is arguing over whose turn it is to build a vehicle will most likely need a teacher to help them find a way to the balance the work in an equitable way. Afterwards, I make it a point to turn it back to the class and say, “Do you see how you …” By naming what it is they did to solve the problem , students can be more independent and productive as they apply and adapt their thinking when engaging in future complex tasks.

After a few weeks, most of the class understands that the teachers aren’t there to solve problems for the students, but to support them in solving the problems themselves. With that important part of our classroom culture established, we can move to focusing on the strategies that students might need.

Here’s one way I do this in the classroom:

I show the broken escalator video to the class. Since my students are fourth graders, they think it’s hilarious and immediately start exclaiming, “Just get off! Walk!”

When the video is over, I say, “Many of us, probably all of us, are like the man in the video yelling for help when we get stuck. When we get stuck, we stop and immediately say ‘Help!’ instead of embracing the challenge and trying new ways to work through it.” I often introduce this lesson during math class, but it can apply to any area of our lives, and I can refer to the experience and conversation we had during any part of our day.

Research shows that just because students know the strategies does not mean they will engage in the appropriate strategies. Therefore, I try to provide opportunities where students can explicitly practice learning how, when, and why to use which strategies effectively so that they can become self-directed learners.

For example, I give students a math problem that will make many of them feel “stuck”. I will say, “Your job is to get yourselves stuck—or to allow yourselves to get stuck on this problem—and then work through it, being mindful of how you’re getting yourselves unstuck.” As students work, I check-in to help them name their process: “How did you get yourself unstuck?” or “What was your first step? What are you doing now? What might you try next?” As students talk about their process, I’ll add to a list of strategies that students are using and, if they are struggling, help students name a specific process. For instance, if a student says he wrote the information from the math problem down and points to a chart, I will say: “Oh that’s interesting. You pulled the important information from the problem out and organized it into a chart.” In this way, I am giving him the language to match what he did, so that he now has a strategy he could use in other times of struggle.

The charts grow with us over time and are something that we refer to when students are stuck or struggling. They become a resource for students and a way for them to talk about their process when they are reflecting on and monitoring what did or did not work.

For me, as a teacher, it is important that I create a classroom environment in which students are problem solvers. This helps tie struggles to strategies so that the students will not only see value in working harder but in working smarter by trying new and different strategies and revising their process. In doing so, they will more successful the next time around.

Don’t Just Tell Students to Solve Problems. Teach Them How.

The positive impact of an innovative uc san diego problem-solving educational curriculum continues to grow.

Daniel Kane - [email protected]

Published Date

Not getting stuck

One of the overarching goals of this project is to teach both problem-identification and problem-solving skills that help students avoid getting stuck during the learning process. Stuck feelings lead to frustration – and when it’s a Science, Technology, Engineering and Math (STEM) project, that frustration can lead students to feel they don’t belong in a STEM major or a STEM career. Instead, the UC San Diego curriculum is designed to give students the tools that lead to reactions like “this class is hard, but I know I can do this!” – as Ogo, a celebrated high school biomedical sciences and technology teacher, put it.

Three years into the curriculum development effort, the light-hearted energy of the students combined with their intense focus points to success. On the last day of the class, Mourad Mjahed PhD, Director of the MESA Program at Southwestern College’s School of Mathematics, Science and Engineering came to UC San Diego to see the final project presentations made by his 22 MESA students.

“Industry is looking for students who have learned from their failures and who have worked outside of their comfort zones,” said Mjahed. The UC San Diego problem-solving curriculum, Mjahed noted, is an opportunity for students to build the skills and the confidence to learn from their failures and to work outside their comfort zone. “And from there, they see pathways to real careers,” he said.

What does it mean to explicitly teach problem solving?

This approach to teaching problem solving includes a significant focus on learning to identify the problem that actually needs to be solved, in order to avoid solving the wrong problem. The curriculum is organized so that each day is a complete experience. It begins with the teacher introducing the problem-identification or problem-solving strategy of the day. The teacher then presents case studies of that particular strategy in action. Next, the students get introduced to the day’s challenge project. Working in teams, the students compete to win the challenge while integrating the day’s technique. Finally, the class reconvenes to reflect. They discuss what worked and didn't work with their designs as well as how they could have used the day’s problem-identification or problem-solving technique more effectively.

The challenges are designed to be engaging – and over three years, they have been refined to be even more engaging. But the student engagement is about much more than being entertained. Many of the students recognize early on that the problem-identification and problem-solving skills they are learning can be applied not just in the classroom, but in other classes and in life in general.

Gabriel from Southwestern College is one of the students who saw benefits outside the classroom almost immediately. In addition to taking the UC San Diego problem-solving course, Gabriel was concurrently enrolled in an online computer science programming class. He said he immediately started applying the UC San Diego problem-identification and troubleshooting strategies to his coding assignments.

Gabriel noted that he was given a coding-specific troubleshooting strategy in the computer science course, but the more general problem-identification strategies from the UC San Diego class had been extremely helpful. It’s critical to “find the right problem so you can get the right solution. The strategies here,” he said, “they work everywhere.”

Phan echoed this sentiment. “We believe this curriculum can prepare students for the technical workforce. It can prepare students to be impactful for any career path.”

The goal is to be able to offer the course in community colleges for course credit that transfers to the UC, and to possibly offer a version of the course to incoming students at UC San Diego.

As the team continues to work towards integrating the curriculum in both standardized high school courses such as physics, and incorporating the content as a part of the general education curriculum at UC San Diego, the project is expected to impact thousands more students across San Diego annually.

Portrait of the Problem-Solving Curriculum

On a sunny Wednesday in July 2023, an experiential-learning classroom was full of San Diego community college students. They were about half-way through the three-week problem-solving course at UC San Diego, held in the campus’ EnVision Arts and Engineering Maker Studio. On this day, the students were challenged to build a contraption that would propel at least six ping pong balls along a kite string spanning the laboratory. The only propulsive force they could rely on was the air shooting out of a party balloon.

A team of three students from Southwestern College – Valeria, Melissa and Alondra – took an early lead in the classroom competition. They were the first to use a plastic bag instead of disposable cups to hold the ping pong balls. Using a bag, their design got more than half-way to the finish line – better than any other team at the time – but there was more work to do.

As the trio considered what design changes to make next, they returned to the problem-solving theme of the day: unintended consequences. Earlier in the day, all the students had been challenged to consider unintended consequences and ask questions like: When you design to reduce friction, what happens? Do new problems emerge? Did other things improve that you hadn’t anticipated?

Other groups soon followed Valeria, Melissa and Alondra’s lead and began iterating on their own plastic-bag solutions to the day’s challenge. New unintended consequences popped up everywhere. Switching from cups to a bag, for example, reduced friction but sometimes increased wind drag.

Over the course of several iterations, Valeria, Melissa and Alondra made their bag smaller, blew their balloon up bigger, and switched to a different kind of tape to get a better connection with the plastic straw that slid along the kite string, carrying the ping pong balls.

One of the groups on the other side of the room watched the emergence of the plastic-bag solution with great interest.

“We tried everything, then we saw a team using a bag,” said Alexander, a student from City College. His team adopted the plastic-bag strategy as well, and iterated on it like everyone else. They also chose to blow up their balloon with a hand pump after the balloon was already attached to the bag filled with ping pong balls – which was unique.

“I don’t want to be trying to put the balloon in place when it's about to explode,” Alexander explained.

Asked about whether the structured problem solving approaches were useful, Alexander’s teammate Brianna, who is a Southwestern College student, talked about how the problem-solving tools have helped her get over mental blocks. “Sometimes we make the most ridiculous things work,” she said. “It’s a pretty fun class for sure.”

Yoshadara, a City College student who is the third member of this team, described some of the problem solving techniques this way: “It’s about letting yourself be a little absurd.”

Alexander jumped back into the conversation. “The value is in the abstraction. As students, we learn to look at the problem solving that worked and then abstract out the problem solving strategy that can then be applied to other challenges. That’s what mathematicians do all the time,” he said, adding that he is already thinking about how he can apply the process of looking at unintended consequences to improve both how he plays chess and how he goes about solving math problems.

Looking ahead, the goal is to empower as many students as possible in the San Diego area and beyond to learn to problem solve more enjoyably. It’s a concrete way to give students tools that could encourage them to thrive in the growing number of technical careers that require sharp problem-solving skills, whether or not they require a four-year degree.

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Problem Solving

Problem solving, a fundamental cognitive process deeply rooted in psychology, plays a pivotal role in various aspects of human existence, especially within educational contexts. This article delves into the nature of problem solving, exploring its theoretical underpinnings, the cognitive and psychological processes that underlie it, and the application of problem-solving skills within educational settings and the broader real world. With a focus on both theory and practice, this article underscores the significance of cultivating problem-solving abilities as a cornerstone of cognitive development and innovation, shedding light on its applications in fields ranging from education to clinical psychology and beyond, thereby paving the way for future research and intervention in this critical domain of human cognition.

Introduction

Problem solving, a quintessential cognitive process deeply embedded in the domains of psychology and education, serves as a linchpin for human intellectual development and adaptation to the ever-evolving challenges of the world. The fundamental capacity to identify, analyze, and surmount obstacles is intrinsic to human nature and has been a subject of profound interest for psychologists, educators, and researchers alike. This article aims to provide a comprehensive exploration of problem solving, investigating its theoretical foundations, cognitive intricacies, and practical applications in educational contexts. With a clear understanding of its multifaceted nature, we will elucidate the pivotal role that problem solving plays in enhancing learning, fostering creativity, and promoting cognitive growth, setting the stage for a detailed examination of its significance in both psychology and education. In the continuum of psychological research and educational practice, problem solving stands as a cornerstone, enabling individuals to navigate the complexities of their world. This article’s thesis asserts that problem solving is not merely a cognitive skill but a dynamic process with profound implications for intellectual growth and application in diverse real-world contexts.

Academic Writing, Editing, Proofreading, And Problem Solving Services

Get 10% off with 24start discount code, the nature of problem solving.

Problem solving, within the realm of psychology, refers to the cognitive process through which individuals identify, analyze, and resolve challenges or obstacles to achieve a desired goal. It encompasses a range of mental activities, such as perception, memory, reasoning, and decision-making, aimed at devising effective solutions in the face of uncertainty or complexity.

Problem solving as a subject of inquiry has drawn from various theoretical perspectives, each offering unique insights into its nature. Among the seminal theories, Gestalt psychology has highlighted the role of insight and restructuring in problem solving, emphasizing that individuals often reorganize their mental representations to attain solutions. Information processing theories, inspired by computer models, emphasize the systematic and step-by-step nature of problem solving, likening it to information retrieval and manipulation. Furthermore, cognitive psychology has provided a comprehensive framework for understanding problem solving by examining the underlying cognitive processes involved, such as attention, memory, and decision-making. These theoretical foundations collectively offer a richer comprehension of how humans engage in and approach problem-solving tasks.

Problem solving is not a monolithic process but a series of interrelated stages that individuals progress through. These stages are integral to the overall problem-solving process, and they include:

Problem Representation: At the outset, individuals must clearly define and represent the problem they face. This involves grasping the nature of the problem, identifying its constraints, and understanding the relationships between various elements.
Goal Setting: Setting a clear and attainable goal is essential for effective problem solving. This step involves specifying the desired outcome or solution and establishing criteria for success.
Solution Generation: In this stage, individuals generate potential solutions to the problem. This often involves brainstorming, creative thinking, and the exploration of different strategies to overcome the obstacles presented by the problem.
Solution Evaluation: After generating potential solutions, individuals must evaluate these alternatives to determine their feasibility and effectiveness. This involves comparing solutions, considering potential consequences, and making choices based on the criteria established in the goal-setting phase.

These components collectively form the roadmap for navigating the terrain of problem solving and provide a structured approach to addressing challenges effectively. Understanding these stages is crucial for both researchers studying problem solving and educators aiming to foster problem-solving skills in learners.

Cognitive and Psychological Aspects of Problem Solving

Problem solving is intricately tied to a range of cognitive processes, each contributing to the effectiveness of the problem-solving endeavor.

Perception: Perception serves as the initial gateway in problem solving. It involves the gathering and interpretation of sensory information from the environment. Effective perception allows individuals to identify relevant cues and patterns within a problem, aiding in problem representation and understanding.
Memory: Memory is crucial in problem solving as it enables the retrieval of relevant information from past experiences, learned strategies, and knowledge. Working memory, in particular, helps individuals maintain and manipulate information while navigating through the various stages of problem solving.
Reasoning: Reasoning encompasses logical and critical thinking processes that guide the generation and evaluation of potential solutions. Deductive and inductive reasoning, as well as analogical reasoning, play vital roles in identifying relationships and formulating hypotheses.

While problem solving is a universal cognitive function, individuals differ in their problem-solving skills due to various factors.

Intelligence: Intelligence, as measured by IQ or related assessments, significantly influences problem-solving abilities. Higher levels of intelligence are often associated with better problem-solving performance, as individuals with greater cognitive resources can process information more efficiently and effectively.
Creativity: Creativity is a crucial factor in problem solving, especially in situations that require innovative solutions. Creative individuals tend to approach problems with fresh perspectives, making novel connections and generating unconventional solutions.
Expertise: Expertise in a specific domain enhances problem-solving abilities within that domain. Experts possess a wealth of knowledge and experience, allowing them to recognize patterns and solutions more readily. However, expertise can sometimes lead to domain-specific biases or difficulties in adapting to new problem types.

Despite the cognitive processes and individual differences that contribute to effective problem solving, individuals often encounter barriers that impede their progress. Recognizing and overcoming these barriers is crucial for successful problem solving.

Functional Fixedness: Functional fixedness is a cognitive bias that limits problem solving by causing individuals to perceive objects or concepts only in their traditional or “fixed” roles. Overcoming functional fixedness requires the ability to see alternative uses and functions for objects or ideas.
Confirmation Bias: Confirmation bias is the tendency to seek, interpret, and remember information that confirms preexisting beliefs or hypotheses. This bias can hinder objective evaluation of potential solutions, as individuals may favor information that aligns with their initial perspectives.
Mental Sets: Mental sets are cognitive frameworks or problem-solving strategies that individuals habitually use. While mental sets can be helpful in certain contexts, they can also limit creativity and flexibility when faced with new problems. Recognizing and breaking out of mental sets is essential for overcoming this barrier.

Understanding these cognitive processes, individual differences, and common obstacles provides valuable insights into the intricacies of problem solving and offers a foundation for improving problem-solving skills and strategies in both educational and practical settings.

Problem Solving in Educational Settings

Problem solving holds a central position in educational psychology, as it is a fundamental skill that empowers students to navigate the complexities of the learning process and prepares them for real-world challenges. It goes beyond rote memorization and standardized testing, allowing students to apply critical thinking, creativity, and analytical skills to authentic problems. Problem-solving tasks in educational settings range from solving mathematical equations to tackling complex issues in subjects like science, history, and literature. These tasks not only bolster subject-specific knowledge but also cultivate transferable skills that extend beyond the classroom.

Problem-solving skills offer numerous advantages to both educators and students. For teachers, integrating problem-solving tasks into the curriculum allows for more engaging and dynamic instruction, fostering a deeper understanding of the subject matter. Additionally, it provides educators with insights into students’ thought processes and areas where additional support may be needed. Students, on the other hand, benefit from the development of critical thinking, analytical reasoning, and creativity. These skills are transferable to various life situations, enhancing students’ abilities to solve complex real-world problems and adapt to a rapidly changing society.

Teaching problem-solving skills is a dynamic process that requires effective pedagogical approaches. In K-12 education, educators often use methods such as the problem-based learning (PBL) approach, where students work on open-ended, real-world problems, fostering self-directed learning and collaboration. Higher education institutions, on the other hand, employ strategies like case-based learning, simulations, and design thinking to promote problem solving within specialized disciplines. Additionally, educators use scaffolding techniques to provide support and guidance as students develop their problem-solving abilities. In both K-12 and higher education, a key component is metacognition, which helps students become aware of their thought processes and adapt their problem-solving strategies as needed.

Assessing problem-solving abilities in educational settings involves a combination of formative and summative assessments. Formative assessments, including classroom discussions, peer evaluations, and self-assessments, provide ongoing feedback and opportunities for improvement. Summative assessments may include standardized tests designed to evaluate problem-solving skills within a particular subject area. Performance-based assessments, such as essays, projects, and presentations, offer a holistic view of students’ problem-solving capabilities. Rubrics and scoring guides are often used to ensure consistency in assessment, allowing educators to measure not only the correctness of answers but also the quality of the problem-solving process. The evolving field of educational technology has also introduced computer-based simulations and adaptive learning platforms, enabling precise measurement and tailored feedback on students’ problem-solving performance.

Understanding the pivotal role of problem solving in educational psychology, the diverse pedagogical strategies for teaching it, and the methods for assessing and measuring problem-solving abilities equips educators and students with the tools necessary to thrive in educational environments and beyond. Problem solving remains a cornerstone of 21st-century education, preparing students to meet the complex challenges of a rapidly changing world.

Applications and Practical Implications

Problem solving is not confined to the classroom; it extends its influence to various real-world contexts, showcasing its relevance and impact. In business, problem solving is the driving force behind product development, process improvement, and conflict resolution. For instance, companies often use problem-solving methodologies like Six Sigma to identify and rectify issues in manufacturing. In healthcare, medical professionals employ problem-solving skills to diagnose complex illnesses and devise treatment plans. Additionally, technology advancements frequently stem from creative problem solving, as engineers and developers tackle challenges in software, hardware, and systems design. Real-world problem solving transcends specific domains, as individuals in diverse fields address multifaceted issues by drawing upon their cognitive abilities and creative problem-solving strategies.

Clinical psychology recognizes the profound therapeutic potential of problem-solving techniques. Problem-solving therapy (PST) is an evidence-based approach that focuses on helping individuals develop effective strategies for coping with emotional and interpersonal challenges. PST equips individuals with the skills to define problems, set realistic goals, generate solutions, and evaluate their effectiveness. This approach has shown efficacy in treating conditions like depression, anxiety, and stress, emphasizing the role of problem-solving abilities in enhancing emotional well-being. Furthermore, cognitive-behavioral therapy (CBT) incorporates problem-solving elements to help individuals challenge and modify dysfunctional thought patterns, reinforcing the importance of cognitive processes in addressing psychological distress.

Problem solving is the bedrock of innovation and creativity in various fields. Innovators and creative thinkers use problem-solving skills to identify unmet needs, devise novel solutions, and overcome obstacles. Design thinking, a problem-solving approach, is instrumental in product design, architecture, and user experience design, fostering innovative solutions grounded in human needs. Moreover, creative industries like art, literature, and music rely on problem-solving abilities to transcend conventional boundaries and produce groundbreaking works. By exploring alternative perspectives, making connections, and persistently seeking solutions, creative individuals harness problem-solving processes to ignite innovation and drive progress in all facets of human endeavor.

Understanding the practical applications of problem solving in business, healthcare, technology, and its therapeutic significance in clinical psychology, as well as its indispensable role in nurturing innovation and creativity, underscores its universal value. Problem solving is not only a cognitive skill but also a dynamic force that shapes and improves the world we inhabit, enhancing the quality of life and promoting progress and discovery.

In summary, problem solving stands as an indispensable cornerstone within the domains of psychology and education. This article has explored the multifaceted nature of problem solving, from its theoretical foundations rooted in Gestalt psychology, information processing theories, and cognitive psychology to its integral components of problem representation, goal setting, solution generation, and solution evaluation. It has delved into the cognitive processes underpinning effective problem solving, including perception, memory, and reasoning, as well as the impact of individual differences such as intelligence, creativity, and expertise. Common barriers to problem solving, including functional fixedness, confirmation bias, and mental sets, have been examined in-depth.

The significance of problem solving in educational settings was elucidated, underscoring its pivotal role in fostering critical thinking, creativity, and adaptability. Pedagogical approaches and assessment methods were discussed, providing educators with insights into effective strategies for teaching and evaluating problem-solving skills in K-12 and higher education.

Furthermore, the practical implications of problem solving were demonstrated in the real world, where it serves as the driving force behind advancements in business, healthcare, and technology. In clinical psychology, problem-solving therapies offer effective interventions for emotional and psychological well-being. The symbiotic relationship between problem solving and innovation and creativity was explored, highlighting the role of this cognitive process in pushing the boundaries of human accomplishment.

As we conclude, it is evident that problem solving is not merely a skill but a dynamic process with profound implications. It enables individuals to navigate the complexities of their environment, fostering intellectual growth, adaptability, and innovation. Future research in the field of problem solving should continue to explore the intricate cognitive processes involved, individual differences that influence problem-solving abilities, and innovative teaching methods in educational settings. In practice, educators and clinicians should continue to incorporate problem-solving strategies to empower individuals with the tools necessary for success in education, personal development, and the ever-evolving challenges of the real world. Problem solving remains a steadfast ally in the pursuit of knowledge, progress, and the enhancement of human potential.

References:

Anderson, J. R. (1995). Cognitive psychology and its implications. W. H. Freeman.
Atkinson, R. C., & Shiffrin, R. M. (1968). Human memory: A proposed system and its control processes. In The psychology of learning and motivation (Vol. 2, pp. 89-195). Academic Press.
Duncker, K. (1945). On problem-solving. Psychological Monographs, 58(5), i-113.
Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12(3), 306-355.
Jonassen, D. H., & Hung, W. (2008). All problems are not equal: Implications for problem-based learning. Interdisciplinary Journal of Problem-Based Learning, 2(2), 6.
Kitchener, K. S., & King, P. M. (1981). Reflective judgment: Concepts of justification and their relation to age and education. Journal of Applied Developmental Psychology, 2(2), 89-116.
Luchins, A. S. (1942). Mechanization in problem solving: The effect of Einstellung. Psychological Monographs, 54(6), i-95.
Mayer, R. E. (1992). Thinking, problem solving, cognition. W. H. Freeman.
Newell, A., & Simon, H. A. (1972). Human problem solving (Vol. 104). Prentice-Hall Englewood Cliffs, NJ.
Osborn, A. F. (1953). Applied imagination: Principles and procedures of creative problem solving (3rd ed.). Charles Scribner’s Sons.
Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press.
Sternberg, R. J. (2003). Wisdom, intelligence, and creativity synthesized. Cambridge University Press.

New Designs for School 5 Steps to Teaching Students a Problem-Solving Routine

Jeff Heyck-Williams (He, His, Him) Director of the Two Rivers Learning Institute in Washington, DC

We’ve all had the experience of truly purposeful, authentic learning and know how valuable it is. Educators are taking the best of what we know about learning, student support, effective instruction, and interpersonal skill-building to completely reimagine schools so that students experience that kind of purposeful learning all day, every day.

Students can use the 5 steps in this simple routine to solve problems across the curriculum and throughout their lives.

When I visited a fifth-grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

There were students on the rug modeling people with Unifix cubes. There were kids at one table vigorously shaking each other’s hand. There were kids at another table writing out a diagram with numbers. At yet another table, students were working on creating a numeric expression. What was common across this class was that all of the students were productively grappling around the problem.

On a different day, I was out at recess with a group of kindergarteners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics which they took to Capitol Hill to share with legislators. Through the process students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios, and an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in Washington, D.C., we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School

Before Problem-Solving: The KWI

The three steps before problem solving: we call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

The “I” stands for “ideas” and refers to ideas that a student brings to the table to solve a problem effectively. In this portion of the routine, students list the strategies that they will use to solve a problem. In the example from the math class, this step involved all of the different ways that students tackled the problem from Unifix cubes to creating mathematical expressions.

This KWI routine before problem solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem solving.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits they also consider if their path to a solution was efficient and how it compares to other students’ solutions.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them. This empowers students to be the problem solvers that we know they can become.

Jeff Heyck-Williams (He, His, Him)

Director of the two rivers learning institute.

Jeff Heyck-Williams is the director of the Two Rivers Learning Institute and a founder of Two Rivers Public Charter School. He has led work around creating school-wide cultures of mathematics, developing assessments of critical thinking and problem-solving, and supporting project-based learning.

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Rebecca Horrace, Playful Insights Consulting, and Laura Dattile, PlanToys USA

March 5, 2024

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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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Science, technology and society

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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Deborah Martin

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 .

Bensley DA, Spero RA (2014) Improving critical thinking skills and meta-cognitive monitoring through direct infusion. Think Skills Creat 12:55–68. https://doi.org/10.1016/j.tsc.2014.02.001

Article Google Scholar

Castle A (2009) Defining and assessing critical thinking skills for student radiographers. Radiography 15(1):70–76. https://doi.org/10.1016/j.radi.2007.10.007

Chen XD (2013) An empirical study on the influence of PBL teaching model on critical thinking ability of non-English majors. J PLA Foreign Lang College 36 (04):68–72

Google Scholar

Cohen A (1992) Antecedents of organizational commitment across occupational groups: a meta-analysis. J Organ Behav. https://doi.org/10.1002/job.4030130602

Cooper H (2010) Research synthesis and meta-analysis: a step-by-step approach, 4th edn. Sage, London, England

Cindy HS (2004) Problem-based learning: what and how do students learn? Educ Psychol Rev 51(1):31–39

Duch BJ, Gron SD, Allen DE (2001) The power of problem-based learning: a practical “how to” for teaching undergraduate courses in any discipline. Stylus Educ Sci 2:190–198

Ennis RH (1989) Critical thinking and subject specificity: clarification and needed research. Educ Res 18(3):4–10. https://doi.org/10.3102/0013189x018003004

Facione PA (1990) Critical thinking: a statement of expert consensus for purposes of educational assessment and instruction. Research findings and recommendations. Eric document reproduction service. https://eric.ed.gov/?id=ed315423

Facione PA, Facione NC (1992) The California Critical Thinking Dispositions Inventory (CCTDI) and the CCTDI test manual. California Academic Press, Millbrae, CA

Forawi SA (2016) Standard-based science education and critical thinking. Think Skills Creat 20:52–62. https://doi.org/10.1016/j.tsc.2016.02.005

Halpern DF (2001) Assessing the effectiveness of critical thinking instruction. J Gen Educ 50(4):270–286. https://doi.org/10.2307/27797889

Hu WP, Liu J (2015) Cultivation of pupils’ thinking ability: a five-year follow-up study. Psychol Behav Res 13(05):648–654. https://doi.org/10.3969/j.issn.1672-0628.2015.05.010

Huber K (2016) Does college teach critical thinking? A meta-analysis. Rev Educ Res 86(2):431–468. https://doi.org/10.3102/0034654315605917

Kek MYCA, Huijser H (2011) The power of problem-based learning in developing critical thinking skills: preparing students for tomorrow’s digital futures in today’s classrooms. High Educ Res Dev 30(3):329–341. https://doi.org/10.1080/07294360.2010.501074

Kuncel NR (2011) Measurement and meaning of critical thinking (Research report for the NRC 21st Century Skills Workshop). National Research Council, Washington, DC

Kyndt E, Raes E, Lismont B, Timmers F, Cascallar E, Dochy F (2013) A meta-analysis of the effects of face-to-face cooperative learning. Do recent studies falsify or verify earlier findings? Educ Res Rev 10(2):133–149. https://doi.org/10.1016/j.edurev.2013.02.002

Leng J, Lu XX (2020) Is critical thinking really teachable?—A meta-analysis based on 79 experimental or quasi experimental studies. Open Educ Res 26(06):110–118. https://doi.org/10.13966/j.cnki.kfjyyj.2020.06.011

Liang YZ, Zhu K, Zhao CL (2017) An empirical study on the depth of interaction promoted by collaborative problem solving learning activities. J E-educ Res 38(10):87–92. https://doi.org/10.13811/j.cnki.eer.2017.10.014

Lipsey M, Wilson D (2001) Practical meta-analysis. International Educational and Professional, London, pp. 92–160

Liu Z, Wu W, Jiang Q (2020) A study on the influence of problem based learning on college students’ critical thinking-based on a meta-analysis of 31 studies. Explor High Educ 03:43–49

Morris SB (2008) Estimating effect sizes from pretest-posttest-control group designs. Organ Res Methods 11(2):364–386. https://doi.org/10.1177/1094428106291059

Article ADS Google Scholar

Mulnix JW (2012) Thinking critically about critical thinking. Educ Philos Theory 44(5):464–479. https://doi.org/10.1111/j.1469-5812.2010.00673.x

Naber J, Wyatt TH (2014) The effect of reflective writing interventions on the critical thinking skills and dispositions of baccalaureate nursing students. Nurse Educ Today 34(1):67–72. https://doi.org/10.1016/j.nedt.2013.04.002

National Research Council (2012) Education for life and work: developing transferable knowledge and skills in the 21st century. The National Academies Press, Washington, DC

Niu L, Behar HLS, Garvan CW (2013) Do instructional interventions influence college students’ critical thinking skills? A meta-analysis. Educ Res Rev 9(12):114–128. https://doi.org/10.1016/j.edurev.2012.12.002

Peng ZM, Deng L (2017) Towards the core of education reform: cultivating critical thinking skills as the core of skills in the 21st century. Res Educ Dev 24:57–63. https://doi.org/10.14121/j.cnki.1008-3855.2017.24.011

Reiser BJ (2004) Scaffolding complex learning: the mechanisms of structuring and problematizing student work. J Learn Sci 13(3):273–304. https://doi.org/10.1207/s15327809jls1303_2

Ruggiero VR (2012) The art of thinking: a guide to critical and creative thought, 4th edn. Harper Collins College Publishers, New York

Schellens T, Valcke M (2006) Fostering knowledge construction in university students through asynchronous discussion groups. Comput Educ 46(4):349–370. https://doi.org/10.1016/j.compedu.2004.07.010

Sendag S, Odabasi HF (2009) Effects of an online problem based learning course on content knowledge acquisition and critical thinking skills. Comput Educ 53(1):132–141. https://doi.org/10.1016/j.compedu.2009.01.008

Sison R (2008) Investigating Pair Programming in a Software Engineering Course in an Asian Setting. 2008 15th Asia-Pacific Software Engineering Conference, pp. 325–331. https://doi.org/10.1109/APSEC.2008.61

Simpson E, Courtney M (2002) Critical thinking in nursing education: literature review. Mary Courtney 8(2):89–98

Stewart L, Tierney J, Burdett S (2006) Do systematic reviews based on individual patient data offer a means of circumventing biases associated with trial publications? Publication bias in meta-analysis. John Wiley and Sons Inc, New York, pp. 261–286

Tiwari A, Lai P, So M, Yuen K (2010) A comparison of the effects of problem-based learning and lecturing on the development of students’ critical thinking. Med Educ 40(6):547–554. https://doi.org/10.1111/j.1365-2929.2006.02481.x

Wood D, Bruner JS, Ross G (2006) The role of tutoring in problem solving. J Child Psychol Psychiatry 17(2):89–100. https://doi.org/10.1111/j.1469-7610.1976.tb00381.x

Wei T, Hong S (2022) The meaning and realization of teachable critical thinking. Educ Theory Practice 10:51–57

Xu EW, Wang W, Wang QX (2022) A meta-analysis of the effectiveness of programming teaching in promoting K-12 students’ computational thinking. Educ Inf Technol. https://doi.org/10.1007/s10639-022-11445-2

Yang YC, Newby T, Bill R (2008) Facilitating interactions through structured web-based bulletin boards: a quasi-experimental study on promoting learners’ critical thinking skills. Comput Educ 50(4):1572–1585. https://doi.org/10.1016/j.compedu.2007.04.006

Yore LD, Pimm D, Tuan HL (2007) The literacy component of mathematical and scientific literacy. Int J Sci Math Educ 5(4):559–589. https://doi.org/10.1007/s10763-007-9089-4

Zhang T, Zhang S, Gao QQ, Wang JH (2022) Research on the development of learners’ critical thinking in online peer review. Audio Visual Educ Res 6:53–60. https://doi.org/10.13811/j.cnki.eer.2022.06.08

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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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Teaching high school students how to plan to solve a problem in science, technology, engineering, and math is a crucial step.

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Teaching students to become independent problem-solvers can be a challenging task, especially with virtual teaching during the pandemic. For some students, solving problems is not intuitive, and they need to learn how to think about solving problems from a general perspective. As experts, teachers often do not realize that there are implicit skills and ways of thinking that may not be obvious or known to our students.

5 Strategies to Explicitly Model and Teach Problem-Solving Skills

1. Model hidden thinking involved in solving a problem. When solving a problem, I talk about every aspect of what I am doing out loud. In fact, I over-talk, providing reasoning for every step. For example, when solving a dimensional-analysis problem, I will include descriptions like, “OK, I am going to look for any numbers that I can cancel. I know I can cancel or reduce if I see a number in the numerator and another number in the denominator that have a common factor.”

I will even include moments of vulnerability and model the fact that I don’t always know what to do, but I will discuss my options and my decision process. I sometimes intentionally make mistakes and then use methods to check my work to correct my errors. It’s essential that we explicitly show students this internal dialogue to model problem-solving.

2. Facilitate student talk during problem-solving. I do my best to never solve problems for students, even if they ask me. This includes whole-class lessons and working with students in small groups or individually. Using the Socratic method, I ask many questions of the students. The questions can be as simple as “What do we do next?” or “What are options of what we can do?”

Once during a classroom observation, I was told that in a span of 10 minutes, I asked more than 72 questions. This models the questions that the students can use in self-talk to guide them in the problem-solving process. After the first test, many students say that they could hear my voice asking them the same questions over and over, but what they’re really learning are advanced problem-solving skills they can extend to future contexts.

We can also provide deeper understanding with questions such as “Why do we do that?” These provide reasoning and value to the actions of each step in the problem-solving process, further solidifying the students’ understanding of the concepts and skills.

3. Include discussion for planning for each problem. Teachers instinctively plan problems. Students, as novice learners, often do not know how to plan a problem. They look at a problem, see it as foreign, and don’t know where to begin. They give up.

Research shows that planning how to solve the problem is an essential step for novice learners. Provide a structure or protocol for students. It can include the following: identify and write the data with units for a problem, identify equations to be used, identify and write what they’re trying to solve for, draw a relevant vector diagram, and brainstorm possible steps.

4. Emphasize the process, not final answers. Often, when checking individual work, we ask for the final answers. But what if instead of asking who has the answer, we ask who has the method to solve it? When students ask for correct answers, it’s natural to provide an immediate response. Instead, we should reply with guiding questions to facilitate the process of their solving the problems for themselves.

Often, I don’t even calculate the answer in the final step and ask if we all agree on the steps. The conversation is especially valuable when different methods are volunteered, and we can analyze the advantages of each. I want the students to check our work and not look at a simple result at the end of the problem to confirm their work. This shifts students’ attention to look at the details of the steps and not glance at the end of the work for the final answer. Further, grading can include points for steps and not the final solution.

5. Teach explicitly problem solving. After solving problems, students can create their own problem-solving strategy that they write on a note card. Collect responses from students and create a class protocol that you post on your learning management system or in your physical classroom space. Scaffold further with a two-column approach. In the left column, students show the work, and in the right column, they explain and justify what they did and why. The act of adding a justification will make students think about their actions. This will improve the connection between conceptual ideas and the problem-solving itself.

These are only a few strategies to get your students intentionally thinking about problem-solving from a general perspective beyond focusing on specific problems and memorizing steps. There are many ways to model and teach the skill of problem-solving that encourage them to think about the process explicitly.

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How to Teach Kids Problem-Solving Skills

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Steps to Follow
Allow Consequences

Whether your child can't find their math homework or has forgotten their lunch, good problem-solving skills are the key to helping them manage their life.

A 2010 study published in Behaviour Research and Therapy found that kids who lack problem-solving skills may be at a higher risk of depression and suicidality. Additionally, the researchers found that teaching a child problem-solving skills can improve mental health .

You can begin teaching basic problem-solving skills during preschool and help your child sharpen their skills into high school and beyond.

Why Problem-Solving Skills Matter

Kids face a variety of problems every day, ranging from academic difficulties to problems on the sports field. Yet few of them have a formula for solving those problems.

Kids who lack problem-solving skills may avoid taking action when faced with a problem.

Rather than put their energy into solving the problem, they may invest their time in avoiding the issue. That's why many kids fall behind in school or struggle to maintain friendships .

Other kids who lack problem-solving skills spring into action without recognizing their choices. A child may hit a peer who cuts in front of them in line because they are not sure what else to do.

Or, they may walk out of class when they are being teased because they can't think of any other ways to make it stop. Those impulsive choices may create even bigger problems in the long run.

The 5 Steps of Problem-Solving

Kids who feel overwhelmed or hopeless often won't attempt to address a problem. But when you give them a clear formula for solving problems, they'll feel more confident in their ability to try. Here are the steps to problem-solving:

Identify the problem . Just stating the problem out loud can make a big difference for kids who are feeling stuck. Help your child state the problem, such as, "You don't have anyone to play with at recess," or "You aren't sure if you should take the advanced math class."
Develop at least five possible solutions . Brainstorm possible ways to solve the problem. Emphasize that all the solutions don't necessarily need to be good ideas (at least not at this point). Help your child develop solutions if they are struggling to come up with ideas. Even a silly answer or far-fetched idea is a possible solution. The key is to help them see that with a little creativity, they can find many different potential solutions.
Identify the pros and cons of each solution . Help your child identify potential positive and negative consequences for each potential solution they identified.
Pick a solution. Once your child has evaluated the possible positive and negative outcomes, encourage them to pick a solution.
Test it out . Tell them to try a solution and see what happens. If it doesn't work out, they can always try another solution from the list that they developed in step two.

Practice Solving Problems

When problems arise, don’t rush to solve your child’s problems for them. Instead, help them walk through the problem-solving steps. Offer guidance when they need assistance, but encourage them to solve problems on their own. If they are unable to come up with a solution, step in and help them think of some. But don't automatically tell them what to do.

When you encounter behavioral issues, use a problem-solving approach. Sit down together and say, "You've been having difficulty getting your homework done lately. Let's problem-solve this together." You might still need to offer a consequence for misbehavior, but make it clear that you're invested in looking for a solution so they can do better next time.

Use a problem-solving approach to help your child become more independent.

If they forgot to pack their soccer cleats for practice, ask, "What can we do to make sure this doesn't happen again?" Let them try to develop some solutions on their own.

Kids often develop creative solutions. So they might say, "I'll write a note and stick it on my door so I'll remember to pack them before I leave," or "I'll pack my bag the night before and I'll keep a checklist to remind me what needs to go in my bag."

Provide plenty of praise when your child practices their problem-solving skills.

Allow for Natural Consequences

Natural consequences may also teach problem-solving skills. So when it's appropriate, allow your child to face the natural consequences of their action. Just make sure it's safe to do so.

For example, let your teenager spend all of their money during the first 10 minutes you're at an amusement park if that's what they want. Then, let them go for the rest of the day without any spending money.

This can lead to a discussion about problem-solving to help them make a better choice next time. Consider these natural consequences as a teachable moment to help work together on problem-solving.

Becker-Weidman EG, Jacobs RH, Reinecke MA, Silva SG, March JS. Social problem-solving among adolescents treated for depression . Behav Res Ther . 2010;48(1):11-18. doi:10.1016/j.brat.2009.08.006

Pakarinen E, Kiuru N, Lerkkanen M-K, Poikkeus A-M, Ahonen T, Nurmi J-E. Instructional support predicts childrens task avoidance in kindergarten . Early Child Res Q . 2011;26(3):376-386. doi:10.1016/j.ecresq.2010.11.003

Schell A, Albers L, von Kries R, Hillenbrand C, Hennemann T. Preventing behavioral disorders via supporting social and emotional competence at preschool age . Dtsch Arztebl Int . 2015;112(39):647–654. doi:10.3238/arztebl.2015.0647

Cheng SC, She HC, Huang LY. The impact of problem-solving instruction on middle school students’ physical science learning: Interplays of knowledge, reasoning, and problem solving . EJMSTE . 2018;14(3):731-743.

Vlachou A, Stavroussi P. Promoting social inclusion: A structured intervention for enhancing interpersonal problem‐solving skills in children with mild intellectual disabilities . Support Learn . 2016;31(1):27-45. doi:10.1111/1467-9604.12112

Öğülmüş S, Kargı E. The interpersonal cognitive problem solving approach for preschoolers . Turkish J Educ . 2015;4(17347):19-28. doi:10.19128/turje.181093

American Academy of Pediatrics. What's the best way to discipline my child? .

Kashani-Vahid L, Afrooz G, Shokoohi-Yekta M, Kharrazi K, Ghobari B. Can a creative interpersonal problem solving program improve creative thinking in gifted elementary students? . Think Skills Creat . 2017;24:175-185. doi:10.1016/j.tsc.2017.02.011

Shokoohi-Yekta M, Malayeri SA. Effects of advanced parenting training on children's behavioral problems and family problem solving . Procedia Soc Behav Sci . 2015;205:676-680. doi:10.1016/j.sbspro.2015.09.106

By Amy Morin, LCSW Amy Morin, LCSW, is the Editor-in-Chief of Verywell Mind. She's also a psychotherapist, an international bestselling author of books on mental strength and host of The Verywell Mind Podcast. She delivered one of the most popular TEDx talks of all time.

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5 Problem-Solving Activities for the Classroom

Problem-solving skills are necessary in all areas of life, and classroom problem solving activities can be a great way to get students prepped and ready to solve real problems in real life scenarios. Whether in school, work or in their social relationships, the ability to critically analyze a problem, map out all its elements and then prepare a workable solution is one of the most valuable skills one can acquire in life.

Educating your students about problem solving skills from an early age in school can be facilitated through classroom problem solving activities. Such endeavors encourage cognitive as well as social development, and can equip students with the tools they’ll need to address and solve problems throughout the rest of their lives. Here are five classroom problem solving activities your students are sure to benefit from as well as enjoy doing:

1. Brainstorm bonanza

Having your students create lists related to whatever you are currently studying can be a great way to help them to enrich their understanding of a topic while learning to problem-solve. For example, if you are studying a historical, current or fictional event that did not turn out favorably, have your students brainstorm ways that the protagonist or participants could have created a different, more positive outcome. They can brainstorm on paper individually or on a chalkboard or white board in front of the class.

2. Problem-solving as a group

Have your students create and decorate a medium-sized box with a slot in the top. Label the box “The Problem-Solving Box.” Invite students to anonymously write down and submit any problem or issue they might be having at school or at home, ones that they can’t seem to figure out on their own. Once or twice a week, have a student draw one of the items from the box and read it aloud. Then have the class as a group figure out the ideal way the student can address the issue and hopefully solve it.

3. Clue me in

This fun detective game encourages problem-solving, critical thinking and cognitive development. Collect a number of items that are associated with a specific profession, social trend, place, public figure, historical event, animal, etc. Assemble actual items (or pictures of items) that are commonly associated with the target answer. Place them all in a bag (five-10 clues should be sufficient.) Then have a student reach into the bag and one by one pull out clues. Choose a minimum number of clues they must draw out before making their first guess (two- three). After this, the student must venture a guess after each clue pulled until they guess correctly. See how quickly the student is able to solve the riddle.

4. Survivor scenarios

Create a pretend scenario for students that requires them to think creatively to make it through. An example might be getting stranded on an island, knowing that help will not arrive for three days. The group has a limited amount of food and water and must create shelter from items around the island. Encourage working together as a group and hearing out every child that has an idea about how to make it through the three days as safely and comfortably as possible.

5. Moral dilemma

Create a number of possible moral dilemmas your students might encounter in life, write them down, and place each item folded up in a bowl or bag. Some of the items might include things like, “I saw a good friend of mine shoplifting. What should I do?” or “The cashier gave me an extra $1.50 in change after I bought candy at the store. What should I do?” Have each student draw an item from the bag one by one, read it aloud, then tell the class their answer on the spot as to how they would handle the situation.

Classroom problem solving activities need not be dull and routine. Ideally, the problem solving activities you give your students will engage their senses and be genuinely fun to do. The activities and lessons learned will leave an impression on each child, increasing the likelihood that they will take the lesson forward into their everyday lives.

Number and algebra

The Number System and Place Value
Calculations and Numerical Methods
Fractions, Decimals, Percentages, Ratio and Proportion
Properties of Numbers
Patterns, Sequences and Structure
Algebraic expressions, equations and formulae
Coordinates, Functions and Graphs

Geometry and measure

Angles, Polygons, and Geometrical Proof
3D Geometry, Shape and Space
Measuring and calculating with units
Transformations and constructions
Pythagoras and Trigonometry
Vectors and Matrices

Probability and statistics

Handling, Processing and Representing Data
Probability

Working mathematically

Thinking mathematically
Mathematical mindsets
Cross-curricular contexts
Physical and digital manipulatives

For younger learners

Early Years Foundation Stage

Advanced mathematics

Decision Mathematics and Combinatorics
Advanced Probability and Statistics

Problem-solving Schools

Problem-solving Schools supports learners embed key problem-solving strategies as they progress through their schooling, backed by our Problem-solving Schools' Charter .

Want to raise the profile of mathematical problem-solving in your school?

Looking for support to help your students become better problem-solvers?

Want to be connected to like-minded teachers?

Become a Problem-solving School

What is the Problem-solving Schools initiative?

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We aim to help you raise the profile of mathematical problem-solving in your school. Our Charter offers a framework intended to inform policy and practice.

Becoming a Problem-solving School

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Everything you need to know about joining this initiative.

The Problem-solving Schools’ Charter

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Use our Charter to help you reflect on your current practice and to agree on areas for development.

Resources and professional development

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Our support material and webinars aim to help your school move forward on its problem-solving journey.

Welcoming our latest schools

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Coming soon… Find out which schools in your area are raising the status of problem-solving in their mathematics classrooms.

Author Rights
Diversity, Equity & Inclusion

JOLE 2023 Special Issue
Editorial Staff
20th Anniversary Issue
The Development of Problem-Solving Skills for Aspiring Educational Leaders

Jeremy D. Visone 10.12806/V17/I4/R3

Introduction

Solving problems is a quintessential aspect of the role of an educational leader. In particular, building leaders, such as principals, assistant principals, and deans of students, are frequently beset by situations that are complex, unique, and open-ended. There are often many possible pathways to resolve the situations, and an astute educational leader needs to consider many factors and constituencies before determining a plan of action. The realm of problem solving might include student misconduct, personnel matters, parental complaints, school culture, instructional leadership, as well as many other aspects of educational administration. Much consideration has been given to the development of problem-solving skills for educational leaders. This study was designed to answer the following research question: “How do aspiring educational leaders’ problem solving skills, as well as perceptions of their problem-solving skills, develop during a year-long graduate course sequence focused on school-level leadership that includes the presentation of real-world scenarios?” This mixed-methods study extends research about the development of problem-solving skills conducted with acting administrators (Leithwood & Steinbach, 1992, 1995).

The Nature of Problems

Before examining how educational leaders can process and solve problems effectively, it is worth considering the nature of problems. Allison (1996) posited simply that problems are situations that require thought and/or actions. Further, there are different types of problems presented to educational leaders. First, there are well-structured problems , which can be defined as those with clear goals and relatively prescribed resolution pathways, including an easy way of determining whether goals were met (Allison, 1996).

Conversely, ill-structured problems are those with more open-ended profiles, whereby the goals, resolution pathways, or evidence of success are not necessarily clear. These types of problems could also be considered unstructured (Leithwood & Steinbach, 1995) or open-design (Allison, 1996). Many of the problems presented to educational leaders are unstructured problems. For example, a principal must decide how to discipline children who misbehave, taking into consideration their disciplinary history, rules and protocols of the school, and other contextual factors; determine how best to raise student achievement (Duke, 2014); and resolve personnel disputes among staff members. None of these problems point to singular solutions that can be identified as “right” or “wrong.” Surely there are responses that are less desirable than others (i.e. suspension or recommendation for expulsion for minor infractions), but, with justification and context, many possible solutions exist.

Problem-Solving Perspectives and Models

Various authors have shared perspectives about effective problem solving. Marzano, Waters, and McNulty (2005) outlined the “21 Responsibilities of the School Leader.” These responsibilities are highly correlated with student achievement based upon the authors’ meta- analysis of 69 studies about leadership’s effect on student achievement. The most highly correlated of the responsibilities was situational awareness , which refers to understanding the school deeply enough to anticipate what might go wrong from day-to-day, navigate the individuals and groups within the school, and recognize issues that might surface at a later time (Marzano et al., 2005). Though the authors discuss the utility of situational awareness for long- term, large-scale decision making, in order for an educational leader to effectively solve the daily problems that come her way, she must again have a sense of situational awareness, lest she make seemingly smaller-scale decisions that will lead to large-scale problems later.

Other authors have focused on problems that can be considered more aligned with the daily work of educational leaders. Considering the problem-type classification dichotomies of Allison (1996) and Leithwood and Steinbach (1995), problems that educational leaders face on a daily basis can be identified as either well-structured or unstructured. Various authors have developed problem-solving models focused on unstructured problems (Bolman & Deal, 2008; Leithwood & Steinbach, 1995; Simon, 1993), and these models will be explored next.

Simon (1993) outlined three phases of the decision-making process. The first is to find problems that need attention. Though many problems of educational leaders are presented directly to them via, for example, an adult referring a child for discipline, a parent registering a complaint about a staff member, or a staff member describing a grievance with a colleague, there is a corollary skill of identifying what problems—of the many that come across one’s desk— require immediate attention, or ultimately, any attention, at all. Second, Simon identified “designing possible courses of action” (p. 395). Finally, educational leaders must evaluate the quality of their decisions. From this point of having selected a viable and positively evaluated potential solution pathway, implementation takes place.

Bolman and Deal (2008) outlined a model of reframing problems using four different frames, through which problems of practice can be viewed. These frames provide leaders with a more complete set of perspectives than they would likely utilize on their own. The structural frame represents the procedural and systems-oriented aspects of an organization. Within this frame, a leader might ask whether there is a supervisory relationship involved in a problem, if a protocol exists to solve such a problem, or what efficiencies or logical processes can help steer a leader toward a resolution that meets organizational goals. The human resource frame refers to the needs of individuals within the organization. A leader might try to solve a problem of practice with the needs of constituents in mind, considering the development of employees and the balance between their satisfaction and intellectual stimulation and the organization’s needs. The political frame includes the often competing interests among individuals and groups within the organization, whereby alliances and negotiations are needed to navigate the potential minefield of many groups’ overlapping aims. From the political frame, a leader could consider what the interpersonal costs will be for the leader and organization among different constituent groups, based upon which alternatives are selected. Last, the symbolic frame includes elements of meaning within an organization, such as traditions, unspoken rules, and myths. A leader may need to consider this frame when proposing a solution that might interfere with a long-standing organizational tradition.

Bolman and Deal (2008) identified the political and symbolic frames as weaknesses in most leaders’ consideration of problems of practice, and the weakness in recognizing political aspects of decision making for educational leaders was corroborated by Johnson and Kruse (2009). An implication for leadership preparation is to instruct students in the considerations of these frames and promote their utility when examining problems.

Authors have noted that experts use different processes than novice problem solvers (Simon, 1993; VanLehn, 1991). An application of this would be Simon’s (1993) assertion that experts can rely on their extensive experience to remember solutions to many problems, without having to rely on an extensive analytical process. Further, they may not even consider a “problem” identified by a novice a problem, at all. With respect to educational leaders, Leithwood and Steinbach (1992, 1995) outlined a set of competencies possessed by expert principals, when compared to their typical counterparts. Expert principals were better at identifying the nature of problems; possessing a sense of priority, difficulty, how to proceed, and connectedness to prior situations; setting meaningful goals for problem solving, such as seeking goals that are student-centered and knowledge-focused; using guiding principles and long-term purposes when determining the best courses of action; seeing fewer obstacles and constraints when presented with problems; outlining detailed plans for action that include gathering extensive information to inform decisions along the plan’s pathway; and responding with confidence and calm to problem solving. Next, I will examine how problem-solving skills are developed.

Preparation for Educational Leadership Problem Solving

How can the preparation of leaders move candidates toward the competencies of expert principals? After all, leading a school has been shown to be a remarkably complex enterprise (Hallinger & McCary, 1990; Leithwood & Steinbach, 1992), especially if the school is one where student achievement is below expectations (Duke, 2014), and the framing of problems by educational leaders has been espoused as a critically important enterprise (Bolman & Deal, 2008; Dimmock, 1996; Johnson & Kruse, 2009; Leithwood & Steinbach, 1992, 1995; Myran & Sutherland, 2016). In other disciplines, such as business management, simulations and case studies are used to foster problem-solving skills for aspiring leaders (Rochford & Borchert, 2011; Salas, Wildman, & Piccolo, 2009), and attention to problem-solving skills has been identified as an essential curricular component in the training of journalism and mass communication students (Bronstein & Fitzpatrick, 2015). Could such real-world problem solving methodologies be effective in the preparation of educational leaders? In a seminal study about problem solving for educational leaders, Leithwood and Steinbach (1992, 1995) sought to determine if effective problem-solving expertise could be explicitly taught, and, if so, could teaching problem- processing expertise be helpful in moving novices toward expert competence? Over the course of four months and four separate learning sessions, participants in the control group were explicitly taught subskills within six problem-solving components: interpretation of the problem for priority, perceived difficulty, data needed for further action, and anecdotes of prior experience that can inform action; goals for solving the problem; large-scale principles that guide decision making; barriers or obstacles that need to be overcome; possible courses of action; and the confidence of the leader to solve the problem. The authors asserted that providing conditions to participants that included models of effective problem-solving, feedback, increasingly complex problem-solving demands, frequent opportunities for practice, group problem-solving, individual reflection, authentic problems, and help to stimulate metacognition and reflection would result in educational leaders improving their problem-solving skills.

The authors used two experts’ ratings of participants’ problem-solving for both process (their methods of attacking the problem) and product (their solutions) using a 0-3 scale in a pretest-posttest design. They found significant increases in some problem-solving skills (problem interpretation, goal setting, and identification of barriers or obstacles that need to be overcome) after explicit instruction (Leithwood & Steinbach, 1992, 1995). They recommended conducting more research on the preparation of educational leaders, with particular respect to approaches that would improve the aspiring leaders’ problem-solving skills.

Solving problems for practicing principals could be described as constructivist, since most principals do solve problems within a social context of other stakeholders, such as teachers, parents, and students (Leithwood & Steinbach, 1992). Thus, some authors have examined providing opportunities for novice or aspiring leaders to construct meaning from novel scenarios using the benefits of, for example, others’ point of view, expert modeling, simulations, and prior knowledge (Duke, 2014; Leithwood & Steinbach, 1992, 1995; Myran & Sutherland, 2016; Shapira-Lishchinsky, 2015). Such collaborative inquiry has been effective for teachers, as well (DeLuca, Bolden, & Chan, 2017). Such learning can be considered consistent with the ideas of other social constructivist theorists (Berger & Luckmann, 1966; Vygotsky, 1978) as well, since individuals are working together to construct meaning, and they are pushing into areas of uncertainty and lack of expertise.

Shapira-Lishchinsky (2015) added some intriguing findings and recommendations to those of Leithwood and Steinbach (1992, 1995). In this study, 50 teachers with various leadership roles in their schools were presented regularly with ethical dilemmas during their coursework. Participants either interacted with the dilemmas as members of a role play or by observing those chosen. When the role play was completed, the entire group debriefed and discussed the ethical dilemmas and role-playing participants’ treatment of the issues. This method was shown, through qualitative analysis of participants’ discussions during the simulations, to produce rich dialogue and allow for a safe and controlled treatment of difficult issues. As such, the use of simulations was presented as a viable means through which to prepare aspiring educational leaders. Further, the author suggested the use of further studies with simulation-based learning that seek to gain information about aspiring leaders’ self-efficacy and psychological empowerment. A notable example of project-based scenarios in a virtual collaboration environment to prepare educational leaders is the work of Howard, McClannon, and Wallace (2014). Shapira-Lishchinsky (2015) also recommended similar research in other developed countries to observe the utility of the approaches of simulation and social constructivism to examine them for a wider and diverse aspiring administrator candidate pool.

Further, in an extensive review of prior research studies on the subject, Hallinger and Bridges (2017) noted that Problem-Based Learning (PBL), though applied successfully in other professions and written about extensively (Hallinger & Bridges, 1993, 2017; Stentoft, 2017), was relatively unheralded in the preparation of educational leaders. According to the authors, characteristics of PBL included problems replacing theory as the organization of course content, student-led group work, creation of simulated products by students, increased student ownership over learning, and feedback along the way from professors. Their review noted that PBL had positive aspects for participants, such as increased motivation, real-world connections, and positive pressure that resulted from working with a team. However, participants also expressed concerns about time constraints, lack of structure, and interpersonal dynamics within their teams. There were positive effects found on aspiring leaders’ problem-solving skill development with PBL (Copland, 2000; Hallinger & Bridges, 2017). Though PBL is much more prescribed than the scenarios strategy described in the Methods section below, the applicability of real-world problems to the preparation of educational leaders is summarized well by Copland (2000):

[I]nstructional practices that activate prior knowledge and situate learning in contexts similar to those encountered in practice are associated with the development of students’ ability to understand and frame problems. Moreover, the incorporation of debriefing techniques that encourage students’ elaboration of knowledge and reflection on learning appear to help students solidify a way of thinking about problems. (p. 604)

This study involved a one-group pretest-posttest design. No control group was assigned, as the pedagogical strategy in question—the use of real-world scenarios to build problem-solving skill for aspiring educational leaders—is integral to the school’s curriculum that prepares leaders, and, therefore, it is unethical to deny to student participants (Gay & Airasian, 2003). Thus, all participants were provided instruction with the use of real-world scenarios.

Participants. Graduate students at a regional, comprehensive public university in the Northeast obtaining a 6 th -year degree (equivalent to a second master’s degree) in educational leadership and preparing for certification as educational administrators served as participants. Specifically, students in three sections of the same full-year, two-course sequence, entitled “School Leadership I and II” were invited to participate. This particular course was selected from the degree course sequence, as it deals most directly with the problem-solving nature and daily work of school administrators. Some key outcomes of the course include students using data to drive school improvement action plans, communicating effectively with a variety of stakeholders, creating a safe and caring school climate, creating and maintaining a strategic and viable school budget, articulating all the steps in a hiring process for teachers and administrators, and leading with cultural proficiency.

The three sections were taught by two different professors. The professors used real- world scenarios in at least half of their class meetings throughout the year, or in approximately 15 classes throughout the year. During these classes, students were presented with realistic situations that have occurred, or could occur, in actual public schools. Students worked with their classmates to determine potential solutions to the problems and then discussed their responses as a whole class under the direction of their professor, a master practitioner. Both professors were active school administrators, with more than 25 years combined educational leadership experience in public schools. It should be noted that the scenario presentation and discussions took place during the class sessions, only. These were not presented for homework or in online forums.

Of the 44 students in these three sections, 37 volunteered to participate at some point in the data collection sequence, but not all students in the pretest session attended the posttest session months later and vice versa. As a result, only 20 students’ data were used for the matched pairs analysis. All 37 participants were certified professional educators in public schools in Connecticut. The participants’ professional roles varied and included classroom teachers, instructional coaches, related service personnel, unified arts teachers, as well as other non- administrative educational roles. Characteristics of participants in the overall and matched pairs groups can be found in Table 1.

Table 1 Participant Characteristics

Procedure. Participants’ data were compared between a fall of 2016 baseline data collection period and a spring of 2017 posttest data collection period. During the fall data collection period, participants were randomly assigned one of two versions of a Google Forms survey. After items about participant characteristics, the survey consisted of 11 items designed to elicit quantitative and qualitative data about participants’ perceptions of their problem-solving abilities, as well as their ability to address real-world problems faced by educational leaders. The participants were asked to rate their perception of their situational awareness, flexibility, and problem solving ability on a 10-point (1-10) Likert scale, following operational definitions of the terms (Marzano, Waters, & McNulty, 2005; Winter, 1982). They were asked, for each construct, to write open-ended responses to justify their numerical rating. They were then asked to write what they perceived they still needed to improve their problem-solving skills. The final four items included two real-world, unstructured, problem-based scenarios for which participants were asked to create plans of action. They were also asked to rate their problem-solving confidence with respect to their proposed action plans for each scenario on a 4-point (0-3) Likert scale.

During the spring data collection period, participants accessed the opposite version of the Google Forms survey from the one they completed in the fall. All items were identical on the two survey versions, except the scenarios, which were different on each survey version. The use of two versions was to ensure that any differences in perceived or actual difficulty among the four scenarios provided would not alter results based upon the timing of participant access (Leithwood & Steinbach, 1995). In order to link participants’ fall and spring data in a confidential manner, participants created a unique, six-digit alphanumeric code.

A focus group interview followed each spring data collection session. The interviews were recorded to allow for accurate transcription. The list of standard interview questions can be found in Table 2. This interview protocol was designed to elicit qualitative data with respect to aspiring educational leaders’ perceptions about their developing problem-solving abilities.

Table 2 Focus Group Interview Questions ___________________________________________________________________________________________

Please describe the development of your problem-solving skills as an aspiring educational leader over the course of this school year. In what ways have you improved your skills? Be as specific as you can.

What has been helpful to you (i.e. coursework, readings, experiences, etc.) in this development of your problem-solving skills? Why?

What do you believe you still need for the development in your problem-solving skills as an aspiring educational leader?

Discuss your perception of your ability to problem solve as an aspiring educational leader. How has this changed from the beginning of this school year? Why?

Please add anything else you perceive is relevant to this conversation about the development of your problem-solving skills as an aspiring educational leader.

___________________________________________________________________________________________

Data Analysis.

Quantitative data . Data were obtained from participants’ responses to Likert-scale items relating to their confidence levels with respect to aspects of problem solving, as well as from the rating of participants’ responses to the given scenarios against a rubric. The educational leadership problem-solving rubric chosen (Leithwood & Steinbach, 1995) was used with permission, and it reflects the authors’ work with explicitly teaching practicing educational leaders components of problem solving. The adapted rubric can be found in Figure 1. Through the use of this rubric, each individual response by a participant to a presented scenario was assigned a score from 0-15. It should be noted that affect data (representing the final 3 possible points on the 18-point rubric) were obtained via participants’ self-reporting their confidence with respect to their proposed plans of action. To align with the rubric, participants self-assessed their confidence through this item with a 0-3 scale.

0 = No Use of the Subskill 1 = There is Some Indication of Use of the Subskill 2 = The Subskill is Present to Some Degree 3 = The Subskill is Present to a Marked Degree; This is a Fine Example of this Subskill

Figure 1. Problem-solving model for unstructured problems. Adapted from “Expert Problem Solving: Evidence from School and District Leaders,” by K. Leithwood and R. Steinbach, pp. 284-285. Copyright 1995 by the State University of New York Press.

I compared Likert-scale items and rubric scores via descriptive statistics and rubric scores also via a paired sample t -test and Cohen’s d , all using the software program IBM SPSS. I did not compare the Likert-scale items about situational awareness, flexibility, and problem solving ability with t -tests or Cohen’s d , since these items did not represent a validated instrument. They were only single items based upon participants’ ratings compared to literature-based definitions. However, the value of the comparison of means from fall to spring was triangulated with qualitative results to provide meaning. For example, to say that participants’ self-assessment ratings for perceived problem-solving abilities increased, I examined both the mean difference for items from fall to spring and what participants shared throughout the qualitative survey items and focus group interviews.

Prior to scoring participants’ responses to the scenarios using the rubric, and in an effort to maximize the content validity of the rubric scores, I calibrated my use of the rubric with two experts from the field. Two celebrated principals, representing more than 45 combined years of experience in school-level administration, collaboratively and comparatively scored participant responses. Prior to scoring, the team worked collaboratively to construct appropriate and comprehensive exemplar responses to the four problem-solving scenarios. Then the team blindly scored fall pretest scenario responses using the Leithwood and Steinbach (1995) rubric, and upon comparing scores, the interrater reliability correlation coefficient was .941, indicating a high degree of agreement throughout the team.

Qualitative data. These data were obtained from open-ended items on the survey, including participants’ responses to the given scenarios, as well as the focus group interview transcripts. I analyzed qualitative data consistent with the grounded theory principles of Strauss and Corbin (1998) and the constant comparative methods of Glaser (1965), including a period of open coding of results, leading to axial coding to determine the codes’ dimensions and relationships between categories and their subcategories, and selective coding to arrive at themes. Throughout the entire data analysis process, I repeatedly returned to raw data to determine the applicability of emergent codes to previously analyzed data. Some categorical codes based upon the review of literature were included in the initial coding process. These codes were derived from the existing theoretical problem-solving models of Bolman and Deal (2008) and Leithwood and Steinbach (1995). These codes included modeling , relationships , and best for kids . Open codes that emerged from the participants’ responses included experience , personality traits , current job/role , and team . Axial coding revealed, for example, that current jobs or roles cited, intuitively, provided both sufficient building-wide perspective and situational memory (i.e. for special education teachers and school counselors) and insufficient experiences (i.e. for classroom teachers) to solve the given problems with confidence. From such understandings of the codes, categories, and their dimensions, themes were developed.

Quantitative Results. First, participants’ overall, aggregate responses (not matched pairs) were compared from the fall to spring, descriptively. These findings are outlined in Table 3. As is seen in the table, each item saw a modest increase over the course of the year. Participant perceptions of their problem-solving abilities across the three constructs presented (situational awareness, flexibility, and problem solving) did increase over the course of the year, as did the average group score for the problem-solving scenarios. However, due to participant differences in the two data collection periods, these aggregate averages do not represent a matched-pair dataset.

Table 3 Fall to Spring Comparison of Likert-Scale and Rubric-Scored Items

a These problem-solving dimensions from literature were rated by participants on a scale from 1- 10. b Participants received a rubric score for each scenario between 0-18. Participants’ two scenario scores for each data collection period (fall, spring) were averaged to arrive at the scores represented here.

In order to determine the statistical significance of the increase in participants’ problem- solving rubric scores, a paired-samples t -test was applied to the fall ( M = 9.15; SD = 2.1) and spring ( M = 9.25; SD = 2.3) averages. Recall that 20 participants had valid surveys for both the fall and spring. The t -test ( t = -.153; df = 19; p = .880) revealed no statistically significant change from fall to spring, despite the minor increase (0.10). I applied Cohen’s d to calculate the effect size. The small sample size ( n = 20) for the paired-sample t -test may have contributed to the lack of statistical significance. However, standard deviations were also relatively small, so the question of effect size was of particular importance. Cohen’s d was 0.05, which is also very small, indicating that little change—really no improvement, from a statistical standpoint—in participants’ ability to create viable action plans to solve real-world problems occurred throughout the year. However, the participants’ perceptions of their problem-solving abilities did increase, as evidenced by the increases in the paired-samples perception means shown in Table 3, though these data were only examined descriptively (from a quantitative perspective) due to the fact that these questions were individual items that are not part of a validated instrument.

Qualitative Results. Participant responses to open-ended items on the questionnaire, responses to the scenarios, and oral responses to focus group interview questions served as sources of qualitative data. Since the responses to the scenarios were focused on participant competence with problem solving, as measured by the aforementioned rubric (Leithwood & Steinbach, 1995), these data were examined separately from data collected from the other two sources.

Responses to scenarios. As noted, participants’ rubric ratings for the scenarios did not display a statistically significant increase from fall to spring. As such, this outline will not focus upon changes in responses from fall to spring. Rather, I examined the responses, overall, through the lens of the Leithwood and Steinbach (1995) problem-solving framework indicators against which they were rated. Participants typically had outlined reasonable, appropriate, and logical solution processes. For example, in a potential bullying case scenario, two different participants offered, “I would speak to the other [students] individually if they have said or done anything mean to other student [ sic ] and be clear that it is not tolerable and will result in major consequences” and “I would initiate an investigation into the situation beginning with [an] interview with the four girls.” These responses reflect actions that the consulted experts anticipated from participants and deemed as logical and needed interventions. However, these two participants omitted other needed steps, such as addressing the bullied student’s mental health needs, based upon her mother’s report of suicidal ideations. Accordingly, participants earned points for reasonable and logical responses very consistently, yet, few full-credit responses were observed.

Problem interpretation scores were much more varied. For this indicator, some participants were able to identify many, if not all, the major issues in the scenarios that needed attention. For example, for a scenario where two teachers were not interacting professionally toward each other, many participants correctly identified that this particular scenario could include elements of sexual harassment, professionalism, teaching competence, and personality conflict. However, many other participants missed at least two of these key elements of the problem, leaving their solution processes incomplete. The categories of (a) goals and (b) principles and values also displayed a similarly wide distribution of response ratings.

One category, constraints, presented consistent difficulty for the participants. Ratings were routinely 0 and 1. Participants could not consistently report what barriers or obstacles would need addressing prior to success with their proposed solutions. To be clear, it was not a matter of participants listing invalid or unrealistic barriers or obstacles; rather, the participants were typically omitting constraints altogether from their responses. For example, for a scenario involving staff members arriving late and unprepared to data team meetings, many participants did not identify that a school culture of not valuing data-driven decision making or lack of norms for data team work could be constraints that the principal could likely face prior to reaching a successful resolution.

Responses to open-ended items. When asked for rationale regarding their ratings for situational awareness, flexibility, and problem solving, participants provided open-ended responses. These responses revealed patterns worth considering, and, again, this discussion will consider, in aggregate, responses made in both the pre- and post- data collection periods, again due to the similarities in responses between the two data collection periods. The most frequently observed code (112 incidences) was experience . Closely related were the codes current job/role (50 incidences). Together, these codes typically represented a theme that participants were linking their confidence with respect to problem solving with their exposure (or lack thereof) in their professional work. For example, a participant reported, “As a school counselor, I have a lot of contact with many stakeholders in the school -admin [ sic ], parents, teachers, staff, etc. I feel that I have a pretty good handle on the systemic issues.” This example is one of many where individuals working in counseling, instructional coaching, special education, and other support roles expressed their advanced levels of perspective based upon their regular contact with many stakeholders, including administrators. Thus, they felt they had more prior knowledge and situational memory about problems in their schools.

However, this category of codes also included those, mostly classroom or unified arts teachers, who expressed that their relative lack of experiences outside their own classrooms limited their perspective for larger-scale problem solving. One teacher succinctly summarized this sentiment, “I have limited experience in being part of situations outside of my classroom.” Another focused on the general problem solving skill in her classroom not necessarily translating to confidence with problem solving at the school level: “I feel that I have a high situational awareness as a teacher in the classroom, but as I move through these leadership programs I find that I struggle to take the perspective of a leader.” These experiences were presented in opposition to their book learning or university training. There were a number of instances (65 combined) of references to the value of readings, class discussions, group work, scenarios presented, research, and coursework in the spring survey. When asked what the participants need more, again, experience was referenced often. One participant summarized this concept, “I think that I, personally, need more experience in the day-to-day . . . setting.” Another specifically separated experiences from scenario work, “[T]here is [ sic ] some things you can not [ sic ] learn from merely discussing a ‘what if” scenario. A seasoned administrator learns problem solving skills on the job.”

Another frequently cited code was personality traits (63 incidences), which involved participants linking elements of their own personalities to their perceived abilities to process problems, almost exclusively from an assets perspective. Examples of traits identified by participants as potentially helpful in problem solving included: open-mindedness, affinity for working with others, not being judgmental, approachability, listening skills, and flexibility. One teacher exemplified this general approach by indicating, “I feel that I am a good listener in regards to inviting opinions. I enjoy learning through cooperation and am always willing to adapt my teaching to fit needs of the learners.” However, rare statements of personality traits interfering with problem solving included, “I find it hard to trust others [ sic ] abilities” and “my personal thoughts and biases.”

Another important category of the participant responses involved connections with others. First, there were many references to relationships (27 incidences), mostly from the perspective that building positive relationships leads to greater problem-solving ability, as the aspiring leader knows stakeholders better and can rely on them due to the history of positive interactions. One participant framed this idea from a deficit perspective, “Not knowing all the outlying relationships among staff members makes situational awareness difficult.” Another identified that established positive relationships are already helpful to an aspiring leader, “I have strong rapport with fellow staff members and administrators in my building.” In a related way, many instances of the code team were identified (29). These references overwhelmingly identified that solving problems within a team context is helpful. One participant stated, “I often team with people to discuss possible solutions,” while another elaborated,

I recognize that sometimes problems may arise for which I am not the most qualified or may not have the best answer. I realize that I may need to rely on others or seek out help/opinions to ensure that I make the appropriate decision.

Overall, participants recognized that problem-solving for leaders does not typically occur in a vacuum.

Responses to focus group interview questions. As with the open-ended responses, patterns were evident in the interview responses, and many of these findings were supportive of the aforementioned themes. First, participants frequently referenced the power of group work to help build their understanding about problems and possible solutions. One participant stated, “hearing other people talk and realizing other concerns that you may not have thought of . . . even as a teacher sometimes, you look at it this way, and someone else says to see it this way.” Another added, “seeing it from a variety of persons [ sic ] point of views. How one person was looking at it, and how another person was looking at it was really helpful.” Also, the participants noted the quality of the discussion was a direct result of “professors who have had real-life experience” as practicing educational leaders, so they could add more realistic feedback and insight to the discussions.

Perhaps most notable in the participant responses during the focus groups was the emphasis on the value of real-world scenarios for the students. These were referenced, without prompting, in all three focus groups by many participants. Answers to the question about what has been most helpful in the development of their problem-solving skills included, “I think the real-world application we are doing,” “I think being presented with all the scenarios,” and “[the professor] brought a lot of real situations.”

With respect to what participants believed they still needed to become better and more confident problem solvers, two patterns emerged. First, students recognized that they have much more to learn, especially with respect to policy and law. It is noteworthy that, with few exceptions, these students had not taken the policy or law courses in the program, and they had not yet completed their administrative internships. Some students actually reported rating themselves as less capable problem solvers in the spring because they now understood more clearly what they lacked in knowledge. One student exemplified this sentiment, “I might have graded myself higher in the fall than I did now . . . [I now can] self identify areas I could improve in that I was not as aware of.” Less confidence in the spring was a minority opinion, however. In a more typical response, another participant stated, “I feel much more prepared for that than I did at the beginning of the year.”

Overall, the most frequently discussed future need identified was experience, either through the administrative internship or work as a formal school administrator. Several students summarized this idea, “That real-world experience to have to deal with it without being able to talk to 8 other people before having to deal with it . . . until you are the person . . . you don’t know” and “They tell you all they want. You don’t know it until you are in it.” Overall, most participants perceived themselves to have grown as problem solvers, but they overwhelmingly recognized that they needed more learning and experience to become confident and effective problem solvers.

This study continues a research pathway about the development of problem-solving skills for administrators by focusing on their preparation. The participants did not see a significant increase in their problem-solving skills over the year-long course in educational leadership.

Whereas, this finding is not consistent with the findings of others who focused on the development of problem-solving skills for school leaders (Leithwood & Steinbach, 1995; Shapira-Lishchinsky, 2015), nor is it consistent with PBL research about the benefits of that approach for aspiring educational leaders (Copland, 2000; Hallinger & Bridges, 2017), it is important to note that the participants in this study were at a different point in their careers. First, they were aspirants, as opposed to practicing leaders. Also, the studied intervention (scenarios) was not the same or nearly as comprehensive as the prescriptive PBL approach. Further, unlike the participants in either the practicing leader or PBL studies, because these individuals had not yet had their internship experiences, they had no practical work as educational leaders. This theme of lacking practical experience was observed in both open-ended responses and focus group interviews, with participants pointing to their upcoming internship experiences, or even their eventual work as administrators, as a key missing piece of their preparation.

Despite the participants’ lack of real gains across the year of preparation in their problem- solving scores, the participants did, generally, report an increase in their confidence in problem solving, which they attributed to a number of factors. The first was the theme of real-world context. This finding was consistent with others who have advocated for teaching problem solving through real-world scenarios (Duke, 2014; Leithwood & Steinbach, 1992, 1995; Myran & Sutherland, 2016; Shapira-Lishchinsky, 2015). This study further adds to this conversation, not only a corroboration of the importance of this method (at least in aspiring leaders’ minds), but also that participants specifically recognized their professors’ experiences as school administrators as important for providing examples, context, and credibility to the work in the classroom.

In addition to the scenario approach, the participants also recognized the importance of learning from one another. In addition to the experiences of their practitioner-professors, many participants espoused the value of hearing the diverse perspectives of other students. The use of peer discussion was also an element of instruction in the referenced studies (Leithwood & Steinbach, 1995; Shapira-Lishchinsky, 2015), corroborating the power of aspiring leaders learning from one another and supporting existing literature about the social nature of problem solving (Berger & Luckmann, 1966; Leithwood & Steinbach, 1992; Vygotsky, 1978).

Finally, the ultimate theme identified through this study is the need for real-world experience in the field as an administrator or intern. It is simply not enough to learn about problem solving or learn the background knowledge needed to solve problems, even when the problems presented are real-world in nature. Scenarios are not enough for aspiring leaders to perceive their problem-solving abilities to be adequate or for their actual problem-solving abilities to improve. They need to be, as some of the participants reasoned, in positions of actual responsibility, where the weight of their decisions will have tangible impacts on stakeholders, including students.

The study of participants’ responses to the scenarios connected to the Four Frames model of Bolman and Deal (2008). The element for which participants received the consistently highest scores was identifying solution processes. This area might most logically be connected to the structural and human resource frames, as solutions typically involve working to meet individuals’ needs, as is necessary in the human resource frame, and attending to protocols and procedures, which is the essence of the structural frame. As identified above, the political and symbolic frames have been cited by the authors as the most underdeveloped by educational leaders, and this assertion is corroborated by the finding in this study that participants struggled the most with identifying constraints, which can sometimes arise from an understanding of the competing personal interests in an organization (political frame) and the underlying meaning behind aspects of an organization (symbolic frame), such as unspoken rules and traditions. The lack of success identifying constraints is also consistent with participants’ statements that they needed actual experiences in leadership roles, during which they would likely encounter, firsthand, the types of constraints they were unable to articulate for the given scenarios. Simply, they had not yet “lived” these types of obstacles.

The study includes several notable limitations. First, the study’s size is limited, particularly with only 20 participants’ data available for the matched pairs analysis. Further, this study was conducted at one university, within one particular certification program, and over three sections of one course, which represented about one-half of the time students spend in the program. It is likely that more gains in problem-solving ability and confidence would have been observed if this study was continued through the internship year. Also, the study did not include a control group. The lack of an experimental design limits the power of conclusions about causality. However, this limitation is mitigated by two factors. First, the results did not indicate a statistically significant improvement, so there is not a need to attribute a gain score to a particular variable (i.e. use of scenarios), anyway, and, second, the qualitative results did reveal the perceived value for participants in the use of scenarios, without any prompting of the researcher. Finally, the participant pool was not particularly diverse, though this fact is not particularly unusual for the selected university, in general, representing a contemporary challenge the university’s state is facing to educate its increasingly diverse student population, with a teaching and administrative workforce that is predominantly White.

The findings in this study invite further research. In addressing some of the limitations identified here, expanding this study to include aspiring administrators across other institutions representing different areas of the United States and other developed countries, would provide a more generalizable set of results. Further, studying the development of problem-solving skills during the administrative internship experience would also add to the work outlined here by considering the practical experience of participants.

In short, this study illustrates for those who prepare educational leaders the value of using scenarios in increasing aspiring leaders’ confidence and knowledge. However, intuitively, scenarios alone are not enough to engender significant change in their actual problem-solving abilities. Whereas, real-world context is important to the development of aspiring educational leaders’ problem-solving skills, the best context is likely to be the real work of administration.

Allison, D. J. (1996). Problem finding, classification and interpretation: In search of a theory of administrative problem processing. In K. Leithwood, J. Chapman, D. Corson, P. Hallinger, & A. Hart (Eds.), International handbook of educational leadership and administration (pp. 477–549). Norwell, MA: Kluwer Academic.

Berger, P. L., & Luckmann, T. (1966). The social construction of reality . Garden City, NJ: Doubleday.

Bolman, L. G., & Deal, T. E. (2008). Re-framing organizations: Artistry, choice and leadership (4th ed.). San Francisco: Jossey Bass.

Bronstein, C., & Fitzpatrick, K. R. (2015). Preparing tomorrow’s leaders: Integrating leadership development in journalism and mass communication education. Journalism & Mass Communication Educator, 70 (1), 75–88. https://doi.org/10.1177/1077695814566199

Copland, M. A. (2000). Problem-based learning and prospective principals’ problem-framing ability. Educational Administration Quarterly , 36 , 585–607.

Deluca, C., Bolden, B., & Chan, J. (2017). Systemic professional learning through collaborative inquiry: Examining teachers’ perspectives. Teaching and Teacher Education , 67 , 67–78. https://doi.org/10.1016/j.tate.2017.05.014

Dimmock, C. (1996). Dilemmas for school leaders and administrators in restructuring. In K. Leithwood, J. Chapman, D. Corson, P. Hallinger, & A. Hart (Eds.), International Handbook of Educational Leadership and Administration (pp. 135–170). Norwell, MA: Kluwer Academic.

Duke, D. L. (2014). A bold approach to developing leaders for low-performing schools. Management in Education, 28 (3), 80–85. https://doi.org/10.1177/0892020614537665

Gay, L. R., & Airasian, P. (2003). Educational research: Competancies for analysis and applications (7th ed.). Upper Saddle River, NJ: Pearson Education.

Glaser, B. G. (1965). The constant comparative method of qualitative analysis. Social Problems, 12 (4), 436-445.

Hallinger, P., & Bridges, E. (1993). Problem-based learning in medical and managerial education. In P. Hallinger, K. Leithwood, & J. Murphy (Eds.), Cognitive perspectives on educational leadership (pp. 253–267). New York: Teachers’ College Press.

Hallinger, P., & Bridges, E. M. (2017). A systematic review of research on the use of problem- based learning in the preparation and development of school leaders. Educational Administration Quarterly . 53(2), 255-288. https://doi.org/10.1177/0013161X16659347

Hallinger, P., & McCary, C. E. (1990). Developing the strategic thinking of instructional leaders. Elementary School Journal , 91 (2), 89–108.

Howard, B. B., McClannon, T. W., & Wallace, P. R. (2014). Collaboration through role play among graduate students in educational leadership in distance learning. American Journal of Distance Education , 28 (1), 51–61. https://doi.org/10.1080/08923647.2014.868665

Johnson, B. L., & Kruse, S. D. (2009). Decision making for educational leaders: Underexamined dimensions and issues . Albany, NY: State University of New York Press.

Leithwood, K., & Steinbach, R. (1992). Improving the problem-solving expertise of school administrators: Theory and practice. Education and Urban Society , 24 (3), 317–345. Retrieved from https://journals.sagepub.com.ccsu.idm.oclc.org/doi/pdf/10.1177/0013124592024003003

Leithwood, K., & Steinbach, R. (1995). Expert problem solving: Evidence from school and district leaders . Albany, NY: State University of New York Press.

Marzano, R. J., Waters, T., & McNulty, B. A. (2005). School leadership that works: From research to results . Denver, CO: ASCD.

Myran, S., & Sutherland, I. (2016). Problem posing in leadership education: Using case study to foster more effective problem solving. Journal of Cases in Educational Leadership , 19 (4), 57–71. https://doi.org/10.1177/1555458916664763

Rochford, L., & Borchert, P. S. (2011). Assessing higher level learning: Developing rubrics for case analysis. Journal of Education for Business , 86 , 258–265. https://doi.org/10.1080/08832323.2010.512319

Salas, E., Wildman, J. L., & Piccolo, R. F. (2009). Using simulation based training to enhance management education. Academy of Management Learning & Education , 8 (4), 559–573. https://doi.org/10.5465/AMLE.2009.47785474

Shapira-Lishchinsky, O. (2015). Simulation-based constructivist approach for education leaders. Educational Management Administration & Leadership , 43 (6), 972–988. https://doi.org/10.1177/1741143214543203

Simon, H. A. (1993). Decision making: Rational, nonrational, and irrational. Educational Administration Quarterly , 29 (3), 392–411. https://doi.org/10.1177/0013161X93029003009

Stentoft, D. (2017). From saying to doing interdisciplinary learning: Is problem-based learning the answer? Active Learning in Higher Education , 18 (1), 51–61. https://doi.org/10.1177/1469787417693510

Strauss, A., & Corbin, J. (1998). Basics of qualitative research (2nd ed.). Thousand Oaks, CA: Sage.

VanLehn, K. (1991). Rule acquisition events in the discovery of problem-solving strategies. Cognitive Science , 15 (1), 1–47. https://doi.org/10.1016/0364-0213(91)80012-T

Vygotsky, L. S. (1978). Mind in society . Cambridge, MA: Harvard University Press.

Winter, R. (1982). Dilemma analysis: A contribution to methodology for action research. Cambridge Journal of Education, 12 (3), 166-173.

Author Biography

Dr. Jeremy Visone is an Assistant Professor of Educational Leadership, Policy, & Instructional Technology. Until 2016, he worked as an administrator at both the elementary and secondary levels, most recently at Anna Reynolds Elementary School, a National Blue Ribbon School in 2016. Dr. Visone can be reached at [email protected] .

Principals and Problem-Solving

Posted November 13, 2014
By Bari Walsh

Chalkboard illustration that reads strategy, solutions, ideas, teamwork, success

If you’re a school principal, how does context matter when you’re facing a difficult problem? Where do you find your source of support, and do the people you turn to actually help you to reach effective solutions? Ebony Bridwell-Mitchell explores these questions in a paper published in Organization Science with co-author Theresa Lant, finding that the type of people principals surround themselves with, and to whom they turn for counsel, has a lot to do with how they think about their role and their challenges in the first place. This “cognitive context,” she found, helps determine their social context and is predictive of how they’ll go about solving problems or advancing their agenda.

Bridwell-Mitchell studies educational leadership, management, and organizations, often exploring the tension between structure and agency — “how we make choices within constraints,” as she describes it. “A lot of education policy is focused on what we can do to get people to make better choices — how we can spur them to be more gritty, or how we can incentivize them. But all the choices people make — even if they’re properly incentivized, even if they’re extra gritty — are constrained in some way by context. It turns out that when you look at differences across individuals, what best explains the variation is context. People in one context tend to think and do things a certain way, and very differently than people in another context.”

How Context Matters

In the recent paper, she set out to explore just how context matters when school principals are faced with decisions. She wanted to understand not only how principals’ social networks mattered, but also how cognitive context mattered — how they thought about or framed their problems.

She investigated two different ways in which principals might frame a pressing problem: as political, having to do with influence or power, or as strategic, having to do with performance and resources. She wanted to see whether that framing had an effect on the kinds of people they chose to go to for help.

She found that when people frame their problems politically, they are more likely to turn to advisors they think are trustworthy and have influence. But when they frame problems as being strategic, they are more likely to turn to people they think are accessible and have resources.

The Takeaway

What does all this mean in terms of helping principals solve problems? “If people have persistent patterns in how they see problems, then they have a tendency to choose certain kinds of people, irrespective of whether that’s what the problem actually is or those are the people they actually need,” says Bridwell-Mitchell. “You can imagine that people might be thinking about the problem in the wrong way and choosing the wrong people and not ending up with the solutions they need.”

“It really gives us an incentive to invest in what people often call shared decision making or shared leadership,” she continues. “What this is saying is, you need people to help you think carefully about these problems, so you can make sure you’re conceptualizing them in ways that will get you to the right people for help.”

Bridwell-Mitchell is doing a follow-up study to assess which cognitive contexts and social contexts may be more effective at solving which types of problems. She’s asking groups of principals to work through the issues involved in two randomly assigned scenarios, one about bullying and one about increasing achievement in middle-performing students, and then to come up with a solution. A set of experts — other principals and field experts — will assess and rate the solutions. The goal is to shed light on which factors were more helpful in arriving at effective solutions — cognitive framing, social context, or a combination of the two.

The bottom line is that context matters — perhaps more than any other factor — in effective leadership, says Bridwell-Mitchell. “If we’re not thinking about how much context matters, and how to change context, we’re losing most of the leverage that we have to actually get people to behave differently.”

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Problems and Problem Solving

What is a problem?

In common language, a problem is an unpleasant situation, a difficulty.

But in education the first definition in Webster's Dictionary — "a question raised for inquiry, consideration, or solution" — is a common meaning.

More generally in education, it's useful to define problem broadly — as any situation, in any area of life, where you have an opportunity to make a difference, to make things better — so problem solving is converting an actual current state into a desired future state that is better, so you have "made things better." Whenever you are thinking creatively-and-critically about ways to increase the quality of life (or to avoid a decrease in quality) for yourself and/or for others, you are actively involved in problem solving. Defined in this way, problem solving includes almost everything you do in life.

Problem-Solving Skills — Creative and Critical

An important goal of education is helping students learn how to think more productively while solving problems, by combining creative thinking (to generate ideas) and critical thinking (to evaluate ideas) with accurate knowledge (about the truth of reality). Both modes of thinking (creative & critical) are essential for a well-rounded productive thinker, according to experts in both fields:

Richard Paul (a prominent advocate of CRITICAL THINKING ) says, "Alternative solutions are often not given, they must be generated or thought-up. Critical thinkers must be creative thinkers as well, generating possible solutions in order to find the best one. Very often a problem persists, not because we can't tell which available solution is best, but because the best solution has not yet been made available — no one has thought of it yet."

Patrick Hillis & Gerard Puccio (who focus on CREATIVE THINKING ) describe the combining of creative generation with critical evaluation in a strategy of creative-and-critical Problem Solving that "contains many tools which can be used interchangeably within any of the stages. These tools are selected according to the needs of the task and are either divergent (i.e., used to generate options) or convergent (i.e., used to evaluate options)."

Creative Thinking can be motivated and guided by Creative Thinking: One of the interactions between creative thinking and critical thinking occurs when we use critical Evaluation to motivate and guide creative Generation in a critical - and - creative process of Guided Generation that is Guided Creativity . In my links-page for CREATIVITY you can explore this process in three stages, to better understand how a process of Guided Creativity — explored & recognized by you in Part 1 and then described by me in Part 2 — could be used (as illustrated in Part 3 ) to improve “the party atmosphere” during a dinner you'll be hosting, by improving a relationship.

Education for Problem Solving

By using broad definitions for problem solving and education, we can show students how they already are using productive thinking to solve problems many times every day, whenever they try to “make things better” in some way..

Problem Solving: a problem is an opportunity , in any area of life, to make things better. Whenever a decision-and-action helps you “ make it better ” — when you convert an actual state (in the past) into a more desirable actual state (in the present and/or future) — you are problem solving, and this includes almost everything you do in life, in all areas of life. { You can make things better if you increase quality for any aspect of life, or you maintain quality by reducing a potential decrease of quality. } / design thinking ( when it's broadly defined ) is the productive problem-solving thinking we use to solve problems. We can design (i.e. find, invent, or improve ) a better product, activity, relationship, and/or strategy (in General Design ) and/or (in Science-Design ) explanatory theory. { The editor of this links-page ( Craig Rusbult ) describes problem solving in all areas of life .}

note: To help you decide whether to click a link or avoid it, links highlighted with green or purple go to pages I've written, in my website about Education for Problem Solving or in this website for THINKING SKILLS ( CREATIVE and CRITICAL ) we use to SOLVE PROBLEMS .

Education: In another broad definition, education is learning from life-experiences, learning how to improve, to become more effective in making things better. For example, Maya Angelou – describing an essential difference between past and present – says "I did then what I knew how to do. Now that I know better, I do better, " where improved problem solving skills (when "do better" leads to being able to more effectively "make things better") has been a beneficial result of education, of "knowing better" due to learning from life-experiences.

Growth: One of the best ways to learn more effectively is by developing-and-using a better growth mindset so — when you ask yourself “how well am I doing in this area of life?” and honestly self-answer “not well enough” — instead of thinking “not ever” you are thinking “not yet” because you know that your past performance isn't your future performance; and you are confident that in this area of life (and in other areas) you can “grow” by improving your understandings-and-skills, when you invest intelligent effort in your self-education and self-improving. And you can "be an educator" by supporting the self-improving of other people by helping them improve their own growth mindsets. { resources for Growth Mindset }

Growth in Problem-Solving Skills: A main goal of this page is to help educators help students improve their skill in solving problems — by improving their ability to think productively (to more effectively combine creative thinking with critical thinking and accurate knowledge ) — in all areas of their everyday living. {resources: growth mindset for problem solving that is creative-and-critical }

How? You can improve your Education for Problem Solving by creatively-and-critically using general principles & strategies (like those described above & below, and elsewhere) and adapting them to specific situations, customizing them for your students (for their ages, abilities, experiences,...) and teachers, for your community and educational goals.

Promote Productive Thinking:

classroom (with Students & Teachers) actively doing Design Thinking

Build Educational Bridges:

When we show students how they use a similar problem-solving process (with design thinking ) for almost everything they do in life , we can design a wide range of activities that let us build two-way educational bridges:

• from Life into School, building on the experiences of students, to improve confidence: When we help students recognize how they have been using a problem-solving process of design thinking in a wide range of problem-solving situations,... then during a classroom design activity they can think “I have done this before (during design-in-life ) so I can do it again (for design-in-school )” to increase their confidence about learning. They will become more confident that they can (and will) improve the design-thinking skills they have been using (and will be using) to solve problems in life and in school.

• from School into Life, appealing to the hopes of students, to improve motivation: We can show each student how they will be using design thinking for "almost everything they do" in their future life (in their future whole-life, inside & outside school) so the design-thinking skills they are improving in school will transfer from school into life and will help them achieve their personal goals for life . When students want to learn in school because they are learning for life, this will increase their motivations to learn.

Improve Educational Equity:

When we build these bridges (past-to-present from Life into School , and present-to-future from School into Life ) we can improve transfers of learning — in time (past-to-present & present-to-future) and between areas (in school-life & whole-life) for whole-person education — and transitions in attitudes to improve a student's confidence & motivations. This will promote diversity and equity in education by increasing confidence & motivation for a wider range of students, and providing a wider variety of opportunities for learning in school, and for success in school. We want to “open up the options” for all students, so they will say “yes, I can do this” for a wider variety of career-and-life options, in areas of STEM (Science, Technology, Engineering, Math) and non-STEM .

This will help us improve diversity-and-equity in education by increasing confidence & motivations for a wider range of students, and providing a wider variety of opportunities for learning in school, and success in school.

Design Curriculum & Instruction:

• DEFINE GOALS for desired outcomes, for ideas-and-skills we want students to learn,

• DESIGN INSTRUCTION with learning activities (and associated teaching activities ) that will provide opportunities for experience with these ideas & skills, and help students learn more from their experiences. {more about Defining Goals and Designing Instruction } {one valuable activity is using a process-of-inquiry to learn principles-for-inquiry }

Problem-Solving Process for Science and Design

We'll look at problem-solving process for science (below) and design ( later ) separately, and for science-and-design together., problem-solving process for science, is there a “scientific method” we have reasons to say....

NO, because there is not a rigid sequence of steps that is used in the same way by all scientists, in all areas of science, at all times, but also...

YES, because expert scientists (and designers) tend to be more effective when they use flexible strategies — analogous to the flexible goal-directed improvising of a hockey player, but not the rigid choreography of a figure skater — to coordinate their thinking-and-actions in productive ways, so they can solve problems more effectively.

Below are some models that can help students understand and do the process of science. We'll begin with simplicity, before moving on to models that are more complex so they can describe the process more completely-and-accurately.

A simple model of science is PHEOC (Problem, Hypothesis, Experiment, Observe, Conclude). When PHEOC, or a similar model, is presented — or is misinterpreted — as a rigid sequence of fixed steps, this can lead to misunderstandings of science, because the real-world process of science is flexible. An assumption that “model = rigidity” is a common criticism of all models-for-process, but this unfortunate stereotype of "rigidity" is not logically justifiable because all models emphasize the flexibility of problem-solving process in real life, and (ideally) in the classroom. If a “step by step” model (like PHEOC or its variations) is interpreted properly and is used wisely, the model can be reasonably accurate and educationally useful. For example,...

A model that is even simpler — the 3-step POE (Predict, Observe, Learn) — has the essentials of scientific logic, and is useful for classroom instruction.

Science Buddies has Steps of the Scientific Method with a flowchart showing options for flexibility of timing. They say, "Even though we show the scientific method as a series of steps, keep in mind that new information or thinking might cause a scientist to back up and repeat steps at any point during the process. A process like the scientific method that involves such backing up and repeating is called an iterative process." And they compare Scientific Method with Engineering Design Process .

Lynn Fancher explains - in The Great SM - that "while science can be done (and often is) following different kinds of protocols, the [typical simplified] description of the scientific method includes some very important features that should lead to understanding some very basic aspects of all scientific practice," including Induction & Deduction and more.

From thoughtco.com, many thoughts to explore in a big website .

Other models for the problem solving process of science are more complex, so they can be more thorough — by including a wider range of factors that actually occur in real-life science, that influence the process of science when it's done by scientists who work as individuals and also as members of their research groups & larger communities — and thus more accurate. For example,

Understanding Science (developed at U.C. Berkeley - about ) describes a broad range of science-influencers, * beyond the core of science: relating evidence and ideas . Because "the process of science is exciting" they want to "give users an inside look at the general principles, methods, and motivations that underlie all of science." You can begin learning in their homepage (with US 101, For Teachers, Resource Library,...) and an interactive flowchart for "How Science Works" that lets you explore with mouse-overs and clicking.

* These factors affect the process of science, and occasionally (at least in the short run) the results of science. To learn more about science-influencers,...

Knowledge Building (developed by Bereiter & Scardamalia, links - history ) describes a human process of socially constructing knowledge.

The Ethics of Science by Henry Bauer — author of Scientific Literacy and the Myth of the Scientific Method (click "look inside") — examines The Knowledge Filter and a Puzzle and Filter Model of "how science really works."

[[ i.o.u. - soon, in mid-June 2021, I'll fix the links in this paragraph.]] Another model that includes a wide range of factors (empirical, social, conceptual) is Integrated Scientific Method by Craig Rusbult, editor of this links-page . Part of my PhD work was developing this model of science, in a unifying synthesis of ideas from scholars in many fields, from scientists, philosophers, historians, sociologists, psychologists, educators, and myself. The model is described in two brief outlines ( early & later ), more thoroughly, in a Basic Overview (with introduction, two visual/verbal representations, and summaries for 9 aspects of Science Process ) and a Detailed Overview (examining the 9 aspects more deeply, with illustrations from history & philosophy of science), and even more deeply in my PhD dissertation (with links to the full text, plus a “world record” Table of Contents, references, a visual history of my diagrams for Science Process & Design Process, and using my integrative model for [[ integrative analysis of instruction ). / Later, I developed a model for the basic logic-and-actions of Science Process in the context of a [[ more general Design Process .

Problem-Solving Process for Design

Because "designing" covers a wide range of activities, we'll look at three kinds of designing..

Engineering Design Process: As with Scientific Method,

a basic process of Engineering Design can be outlined in a brief models-with-steps – 5 5 in cycle 7 in cycle 8 10 3 & 11 . {these pages are produced by ==[later, I'll list their names]}

and it can be examined in more depth: here & here and in some of the models-with-steps (5... 3 & 11), and later .

Problem-Solving Process: also has models-with-steps ( 4 4 5 6 7 ) * and models-without-steps (like the editor's model for Design-Thinking Process ) to describe creative-and-critical thinking strategies that are similar to Engineering Design Process, and are used in a wider range of life — for all problem-solving situations (and these include almost everything we do in life) — not just for engineering. { * these pages are produced by ==}

Design-Thinking Process: uses a similar creative-and-critical process, * but with a focus on human - centered problems & solutions & solving - process and a stronger emphasis on using empathy . (and creativity )

* how similar? This depends on whether we define Design Thinking in ways that are narrow or broad. {the wide scope of problem-solving design thinking } {why do I think broad definitions (for objectives & process) are educationally useful ?}

Education for Design Thinking (at Stanford's Design School and beyond)

Problem Solving in Our Schools:

Improving education for problem solving, educators should want to design instruction that will help students improve their thinking skills. an effective strategy for doing this is..., goal-directed designing of curriculum & instruction.

When we are trying to solve a problem (to “make things better”) by improving our education for problem solving, a useful two-part process is to...

1. Define GOALS for desired outcomes, for the ideas-and-skills we want students to learn;

2. Design INSTRUCTION with Learning Activities that will provide opportunities for experience with these ideas & skills, and will help students learn more from their experiences.

Basically, the first part ( Define Goals ) is deciding WHAT to Teach , and the second part ( Design Instruction ) is deciding HOW to Teach .

But before looking at WHAT and HOW , here are some ways to combine them with...

Strategies for Goal-Directed Designing of WHAT-and-HOW.

Understanding by Design ( UbD ) is a team of experts in goal-directed designing,

as described in an overview of Understanding by Design from Vanderbilt U.

Wikipedia describes two key features of UbD: "In backward design, the teacher starts with classroom outcomes [#1 in Goal-Directed Designing above ] and then [#2] plans the curriculum, * choosing activities and materials that help determine student ability and foster student learning," and "The goal of Teaching for Understanding is to give students the tools to take what they know, and what they will eventually know, and make a mindful connection between the ideas. ... Transferability of skills is at the heart of the technique. Jay McTighe and Grant Wiggin's technique. If a student is able to transfer the skills they learn in the classroom to unfamiliar situations, whether academic or non-academic, they are said to truly understand."

* UbD "offers a planning process and structure to guide curriculum, assessment, and instruction. Its two key ideas are contained in the title: 1) focus on teaching and assessing for understanding and learning transfer, and 2) design curriculum “backward” from those ends."

ASCD – the Association for Supervision and Curriculum Development (specializing in educational leadership ) – has a resources-page for Understanding by Design that includes links to The UbD Framework and Teaching for Meaning and Understanding: A Summary of Underlying Theory and Research plus sections for online articles and books — like Understanding by Design ( by Grant Wiggins & Jay McTighe with free intro & U U ) and Upgrade Your Teaching: Understanding by Design Meets Neuroscience ( about How the Brain Learns Best by Jay McTighe & Judy Willis who did a fascinating ASCD Webinar ) and other books — plus DVDs and videos (e.g. overview - summary ) & more .

Other techniques include Integrative Analysis of Instruction and Goal-Directed Aesop's Activities .

In two steps for a goal-directed designing of education , you:

1) Define GOALS (for WHAT you want students to improve) ;

2) Design INSTRUCTION (for HOW to achieve these Goals) .

Although the sections below are mainly about 1. WHAT to Teach (by defining Goals ) and 2. HOW to Teach (by designing Instruction ) there is lots of overlapping, so you will find some "how" in the WHAT, and lots of "what" in the HOW.

P ERSONAL Skills (for Thinking about Self)

A very useful personal skill is developing-and-using a...

Growth Mindset: If self-education is broadly defined as learning from your experiences, better self-education is learning more effectively by learning more from experience, and getting more experiences. One of the best ways to learn more effectively is by developing a better growth mindset so — when you ask yourself “how well am I doing in this area of life?” and honestly answer “not well enough” — you are thinking “not yet” (instead of “not ever”) because you are confident that in this area of life (as in most areas, including those that are most important) you can “grow” by improving your skills, when you invest intelligent effort in your self-education. And you can support the self-education of other people by helping them improve their own growth mindsets. Carol Dweck Revisits the Growth Mindset and (also by Dweck) a video, Increasing Educational Equity and Opportunity . 3 Ways Educators Can Promote A Growth Mindset by Dan LaSalle, for Teach for America. Growth Mindset: A Driving Philosophy, Not Just a Tool by David Hochheiser, for Edutopia. Growth Mindset, Educational Equity, and Inclusive Excellence by Kris Slowinski who links to 5 videos . What’s Missing from the Conversation: The Growth Mindset in Cultural Competency by Rosetta Lee. YouTube video search-pages for [ growth mindset ] & [ mindset in education ] & [ educational equity mindset ].

also: Growth Mindset for Creativity

Self-Perception -- [[a note to myself: accurate understanding/evaluation of self + confidence in ability to improve/grow ]]

M ETA C OGNITIVE Skills (for Solving Problems)

What is metacognition? Thinking is cognition. When you observe your thinking and think about your thinking (maybe asking “how can I think more effectively?”) this is meta- cognition, which is cognition about cognition. To learn more about metacognition — what it is, why it's valuable, and how to use it more effectively — some useful web-resources are:

a comprehensive introductory overview by Nancy Chick, for Vanderbilt U.

my links-section has descriptions of (and links to) pages by other authors: Jennifer Livingston, How People Learn, Marsha Lovett, Carleton College, Johan Lehrer, Rick Sheets, William Peirce, and Steven Shannon, plus links for Self-Efficacy with a Growth Mindset , and more about metacognition.

my summaries about the value of combining cognition-and-metacognition and regulating it for Thinking Strategies (of many kinds ) to improve Performing and/or Learning by Learning More from Experience with a process that is similar to...

the Strategies for Self-Regulated Learning developed by other educators.

videos — search youtube for [ metacognition ] and [ metacognitive strategies ] and [ metacognition in education ].

And in other parts of this links-page,

As one part of guiding students during an inquiry activity a teacher can stimulate their metacognition by helping them reflect on their experiences.

While solving problems, almost always it's useful to think with empathy and also with metacognitive self-empathy by asking “what do they want?” and “what do I want?” and aiming for a win-win solution.

P ROCESS -C OORDINATING Skills (for Solving Problems)

THINKING SKILLS and THINKING PROCESS: When educators develop strategies to improve the problem solving abilities of students, usually their focus is on thinking skills. But thinking process is also important.

Therefore, it's useful to define thinking skills broadly, to include thinking that leads to decisions-about-actions, and actions:

thinking → action-decisions → actions

[[ I.O.U. -- later, in mid-June 2021, the ideas below will be developed -- and i'll connect it with Metacognitive Skills because we use Metacognition to Coordinate Process.

[[ here are some ideas that eventually will be in this section:

Collaborative Problem Solving [[ this major new section will link to creative.htm# collaborative-creativity (with a brief summary of ideas from there) and expand these ideas to include general principles and "coordinating the collaboration" by deciding who will do what, when, with some individual "doing" and some together "doing" ]]

actions can be mental and/or physical (e.g. actualizing Experimental Design to do a Physical Experiment, or actualizing an Option-for-Action into actually doing the Action

[[a note to myself: educational goals: we should help students improve their ability to combine their thinking skills — their creative Generating of Options and critical Generating of Options, plus using their Knowledge-of-Ideas that includes content-area knowledge plus the Empathy that is emphasized in Design Thinking — into an effective thinking process .

[[ Strategies for Coordinating: students can do this by skillfully Coordinating their Problem-Solving Actions (by using their Conditional Knowledge ) into an effective Problem-Solving Process.

[[ During a process of design, you coordinate your thinking-and-actions by making action decisions about “what to do next.” How? When you are "skillfully Coordinating..." you combine cognitive/metacognitive awareness (of your current problem-solving process) with (by knowing, for each skill, what it lets you accomplish, and the conditions in which it will be useful).

[[ a little more about problem-solving process

[[ here are more ideas that might be used here:

Sometimes tenacious hard work is needed, and perseverance is rewarded. Or it may be wise to be flexible – to recognize that what you've been doing may not be the best approach, so it's time to try something new – and when you dig in a new location your flexibility pays off.

Perseverance and flexibility are contrasting virtues. When you aim for an optimal balancing of this complementary pair, self-awareness by “knowing yourself” is useful. Have you noticed a personal tendency to err on the side of either too much perseverance or not enough? Do you tend to be overly rigid, or too flexible?

Making a wise decision about perseverance — when you ask, “Do I want to continue in the same direction, or change course?” * — is more likely when you have an aware understanding of your situation, your actions, the results, and your goals. Comparing results with goals is a Quality Check, providing valuable feedback that you can use as a “compass” to help you move in a useful direction. When you look for signs of progress toward your goals in the direction you're moving, you may have a feeling, based on logic and experience, that your strategy for coordinating the process of problem solving isn't working well, and it probably never will. Or you may feel that the goal is almost in sight and you'll soon reach it.

- How I didn't Learn to Ski (and then did) with Persevering plus Flexible Insight -

PRINCIPLES for PROBLEM SOLVING

Should we explicitly teach principles for thinking, can we use a process of inquiry to teach principles for inquiry, should we use a “model” for problem-solving process.

combining models?

What are the benefits of infusion and separate programs?

Principles & Strategies & Models ?

Should we explicitly teach “principles” for thinking?

Using evidence and logic — based on what we know about the ways people think and learn — we should expect a well-designed combination of “experience + reflection + principles” to be more educationally effective than experience by itself, to help students improve their creative-and-critical thinking skills and whole-process skills in solving problems (for design-inquiry) and answering questions (for science-inquiry).

Can we use a process-of-inquiry to teach principles-for-inquiry?

* In a typical sequence of ERP, students first get Experiences by doing a design activity. During an activity and afterward, they can do Reflections (by thinking about their experiences) and this will help them recognize Principles for doing Design-Thinking Process that is Problem-Solving Process. { design thinking is problem-solving thinking }

During reflections & discussions, typically students are not discovering new thoughts & actions. Instead they are recognizing that during a process of design they are using skills they already know because they already have been using Design Thinking to do almost everything in their life . A teacher can facilitate these recognitions by guiding students with questions about what they are doing now, and what they have done in the past, and how these experiences are similar, but also are different in some ways. When students remember (their prior experience) and recognize (the process they did use, and are using), they can formulate principles for their process of design thinking. But when they formulate principles for their process of problem solving, they are just making their own experience-based prior knowledge — of how they have been solving problems, and are now solving problems — more explicit and organized.

If we help students "make their own experience-based prior knowledge... more explicit and organized" by showing them how their knowledge can be organized into a model for problem-solving process, will this help them improve their problem-solving abilities?

IOU - This mega-section will continue being developed in mid-June 2021.

[[a note to myself: thinking skills and thinking process — What is the difference? - Experience + Reflection + Principles - coordination-decisions

[[are the following links specifically for this section about "experience + principles"? maybe not because these seem to be about principles, not whether to teach principles.]]

An excellent overview is Teaching Thinking Skills by Kathleen Cotton. (the second half of her page is a comprehensive bibliography)

This article is part of The School Improvement Research Series (available from Education Northwest and ERIC ) where you can find many useful articles about thinking skills & other topics, by Cotton & other authors. [[a note to myself: it still is excellent, even though it's fairly old, written in 1991 -- soon, I will search to find more-recent overviews ]]

Another useful page — What Is a Thinking Curriculum ? (by Fennimore & Tinzmann) — begins with principles and then moves into applications in Language Arts, Mathematics, Sciences, and Social Sciences.

My links-page for Teaching-Strategies that promote Active Learning explores a variety of ideas about strategies for teaching (based on principles of constructivism, meaningful reception,...) in ways that are intended to stimulate active learning and improve thinking skills. Later, a continuing exploration of the web will reveal more web-pages with useful “thinking skills & problem solving” ideas (especially for K-12 students & teachers) and I'll share these with you, here and in TEACHING ACTIVITIES .

Of course, thinking skills are not just for scholars and schoolwork, as emphasized in an ERIC Digest , Higher Order Thinking Skills in Vocational Education . And you can get information about 23 ==Programs that Work from the U.S. Dept of Education.

goals can include improving affective factors & character == e.g. helping students learn how to develop & use use non-violent solutions for social problems .

INFUSION and/or SEPARATE PROGRAMS?

In education for problem solving, one unresolved question is "What are the benefits of infusion, or separate programs? " What is the difference?

With infusion , thinking skills are closely integrated with content instruction in a subject area, in a "regular" course.

In separate programs , independent from content-courses, the explicit focus of a course is to help students improve their thinking skills.

In her overview of the field, Kathleen Cotton says,

Of the demonstrably effective programs, about half are of the infused variety, and the other half are taught separately from the regular curriculum. ... The strong support that exists for both approaches... indicates that either approach can be effective. Freseman represents what is perhaps a means of reconciling these differences [between enthusiastic advocates of each approach] when he writes, at the conclusion of his 1990 study: “Thinking skills need to be taught directly before they are applied to the content areas. ... I consider the concept of teaching thinking skills directly to be of value especially when there follows an immediate application to the content area.”

For principles and examples of infusion , check the National Center for Teaching Thinking which lets you see == What is Infusion? (an introduction to the art of infusing thinking skills into content instruction), and == sample lessons (for different subjects, grade levels, and thinking skills). -- resources from teach-think-org -- [also, lessons designed to infuse Critical and Creative Thinking into content instruction]

Infusing Teaching Thinking Into Subject-Area Instruction (by Robert Swarz & David Perkins) - and more about the book

And we can help students improve their problem-solving skills with teaching strategies that provide structure for instruction and strategies for thinking . ==[use structure+strategies only in edu-section?

Adobe [in creative]

MORE about Teaching Principles for Problem Solving

[[ i.o.u. -- this section is an "overlap" between #1 (Goals) and #2 (Methods) so... maybe i'll put it in-between them? -- i'll decide soon, maybe during mid-June 2021 ]]

Two Kinds of Inquiry Activities (for Science and Design )

To more effectively help students improve their problem-solving skills, teachers can provide opportunities for students to be actively involved in solving problems, with inquiry activities . What happens during inquiry? Opportunities for inquiry occur whenever a gap in knowledge — in conceptual knowledge (so students don't understand) or procedural knowledge (so they don't know what to do, or how) — stimulates action (mental and/or physical) and students are allowed to think-do-learn.

Students can be challenged to solve two kinds of problems during two kinds of inquiry activity:

during Science-Inquiry they try to improve their understanding, by asking problem-questions and seeking answers. During their process of solving problems, they are using Science-Design , aka Science , to design a better explanatory theory.

during Design-Inquiry they try to improve some other aspect(s) of life, by defining problem-projects and seeking solutions. During their process of solving problems, they are using General Design (which includes Engineering and more) to design a better product, activity, or strategy.

But... whether the main objective is for Science-Design or General Design, a skilled designer will be flexible, will do whatever will help them solve the problem(s). Therefore a “scientist” sometimes does engineering, and an “engineer” sometimes does science. A teacher can help students recognize how-and-why they also do these “ crossover actions ” during an activity for Science Inquiry or Design Inquiry. Due to these connections, we can build transfer-bridges between the two kinds of inquiry , and combine both to develop “hybrid activities” for Science-and-Design Inquiry.

Goal-Priorities: There are two kinds of inquiry, so (re: Goals for What to Learn) what emphasis do we want to place on activities for Science -Inquiry and Design -Inquiry? (in the limited amount of classroom time that teachers can use for Inquiry Activities)

Two Kinds of Improving (for Performing and Learning )

Goal-Priorities: There are two kinds of improving, so (re: Goals for What to Learn) what emphasis do we want to place on better Performing (now) and Learning (for later)?

When defining goals for education, we ask “How important is improving the quality of performing now, and (by learning now ) of performing later ?” For example, a basketball team (coach & players) will have a different emphasis in an early-season practice (when their main goal is learning well) and end-of-season championship game (when their main goal is performing well). {we can try to optimize the “total value” of performing/learning/enjoying for short-term fun plus long-term satisfactions }

SCIENCE (to use-learn-teach Skills for Problem Solving )

Problem-solving skills used for science.

This section supplements models for Scientific Method that "begin with simplicity, before moving on to models that are more complex so they can describe the process more completely-and-accurately. " On the spectrum of simplicity → complexity , one of the simplest models is...

POE (Predict, Observe, Learn) to give students practice with the basic scientific logic we use to evaluate an explanatory theory about “what happens, how, and why.” POE is often used for classroom instruction — with interactive lectures [iou - their website is temporarily being "restored"] & in other ways — and research has shown it to be effective. A common goal of instruction-with-POE is to improve the conceptual knowledge of students, especially to promote conceptual change their alternative concepts to scientific concepts. But students also improve their procedural knowledge for what the process of science is, and how to do the process. { more – What's missing from POE ( experimental skills ) w hen students use it for evidence-based argumentation and Ecologies - Educational & Conceptual }

Dany Adams (at Smith College) explicitly teaches critical thinking skills – and thus experiment-using skills – in the context of scientific method.

Science Buddies has models for Scientific Method (and for Engineering Design Process ) and offers Detailed Help that is useful for “thinking skills” education. ==[DetH]

Next Generation Science Standards ( NGSS ) emphasizes the importance of designing curriculum & instruction for Three Dimensional Learning with productive interactions between problem-solving Practices (for Science & Engineering ) and Crosscutting Concepts and Disciplinary Core Ideas.

Science: A Process Approach ( SAPA ) was a curriculum program earlier, beginning in the 1960s. Michael Padilla explains how SAPA defined The Science Process Skills as "a set of broadly transferable abilities, appropriate to many science disciplines and reflective of the behavior of scientists. SAPA categorized process skills into two types, basic and integrated. The basic (simpler) process skills provide a foundation for learning the integrated (more complex) skills." Also, What the Research Says About Science Process Skills by Karen Ostlund; and Students' Understanding of the Procedures of Scientific Enquiry by Robin Millar, who examines several approaches and concludes (re: SAPA) that "The process approach is not, therefore, a sound basis for curriculum planning, nor does the analysis on which it is based provide a productive framework for research." But I think parts of it can be used creatively for effective instruction. { more about SAPA }

ENGINEERING (to use-learn-teach Skills for Problem Solving )

Problem-solving skills used for engineering.

Engineering is Elementary ( E i E ) develops activities for students in grades K-8. To get a feeling for the excitement they want to share with teachers & students, watch an "about EiE" video and explore their website . To develop its curriculum products, EiE uses research-based Design Principles and works closely with teachers to get field-testing feedback, in a rigorous process of educational design . During instruction, teachers use a simple 5-phase flexible model of engineering design process "to guide students through our engineering design challenges... using terms [ Ask, Imagine, Plan, Create, Improve ] children can understand." {plus other websites about EiE }

Project Lead the Way ( PLTW ), another major developer of k-12 curriculum & instruction for engineering and other areas, has a website you can explore to learn about their educational philosophy & programs (at many schools ) & resources and more. And you can web-search for other websites about PLTW.

Science Buddies , at level of k-12, has tips for science & engineering .

EPICS ( home - about ), at college level, is an engineering program using EPICS Design Process with a framework supplemented by sophisticated strategies from real-world engineering. EPICS began at Purdue University and is now used at ( 29 schools) (and more with IUCCE ) including Purdue, Princeton, Notre Dame, Texas A&M, Arizona State, UC San Diego, Drexel, and Butler.

DESIGN THINKING (to use-learn-teach Skills for Problem Solving )

Design Thinking emphasizes the importance of using empathy to solve human-centered problems.

Stanford Institute of Design ( d.school ) is an innovative pioneer in teaching a process of human-centered design thinking that is creative-and-critical with empathy . In their Design Thinking Bootleg – that's an updated version of their Bootcamp Bootleg – they share a wide variety of attitudes & techniques — about brainstorming and much more — to stimulate productive design thinking with the objective of solving real-world problems. {their first pioneer was David Kelley }

The d.school wants to "help prepare a generation of students to rise with the challenges of our times." This goal is shared by many other educators, in k-12 and colleges, who are excited about design thinking. Although d.school operates at college level, they (d.school + IDEO ) are active in K-12 education as in their website about Design Thinking in Schools ( FAQ - resources ) that "is a directory [with brief descriptions] of schools and programs that use design thinking in the curriculum for K12 students... design thinking is a powerful way for today’s students to learn, and it’s being implemented by educators all around the world." { more about Education for Design Thinking in California & Atlanta & Pittsburgh & elsewhere} [[a note to myself: @ ws and maybe my broad-definition page]]

On twitter, # DTk12 chat is an online community of enthusiastic educators who are excited about Design Thinking ( DT ) for K-12 Education, so they host a weekly twitter chat (W 9-10 ET) and are twitter-active informally 24/7.

PROBLEM-BASED LEARNING (to use-learn-teach Skills for Problem Solving )

Problem-Based Learning ( PBL ? ) is a way to improve motivation, thinking, and learning. You can learn more from:

overviews of PBL from U of WA & Learning-Theories.com ;

and (in ERIC Digests) using PBL for science & math plus a longer introduction - challenges for students & teachers (we never said it would be easy!) ;

a deeper examination by John Savery (in PDF & [without abstract] web-page );

Most Popular Papers from The Interdisciplinary Journal of Problem-based Learning ( about IJPBL ).

videos about PBL by Edutopia (9:26) and others ;

a search in ACSD for [problem-based learning] → a comprehensive links-page for Problem-Based Learning and an ACSD-book about...

Problems as Possibilities by Linda Torp and Sara Sage: Table of Contents - Introduction (for 2nd Edition) - samples from the first & last chapters - PBL Resources (including WeSites in Part IV) .

PBL in Schools:

Samford University uses PBL (and other activities) for Transformational Learning that "emphasizes the whole person, ... helps students grow physically, mentally, and spiritually, and encourages them to value public service as well as personal gain."

In high school education, Problem-Based Learning Design Institute from Illinois Math & Science Academy ( about ); they used to have an impressive PBL Network ( sitemap & web-resources from 2013, and 9-23-2013 story about Kent, WA ) that has mysteriously disappeared. https://www.imsa.edu/academics/inquiry/resources/ research_ethics

Vanderbilt U has Service Learning thru Community Engagement with Challenges and Opportunities and tips for Teaching Step by Step & Best Practices and Resource-Links for many programs, organizations, articles, and more.

What is PBL? The answer is " Problem-Based Learning and/or Project-Based Learning " because both meanings are commonly used. Here are 3 pages (+ Wikipedia) that compare PBL with PBL, examine similarities & differences, consider definitions:

John Larmer says "we [at Buck Institute for Education which uses Project Based Learning ] decided to call problem-based learning a subset of project-based learning [with these definitions, ProblemBL is a narrower category, so all ProblemBL is ProjectBL, but not vice versa] – that is, one of the ways a teacher could frame a project is to solve a problem, " and concludes that "the semantics aren't worth worrying about, at least not for very long. The two PBLs are really two sides of the same coin. ... The bottom line is the same: both PBLs can powerfully engage and effectively teach your students!" Chris Campbell concludes, "it is probably the importance of conducting active learning with students that is worthy and not the actual name of the task. Both problem-based and project-based learning have their place in today’s classroom and can promote 21st Century learning." Jan Schwartz says "there is admittedly a blurring of lines between these two approaches to education, but there are differences." Wikipedia has Problem-Based Learning (with "both" in P5BL ) and Project-Based Learning .

i.o.u. - If you're wondering "What can I do in my classroom today ?", eventually (maybe in June 2021) there will be a section for "thinking skills activities" in this page, and in the area for TEACHING ACTIVITIES .

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20 Problem-Solving Activities for Middle School Students

Middle School Education

Introduction:

As students progress through middle school, it becomes increasingly important to develop their problem-solving skills. By engaging in problem-solving activities, students can enhance their critical thinking abilities, foster creativity, and become better prepared for the challenges they may face both in and out of the classroom. Here are 20 problem-solving activities that are perfect for middle school students.

1. Brainstorming Sessions: Encourage students to share their ideas on a particular topic or issue, fostering a collaborative environment that promotes creative problem solving.

2. Riddles: Challenge students with riddles that require critical thinking and lateral thinking skills to determine the answers.

3. Sudoku: Introduce sudoku puzzles as a fun and challenging math-based activity.

4. Chess Club: Encourage students to participate in chess clubs or tournaments to practice strategic thinking.

5. Escape Rooms: Plan an age-appropriate escape room activity to develop teamwork and problem-solving skills among the students.

6. Role-Playing Exercises: Use role-playing scenarios to allow students to think critically about real-life situations and practice problem-solving strategies.

7. Science Experiments: Design science experiments that require students to troubleshoot problems and test possible solutions.

8. Word Problems: Incorporate word problems in math lessons, encouraging students to use logic and math skills to solve them.

9. Puzzle Stations: Set up different puzzle stations around the classroom where students can work on spatial reasoning, logic puzzles, and other brain teasers during free time.

10. Debates: Organize debates on controversial topics, allowing students to present and argue their views while developing their critical thinking and persuasion skills.

11. Engineering Challenges: Provide engineering-based challenges such as bridge building or packaging design activities that require teamwork and creative problem solving.

12. Storytelling Workshops: Host a storytelling workshop where students collaborate to create stories from a given prompt and gradually face more complex narrative challenges.

13. Coding Clubs: Support students in learning coding basics and encourage them to develop problem-solving skills through coding projects.

14. Treasure Hunts: Create treasure hunts with clues that require problem solving, reasoning, and collaboration among the students.

15. Cooperative Games: Facilitate games that promote cooperation and communication, such as “human knot” or “cross the lava.”

16. Geocaching: Introduce geocaching as a fun activity where students use GPS devices to locate hidden objects and work as a team to solve puzzle-like tasks.

17. Exploratory Research Projects: Assign open-ended research projects that require students to investigate topics of interest and solve problems or answer questions through their research efforts.

18. Mock Trials: Set up mock trials in which students participate as lawyers, witnesses, or jury members, allowing them to analyze cases and think through legal problem-solving strategies.

19. Creative Writing Prompts: Share creative writing prompts requiring students to think critically about characters’ actions and decisions within fictional scenarios.

20. Invention Convention: Host an invention convention where students present their unique solutions to everyday problems, fostering creativity and innovative thinking.

Conclusion:

Problem-solving activities are essential for middle school students as they help in cultivating valuable life skills necessary to tackle real-world challenges. These 20 activities provide diverse and engaging opportunities for students to develop key problem-solving skills while fostering creativity, communication, critical thinking, and collaboration. Teachers and educators can easily adapt these activities to suit the individual needs of their middle school classrooms.

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Home » Blog » General » Teaching Problem-Solving Skills to Middle School Students

Teaching Problem-Solving Skills to Middle School Students

Introduction

Problem-solving is a vital skill for navigating the complexities of life. It involves understanding a problem, identifying potential solutions, and taking action to resolve the issue. As children grow older, they encounter new and more challenging problems, both at school and at home. Teaching middle school students effective problem-solving techniques can help them become more independent, resilient, and adaptable individuals. In this blog post, we will explore a no-prep activity, discussion questions, and related skills to help educators teach problem-solving to middle school students.

No-Prep Activity: The Problem-Solving Relay

The Problem-Solving Relay is a fun and engaging activity that requires no preparation or materials. Here’s how it works:

Divide the class into teams of 4-5 students.
Ask each team to line up on one side of the room.
Present a problem to the class, such as a disagreement between friends or a challenge at school.
Each team member must take turns contributing one step of the problem-solving process, as outlined in the introduction.
When a student completes their turn, they run to the back of the line, and the next student continues with the next step.
The first team to complete all the steps and come up with a viable solution wins the relay.

This activity encourages students to collaborate and apply the problem-solving steps in a fast-paced, interactive setting.

Discussion Questions

To stimulate further discussion and reflection on problem-solving, consider asking your students these questions:

What challenges did you face when trying to come up with a solution during the relay activity? How did you overcome them?
Can you think of a time when you successfully solved a problem? What steps did you take, and what did you learn from the experience?
How can understanding the size of a problem help you determine the best course of action?
Why is it important to consider the feelings of others when choosing a solution to a problem?
How can practicing problem-solving skills help you in your everyday life, both at school and at home?

Related Skills

Problem-solving is closely connected to several other essential social-emotional learning skills, including:

Empathy: Understanding the feelings and perspectives of others can help students develop more effective solutions to interpersonal problems.
Communication: Clear and respectful communication is crucial for presenting and negotiating solutions with others.
Resilience: Developing strong problem-solving skills can help students bounce back from setbacks and adapt to new challenges.
Decision-making: Weighing the pros and cons of various solutions requires critical thinking and sound judgment.

Teaching problem-solving skills to middle school students is essential for their personal and academic growth. By incorporating activities like the Problem-Solving Relay and engaging in thoughtful discussions, you can help your students become more adept at navigating life’s challenges. To access free samples of problem-solving materials and explore other social-emotional learning resources, sign up at Everyday Speech .

Teaching Conflict Resolution and Problem Solving Skills to Special Education Students

Introduction Conflicts are a normal part of life, and learning how to navigate them is an essential skill for students in Special Education. In this blog post, we will discuss the importance of teaching students to handle conflicts with friends using the Problem...

5 Golden Rules of Play for Elementary Students: A Guide for Educators

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Empower Students to Solve Their Problems

By claire brantley curcio | september 2023.

Adopt an empowerment motto or theme for the year (e.g., “We are Powerful!”), ensuring staff understand its meaning and communicate it to students consistently.
Start the year with an empowerment assembly or pep rally, teaching the circle of control . Introducing foundational concepts in a larger setting saves you time in classrooms to use later for extension.
Connect all subsequent lessons back to this mindset and skillset.
For more practice, offer students extra credit to complete after your lessons.
Don’t do this alone. Provide teachers with videos or PowerPoints. One counselor collaborated with her librarian, computer teacher and art teacher to reinforce this in class projects.
Review circle of control and skills on the morning announcements. One counselor aired a weekly game-show-style question, challenging classes to apply their learning from that week’s announcements in a case scenario. Participating classes were recognized through PBIS.
Find where you can marry empowerment and problem-solving with existing PBIS/MTSS structure, such as your school’s behavior matrix or morning meetings. One school revised their leadership award criteria. Examples of how winners demonstrated exemplary mindset or problem-solving can be included on certificates.
Hang posters in classrooms, the cafeteria, hallways and outside.
Facilitate an “Undercover Kindness” group where Tier 2 problem-solvers brainstorm and perform anonymous acts of kindness at school, strengthening belief in their ability and intrinsic motivation to positively impact others.
One counselor provides parents with laminated half sheets of these resources for use with their child at home. Consistency across environments improves outcomes.

Mathematics Anxiety and Problem-Solving Proficiency Among High School Students: Unraveling the Complex Interplay in the Knowledge Economy

Published: 15 April 2024

Cite this article

Yali Zhu 1 ,
Xinran Liu 1 ,
Yana Xiao 1 &
Stavros Sindakis ORCID: orcid.org/0000-0002-3542-364X 2

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In the context of the knowledge-based economy, the intricate relationship between mathematics anxiety and problem-solving abilities among high school students in China is examined. This research uncovers the pervasive nature of mathematics anxiety, influenced primarily by external factors such as parental expectations, shedding light on the sources of anxiety. Additionally, it highlights the multifaceted nature of problem-solving skills among students, emphasizing their confidence in comprehending mathematical problems but challenges in applying effective problem-solving strategies. The study provides empirical evidence of a significant negative correlation between mathematics anxiety and problem-solving ability, underscoring the detrimental impact of anxiety on cognitive processes, including working memory and metacognition, essential for effective problem solving. Theoretical implications encompass a deeper understanding of the dynamics between mathematics anxiety and problem-solving skills, contributing to educational psychology and curriculum development. Policy implications call for immediate attention to address mathematics anxiety within educational reforms, advocating for comprehensive strategies that alleviate anxiety while enhancing problem-solving skills. Furthermore, this research highlights the importance of gender-inclusive approaches to anxiety in mathematics. This study enriches our theoretical understanding and underscores the urgency of holistic approaches to address mathematics anxiety and nurture problem-solving skills among high school students, empowering them to excel in the knowledge-based economy and shape a brighter future.

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Mathematics Anxiety: Definition, Prevention, Reversal Strategies and School Setting Inclusion

A Cross-national Study of Mathematics Anxiety

Zhenguo Yuan, Jiang Tan & Renmin Ye

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Alowais, T. M. (2019). Influence of transformational leadership style on global competitive advantage through innovation and knowledge. Modern Applied Science, 13 (1), 183–191.

Article Google Scholar

Ashcraft, M. H. (2019). Models of math anxiety. In Mathematics Anxiety , 1–19. Routledge.

Ayuso, N., Fillola, E., Masiá, B., Murillo, A. C., Trillo-Lado, R., Baldassarri, S., & Villarroya-Gaudó, M. (2020). Gender gap in STEM: A cross-sectional study of primary school students’ self-perception and test anxiety in mathematics. IEEE Transactions on Education , 64 (1), 40–49.

Bacolod-Iglesia, A. B., Dundain, H. H., Vegare-Miñoza, M., & Casimiro, A. B. (2021). Teaching mathematics in ‘different tongues’: An analysis of mathematics anxiety and proficiency among elementary-grade learners. Linguistics and Culture Review, 5 (S2), 860–891.

Blakemore, S. J. (2019). Adolescence and mental health. The Lancet, 393 (10185), 2030–2031.

Brumariu, L. E., Waslin, S. M., Gastelle, M., Kochendorfer, L. B., & Kerns, K. A. (2022). Anxiety, academic achievement, and academic self-concept: Meta-analytic syntheses of their relations across developmental periods. Development and Psychopathology , 1–17.

Cargnelutti, E., Tomasetto, C., & Passolunghi, M. C. (2017). The interplay between affective and cognitive factors in shaping early proficiency in mathematics. Trends in Neuroscience and Education, 8 , 28–36.

Caviola, S., Toffalini, E., Giofrè, D., Ruiz, J. M., Szűcs, D., & Mammarella, I. C. (2021). Math performance and academic anxiety forms, from sociodemographic to cognitive aspects: A meta-analysis on 906,311 participants. Educational Psychology Review , 1–37.

Chen, G. A., & Horn, I. S. (2022). A call for critical bifocality: Research on marginalization in mathematics education. Review of Educational Research, 92 (5), 786–828.

Ching, B. H. H., Kong, K. H. C., Wu, H. X., & Chen, T. T. (2020). Examining the reciprocal relations of mathematics anxiety to quantitative reasoning and number knowledge in Chinese children. Contemporary Educational Psychology, 63 , 101919.

Choi, S. S., Taber, J. M., Thompson, C. A., & Sidney, P. G. (2020). Math anxiety, but not induced stress, is associated with objective numeracy. Journal of Experimental Psychology: Applied, 26 (4), 604.

Google Scholar

Costello, E. (2022). An action research investigation into pedagogies of enactment in initial teacher education to support pre-service primary teachers to teach mathematics for relational understanding (doctoral dissertation. National University of Ireland.

Eddy, S. L., & Brownell, S. E. (2016). Beneath the numbers: A review of gender disparities in undergraduate education across science, technology, engineering, and math disciplines. Physical Review Physics Education Research, 12 (2), 020106.

English, L. D., & Gainsburg, J. (2015). 12 problem solving in a 21st-century mathematics curriculum. Handbook of international research in mathematics education , 313–335.

Erdem, S. S., & Arikan, E. E. (2023). The correlation between middle school 8th-grade students’ reflective thinking skill towards problem-solving and their mathematics anxieties. International Journal of Social Inquiry, 16 (1), 95–110.

Fini, E. H., Awadallah, F., Parast, M. M., & Abu-Lebdeh, T. (2018). The impact of project-based learning on improving student learning outcomes of sustainability concepts in transportation engineering courses. European Journal of Engineering Education, 43 (3), 473–488.

Frey, N., Fisher, D., & Smith, D. (2019). All learning is social and emotional: Helping students develop essential skills for the classroom and beyond. Ascd.

Garwood, J. D., Peltier, C., Ciullo, S., Wissinger, D., McKenna, J. W., Giangreco, M. F., & Kervick, C. (2023). The experiences of students with disabilities actually doing service learning: A systematic review. Journal of Experiential Education, 46 (1), 5–31.

Gay, G. (2018). Culturally responsive teaching: Theory, research, and practice. Teachers’ college press.

Genc, M., & Erbas, A. K. (2020). Exploring secondary mathematics teachers’ conceptions of the barriers to mathematical literacy development. International Journal for Mathematics Teaching and Learning, 21 (2), 143–173.

Gresham, G. (2018). Preservice to inservice: Does mathematics anxiety change with teaching experience? Journal of Teacher Education, 69 (1), 90–107.

Guerrero, E. R. (2020). Math anxiety and financial literacy among Latino secondary students in the United States.

Hannula, M. (2018). From anxiety to engagement: History and future of research on mathematics-related affect. In Conference of the international group for the psychology of mathematics education, 42 .

Hashmi, S. S. (2021). The correlation between math anxiety, student placement, and academic achievement in mathematics among Latino high school students enrolled in algebra 1 courses (doctoral dissertation, Northcentral University).

Hassler Hallstedt, M., Klingberg, T., & Ghaderi, A. (2018). Short and long-term effects of a mathematics tablet intervention for low performing second graders. Journal of Educational Psychology, 110 (8), 1127.

Hiller, S. E., Kitsantas, A., Cheema, J. E., & Poulou, M. (2022). Mathematics anxiety and self-efficacy as predictors of mathematics literacy. International Journal of Mathematical Education in Science and Technology, 53 (8), 2133–2151.

Huang, X., Zhang, J., & Hudson, L. (2019). Impact of math self-efficacy, math anxiety, and growth mindset on math and science career interest for middle school students: The gender moderating effect. European Journal of Psychology of Education, 34 , 621–640.

Hudson, C. M. (2020). Mathematics and American fiction: Using mathematics to account for innovative literary forms and narrative mimesis. Illinois State University.

Hunt, T. E., & Maloney, E. A. (2022). Appraisals of previous math experiences play an important role in math anxiety. Annals of the New York Academy of Sciences, 1515 (1), 143–154.

Ismail, N., Garba, A., Osman, S., Ibrahim, N. H., & Bunyamin, M. A. H. (2022). Exploring teacher effects on intensifying and minimizing mathematics anxiety among students in Sokoto State, Nigeria. International Journal of Evaluation and Research in Education, 11 (1), 161–171.

Jorgensen, R. (2020). Teaching mathematics in primary schools: Principles for effective practice. Routledge.

Kress, J. S., & Elias, M. J. (2019). Nurturing students’ character: Everyday teaching activities for social-emotional learning. Routledge.

Kunwar, R., & Sapkota, H. P. (2022). An overview of dyslexia: Some key issues and its effects on learning mathematics. Online Submission, 11 (2), 82–98.

Lai, C. K., & Banaji, M. R. (2020). The psychology of implicit intergroup bias and the prospect of change (pp. 115–146). University of Chicago Press.

Leppma, M., & Darrah, M. (2022). Self-efficacy, mindfulness, and self-compassion as predictors of math anxiety in undergraduate students. International Journal of Mathematical Education in Science and Technology , 1–16.

Li, X., & Li, Y. (2023). Individualized and innovation-centered general education in a Chinese STEM university. Education Sciences, 13 (8), 846.

Liou, D. D., Leigh, P. R., Rotheram-Fuller, E., & Cutler, K. D. (2019). The influence of teachers’ colorblind expectations on the political, normative, and technical dimensions of educational reform. International Journal of Educational Reform, 28 (1), 122–148.

Ma, Y. (2020). Ambitious and anxious: How Chinese college students succeed and struggle in American higher education. Columbia University Press.

Macmull, M. S., & Ashkenazi, S. (2019). Math anxiety: The relationship between parenting style and math self-efficacy. Frontiers in Psychology, 10 , 1721.

Malanchini, M., Rimfeld, K., Wang, Z., Petrill, S. A., Tucker-Drob, E. M., Plomin, R., & Kovas, Y. (2020). Genetic factors underlie the association between anxiety, attitudes and performance in mathematics. Translational Psychiatry, 10 (1), 12.

Mannix, J. P. (2022). Exploring characteristics and experiences of secondary mathematics teachers with math anxiety. North Carolina State University.

Martin, A. E., & Phillips, K. W. (2019). Blind to bias: The benefits of gender-blindness for STEM stereotyping. Journal of Experimental Social Psychology, 82 , 294–306.

Mues, A., Wirth, A., Birtwistle, E., & Niklas, F. (2022). Associations between children’s numeracy competencies, mothers’ and fathers’ mathematical beliefs, and numeracy activities at home. Frontiers in Psychology, 13 , 835433.

National Academies of Sciences, Engineering, and Medicine. (2018). Graduate STEM education for the 21st century. National Academies Press.

Nursyahidah, F., Saputro, B. A., & Rubowo, M. R. (2018). Students problem solving ability based on realistic mathematics with ethnomathematics. Journal of Research and Advances in Mathematics Education, 3 (1), 13–24.

Radišić, J., Videnović, M., & Baucal, A. (2015). Math anxiety—contributing school and individual level factors. European Journal of Psychology of Education, 30 (1), 1–20.

Rahaman, H. A., Bornaa, C. S., Iddrisu, A. B., Kabinaa, E., Suglo, S. A., & Adams, F. X. (2023). Gender and mathematics anxiety among senior high school students.

Ramirez, G., Shaw, S. T., & Maloney, E. A. (2018). Math anxiety: Past research, promising interventions, and a new interpretation framework. Educational Psychologist, 53 (3), 145–164.

Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: psychometric data. Journal of counseling Psychology , 1 9(6), 551.

Robinson, L. E., Valido, A., Drescher, A., Woolweaver, A. B., Espelage, D. L., LoMurray, S., & Dailey, M. M. (2023). Teachers, stress, and the COVID-19 pandemic: A qualitative analysis. School mental health , 15 (1), 78–89.

Rozgonjuk, D., Kraav, T., Mikkor, K., Orav-Puurand, K., & Täht, K. (2020). Mathematics anxiety among STEM and social sciences students: The roles of mathematics self-efficacy, and deep and surface approach to learning. International Journal of STEM Education, 7 (1), 1–11.

Sahagun, M. A., Moser, R., Shomaker, J., & Fortier, J. (2021). Developing a growth-mindset pedagogy for higher education and testing its efficacy. Social Sciences & Humanities Open, 4 (1), 100168.

Samuel, T. S., & Warner, J. (2021). ‘I can math!’: Reducing math anxiety and increasing math self-efficacy using a mindfulness and growth mindset-based intervention in first-year students. Community College Journal of Research and Practice, 45 (3), 205–222.

Semeraro, C., Giofrè, D., Coppola, G., Lucangeli, D., & Cassibba, R. (2020). The role of cognitive and non-cognitive factors in mathematics achievement: The importance of the quality of the student-teacher relationship in middle school. PLoS ONE, 15 (4), e0231381.

Sidney, P. G., Thalluri, R., Buerke, M. L., & Thompson, C. A. (2019). Who uses more strategies? Linking mathematics anxiety to adults’ strategy variability and performance on fraction magnitude tasks. Thinking & Reasoning, 25 (1), 94–131.

Singh, S. (2022). Perceived intelligence and pedagogy: How teachers’ perceptions influence teaching (Doctoral dissertation).

Skagerlund, K., Östergren, R., Västfjäll, D., & Träff, U. (2019). How does mathematics anxiety impair mathematical abilities? Investigating the link between math anxiety, working memory, and number processing. PLoS ONE, 14 (1), e0211283.

Stella, M. (2022). Network psychometrics and cognitive network science open new ways for understanding math anxiety as a complex system. Journal of Complex Networks , 10 (3), cnac012.

Surya, S. F., & Nengah, P. I. (2019). Looking without seeing: The role of metacognitive blindness of student with high math anxiety. International Journal of Cognitive Research in Science, Engineering and Education, 7 (2), 53–65.

Szabo, Z. K., Körtesi, P., Guncaga, J., Szabo, D., & Neag, R. (2020). Examples of problem-solving strategies in mathematics education supporting the sustainability of 21st-century skills. Sustainability, 12 (23), 10113.

Szczygieł, M. (2020). When does math anxiety in parents and teachers predict math anxiety and math achievement in elementary school children? The role of gender and grade year. Social Psychology of Education, 23 (4), 1023–1054.

Tomasetto, C., Morsanyi, K., Guardabassi, V., & O’Connor, P. A. (2021). Math anxiety interferes with learning novel mathematics contents in early elementary school. Journal of Educational Psychology, 113 (2), 315.

Venne, R. A., & Hannay, M. (2018). Generational change, the modern workplace and performance appraisal: Why changing workplaces need a developmental approach to performance appraisal. American Journal of Management , 18 (5).

Villarta, Y. M., Atibula, L. T., & Gagani, F. S. (2021). Performance-based assessment: Self-efficacy, decision-making, and problem-solving skills in learning science. Journal La Edusci, 2 (3), 1–9.

Whyte, J. M. (2022). Mathematics anxiety and primary school teachers: The histories, impacts, and influences: A thesis presented in partial fulfilment of the requirements for the degree of Doctor of Education at Massey University, Manawatū, New Zealand (Doctoral dissertation, Massey University).

Zhang, J., Cheung, S. K., Wu, C., & Meng, Y. (2018). Cognitive and affective correlates of Chinese children’s mathematical word problem solving. Frontiers in Psychology, 9 , 2357.

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This study was financially supported by the Research on the Evaluation Effect of Hybrid Training for Rural Teachers in China, 2019JSJYZD-010, and the 2021 Henan Province Teacher Education Curriculum Reform Project “Research on the Reform of Economics Curriculum for Ideological and Political Majors from the Perspective of Practical Transformation” (2021-JSJYZD-011).

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School of Mathematics and Information, Henan Normal University, Xinxiang, 453002, Henan, China

Yali Zhu, Xinran Liu & Yana Xiao

School of Social Sciences, Hellenic Open University, 18 Aristotelous Street, 26335, Patras, Greece

Stavros Sindakis

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Correspondence to Yali Zhu .

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Zhu, Y., Liu, X., Xiao, Y. et al. Mathematics Anxiety and Problem-Solving Proficiency Among High School Students: Unraveling the Complex Interplay in the Knowledge Economy. J Knowl Econ (2024). https://doi.org/10.1007/s13132-023-01688-w

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What’s Really Holding Schools Back From Implementing SEL?

The biggest barrier schools face in putting social-emotional learning curriculum in place is an age-old foe: time.

A lack of funding and support from teachers are big hurdles too, according to a new survey of school leaders.

The National Center for Education Statistics reached out to 1,700 public schools in February of this year as part of its School Pulse survey , collecting input from principals, vice principals, and other school-level leaders. The feedback received shows that school leaders are confident that their school environments help foster students’ social-emotional skills, even as they face many challenges in adopting and effectively implementing formal SEL curricula.

School leaders see what’s happening on their campuses on a daily basis and the social-emotional skills students are picking up, said Sherrie Raven, the director of SEL implementation for the Collaborative for Academic, Social, and Emotional Learning, or CASEL. But, she said, a formal curriculum remains important. "[T]here are skills that students need to learn that might not be ‘caught’ just from the environment,” she said.

But she added that putting a formal curriculum in place can be difficult.

“Many schools do face barriers in implementing a formal curriculum,” she said. “Most often, these are barriers of time due to the limited number of minutes in each school day and the many areas teachers are asked to address.”

Seventy-two percent of school leaders in schools that had adopted an SEL curriculum cited time as the most limiting factor in executing the curriculum and 46 percent in schools that had not adopted a curriculum pointed to time as the most limiting factor in adopting a curriculum. Nearly two-thirds of schools in the survey said they had a formal SEL curriculum.

But from there, the challenges facing schools diverge.

Among the public schools that have a formal social-emotional learning curriculum, the second and third most-cited challenges limiting the effectiveness of the SEL curriculum were lack of teacher support (24 percent) and lack of parental and guardian buy-in (20 percent). Sixteen percent pointed to a lack of funding and to the curriculum being too burdensome for teachers to implement completely.

A lack of communication or using education jargon that parents don’t understand can work against school leaders’ efforts to implement or adopt an SEL program, said Karen Thierry, the research manager at Committee for Children who oversees the implementation of the organization’s Second Step social-emotional learning program.

Woman finding her way to a happy smile icon in the middle of labyrinth like maze with school subject icons ghosted over a cloudy sky textured background.

“Social-emotional learning is about teaching students life skills like communication and problem-solving, which are critical for success in school and in life,” she said. “Create opportunities to engage families and provide regular updates to help bridge understanding and support for social-emotional learning. You can connect via school newsletters, social media, or during in-person open houses or events when they can hear from leaders and teachers directly and ask questions.”

Among the schools that do not have a formal SEL curriculum, a lack of funding and a lack of materials and resources were the second and third most common barriers to adopting a program: Thirty-seven percent of school leaders said they didn’t have the money for a formal SEL curriculum while 34 percent said they lacked the materials and resources. Twenty-one percent said that a lack of district-level support for the curriculum was a barrier.

Schools without a formal SEL curriculum cited a lack of teacher support as one of the top five barriers to adopting an SEL program, with 17 percent of school leaders citing that as an issue and making it the fifth most-cited barrier for this group.

‘What you need to be doing to build relationships’

Teachers generally care about their students, said Raven, so getting them behind an SEL initiative is a barrier that school leaders can clear. Raven, a former principal, said that one way to get teacher buy-in is to make sure that school leaders are practicing what they preach.

“One time, I was in a training where the leader looked at me as the principal and said, ‘Everything that you expect your teachers to do to build relationships with students is what you need to be doing to build relationships with your staff.’”

Despite the challenges in implementing or adopting an SEL curriculum, school leaders are confident that their schools are places that foster and promote their students’ social-emotional development, whether or not they have a formal curriculum.

Eighty-five percent of school leaders agree that the culture at their school supports their students’ social-emotional growth, while 86 percent feel their discipline practices reinforce students’ social-emotional skills.

Third grade teacher, Stephanie Brugler, works with her class during an SEL lesson at the Jefferson PK-8 school in Warren, Ohio, on Nov. 1, 2022.

A similarly high percentage of school leaders—82 percent—say that their schools provide teachers with the support and resources needed to integrate students’ social-emotional skills into academic content.

Most school leaders also agree that teachers do dedicate time for students to practice social and emotional skills (72 percent) and that most teachers at their schools integrate SEL concepts into their lesson plans (62 percent).

One more important finding to note: School leaders are not raving about the effectiveness of their SEL curriculum, giving it mostly average marks. The plurality of survey respondents—45 percent—rated their SEL curriculum as moderately effective while nearly a quarter said it was either very effective or slightly effective. Only a handful rated their SEL curriculum as either extremely effective or not effective at all.

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Carrie White, a second-grade teacher, makes a heart with her hands for her student, Tyrell King-Harrell, left, during an SEL exercise at Yates Magnet Elementary School in Schenectady, N.Y., on March 28, 2024.

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An elementary school in Kansas is combating bad behavior — by putting kids to work

Suzanne Perez

A pilot program in elementary schools gives kids meaningful work as a way to handle post-pandemic behavior problems.

AILSA CHANG, HOST:

Schoolteachers across the country say they are still struggling with post-pandemic behavior problems in classrooms. The spike in tantrums, outbursts and fidgeting coincides with a national mental health crisis. Suzanne Perez of the Kansas News Service shows us how one elementary school that state is responding to bad behavior by putting kids to work.

SUZANNE PEREZ, BYLINE: Twice a week at Woodman Elementary School in Wichita, a third-grader named Reagan reports for duty with school counselor Shauna Barnes.

SHAUNA BARNES: So you're spraying each one of the tiny plants.

PEREZ: Reagan is the school's official plant waterer. Armed with a kid-sized spray bottle, she checks each plant on the windowsill of the teacher's lounge and gives it a quick drink. Barnes offers direction.

BARNES: See how much water they need?

REAGAN: This one's kind of wet, so I'll give it a little bit.

PEREZ: It may not look like much, but experiences like this can be life-changing for some children. Woodman is experimenting with a program called Meaningful Work. Counselors take kids who regularly misbehave in class and pair them with a mentor, then offer them something constructive to do on a regular schedule - a simple task like feeding fish or making copies. School psychologist Jaime Johnston says the concept is pretty simple.

JAIME JOHNSTON: Students were acting out to get attention with people they like. We have a fun group of supporting adults, and the students enjoyed hanging out with us. But we need them to display appropriate behaviors and stay in class.

PEREZ: Assigning jobs to students is not necessarily new. Elementary school teachers often post job charts denoting things like line leaders or trash collectors, but those are in class and supervised by the regular teacher. With Meaningful Work, students are matched with adults outside the classroom, including counselors, psychologists and social workers. Jessica Sprick is an education consultant with Safe & Civil Schools, an Oregon-based company that promotes the Meaningful Work program. She says, when children get attention for negative behavior, their behavior gets worse. Giving them a job and positive feedback can turn that around.

JESSICA SPRICK: If you can start getting some of that groundwork in place to make the kid feel that you're noticed, that you're wanted - that, when you're not here, there's a piece of our school that isn't as good as when you are - then we can get the kid coming to school, and then the academics improve, and then the behavior improves, right? So it really can be the starting place for whole-scale change.

PEREZ: The program isn't just for kids who misbehave. At Woodman Elementary, some students are selected because they get fidgety and need regular movement breaks. Others have anxiety and need to practice interacting with peers and adults. Jovany, a third-grader, is nonverbal and communicates with a handheld device that can be programmed to say certain phrases. Twice a week, Jovany fills a wagon with fresh fruits or vegetables from the cafeteria and delivers them to classrooms as part of the school's healthy snack program.

JOVANY: (Through handheld device) Here's your vegetables.

UNIDENTIFIED TEACHER: Thank you.

JOVANY: (Through handheld device) You're welcome.

UNIDENTIFIED TEACHER: Can everybody say thank you?

UNIDENTIFIED CHILDREN: Thank you.

UNIDENTIFIED TEACHER: Thank you, Jovany. Bye-bye.

UNIDENTIFIED CHILD: Bye.

PEREZ: Sprick recalls one teacher who assigned a student to be the school's official door unlocker. The child made rounds with the custodian every morning to check locks and welcome staff inside. He took the job so seriously he didn't want to take a sick day.

SPRICK: The mom actually called and said, you know, can you tell my son that the doors will be unlocked if he doesn't come to school? 'Cause he's got 103 fever and he's trying to tell me he needs to come.

PEREZ: School leaders say behavior problems have decreased since they launched the jobs program last fall, and attendance is up. They plan to expand the program next year.

For NPR News, I'm Suzanne Perez in Wichita.

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How to Reduce Student Absenteeism

Readers discuss the reasons for the spike since the pandemic and how to lure students back.

Why School Absences Have ‘Exploded’ Almost Everywhere

The pandemic changed families’ lives and the culture of education: “Our relationship with school became optional.”

To the Editor:

“ Pandemic Effect: Absence From Schools Is Soaring ” (front page, March 30) highlights the persistent challenge of chronic absenteeism in U.S. schools. If pandemic-related “cultural shifts” are among the factors keeping students away from school, bringing them back may require us to rethink the culture of education itself.

Despite the efforts of many visionary educators, too many schools still offer a deskbound, test- and compliance-driven experience that leaves students passive, uninspired and flat-out bored.

Over the last two years, a pilot program in Salem, Mass. , has succeeded in cutting chronic absenteeism among middle schoolers in half by listening to students and designing learning with their interests in mind, including regular field trips, hands-on projects and mentoring with college students. Today, the chronic absenteeism rate among the pilot cohort of seventh and eighth graders hovers at 8 percent, in no small part because students don’t want to miss what’s on offer at school.

Educators can reset school culture by being adaptive, believing in teacher leadership and recognizing that powerful learning can happen outside classroom walls. Unlike the use of Band-Aids and gimmickry that do not result in long-term change, valuing a philosophy of “education everywhere,” as Salem has embraced, will result in improved attendance and academic growth.

Stephen Hinds Laura Tavares Stephen Zrike Chelsea Banks Mr. Hinds is president and Ms. Tavares is executive director of the WPS Institute, an education nonprofit. Dr. Zrike is superintendent and Ms. Banks is dean of innovation for Salem Public Schools.

This article brings light to an issue plaguing school districts across the country. As a former classroom teacher, I remember talking with students who returned to school after being absent. They would ask for the work they missed. While I could share the assignment, I could not possibly share the rest of what they missed, including the social and academic interaction with their peers, the instruction provided, the opportunity to ask questions while working through material and being part of a community.

When done right, school is more than a collection of assignments. It is a vibrant social fabric that provides a culture of belonging, and opportunities to grow and explore with trusted adults guiding the way.

The solution to the absenteeism problem is not easy. As the chief education officer at Mikva Challenge, a group that works to engage young people in the civic process and have their voices part of critical decision making affecting their lives, I know that for any solution to be successful, it must involve youth in the process.

Our default as adults is to make decisions in the best interest of children, without asking them what they think and whether an idea will work. Young people are not apathetic; they are uninvited. They care deeply about the issues that affect them. And when they are engaged in decision making, policy is better.

Jill Bass Chicago

We had mixed feelings when reading “Pandemic Effect: Absence From Schools Is Soaring.” On the one hand, it’s important for the public to understand that chronic absenteeism in America is no small problem. On the other hand, the article unwittingly minimized the deep struggle so many families experience, particularly those from underresourced backgrounds.

You quote a researcher who stated, “The problem got worse for everybody in the same proportional way,” but we question whether this accurately reflects the reality in America today. Based on our own and others’ research, we believe that families who struggled before the pandemic were much more vulnerable to its effects.

We cannot ignore just how much deeper Covid affected communities of color, communities with risk factors, communities in poverty and communities in rural areas. This does not negate anyone’s struggles; yet the struggle has been disproportionate. This cannot be ignored.

Zahava L. Friedman Keri Giordano Hillside, N.J. Dr. Friedman is an assistant professor and Dr. Giordano is an associate professor at the College of Health Professions and Human Services, Kean University.

My 12-year-old son has been absent from school most of this year and is a part of the chronic absenteeism statistics cited in the article. His attendance was excellent until he caught Covid twice in one year from school. He was 9 years old and has been chronically ill ever since.

It is shocking to me that the article never suggests that some absenteeism might be due to chronic illness from Covid.

One recent study suggested that as many as 5.8 million kids in the United States have had their health affected by long Covid. These statistics are highly contested, but given how reluctant our doctors have been to diagnose or treat our child for something that they cannot measure with any blood test, it is not surprising that we do not really know the full extent of this disease.

My child, and many other children like him, cannot go to school because they are struggling with the persistent life-altering symptoms of chronic illness. These children want to go back to school. Don’t leave them out of the story.

Sarah Mathis Pleasanton, Calif.

The root causes of chronic absenteeism in American public schools are as varied as the solutions needed to combat it. One often overlooked and underfunded strategy with the potential to re-engage students in learning is arts education.

A 2021 study on the benefits of arts instruction in the Boston Public Schools showed that increased access to arts education reduced student absenteeism, with a greater impact on students who had been chronically absent.

BPS Arts Expansion is a public-private partnership that has dramatically expanded access to quality arts education throughout the school district and enabled longitudinal research on its impact.

No one strategy will be the panacea for chronic absenteeism. But as districts across the country grapple with this issue, expanding access to in-school arts instruction warrants attention.

Marinell Rousmaniere Boston The writer is the president and C.E.O. of EdVestors, a nonprofit school improvement organization.

Massac County High School Teacher Megan Musselman, center, helps students brainstorm ideas during EcoThink’s “Fast Fashion” sustainability challenge. Teams of students were asked to think of ways to reduce, reuse or recycle clothing, tackling an emerging environmental problem.

PADUCAH, Ky. – Local high school students from western Kentucky and southern Illinois put their problem solving skills to the test during the annual EcoThink project, challenging themselves to address environmental and sustainability issues through critical thinking exercises focused on teamwork and engineering concepts.

“The students really enjoyed this opportunity,” Paducah Tilghman High School Teacher Amy Clark said. “They liked seeing other students’ thought processes and ideas. One student said the word engineering frightened her but realized it wasn't as scary as she thought.”

This year’s project focused on a “Fast Fashion” challenge and the environmental impact of manufacturing cheap, limited-use clothing. Students were tasked with finding ways to reduce, reuse or recycle clothing by determining buying habits, back-to-school shopping needs and how to impact culture changes with their peers. Solutions presented by the teams included creating a phone application and distribution centers for renting clothes and designing clothing that can be modified depending on the season or style.

The EcoThink project was led by U.S. Department of Energy (DOE) Office of Environmental Management (EM) Portsmouth/Paducah Project Office deactivation and remediation contractor Four Rivers Nuclear Partnership (FRNP).

“EcoThink is a great way to emphasize DOE’s mission for sustainability to students in the region,” EM Paducah Site Lead April Ladd said. “Not only does it bring awareness to real world problems, but by encouraging students to think about these problems, they may consider a career in science, technology, engineering and math (STEM), which will be critical as the next generation workforce is developed.”

EcoThink, which was featured at the 2024 Waste Management Symposia ’s STEMZone, is conducted through a partnership between Sprocket, Inc. and University of Kentucky College of Engineering and sponsored by FRNP.

“Each year, I am impressed with the ingenuity displayed by the students who participate in EcoThink,” FRNP Program Manager Myrna Redfield said. “We appreciate all the teachers and volunteers who come together to make this event possible and look forward to growing and improving the program in the future.”

-Contributor: Dylan Nichols

To receive the latest news and updates about the Office of Environment Management, submit your e-mail address.

I'm the superintendent of Ann Arbor schools. Fixing our budget shortfall will be painful. | Letters

Ann Arbor Public Schools is dedicated to providing world-class learning opportunities for our students, and keeping our families, staff, students and community informed about the financial challenges we face.

With our nearly 91% graduation rate, amazing staff and students and supportive community, it is no surprise our district has been hailed as one of the best public school systems in the nation.

That is why we are up to the challenge before us and appreciate the opportunity to detail the factors at play in our financial situation, as highlighted in a recent opinion piece in this newspaper .

More on Ann Arbor schools budget crisis: Layoffs expected as Ann Arbor Public Schools must cut $25 million from budget

This past November, as part of our regular budget review and audit process, the prior superintendent made the Board of Education aware of a shortfall in our current school year budget. After being named interim superintendent, to thoroughly assess our financial picture, I authorized a comprehensive top-to-bottom review of school finances — and called in a third-party financial expert to ensure we have an accurate picture to proceed on solid footing.

More on Ann Arbor schools budget crisis: Ann Arbor Public Schools is short $25 million. How did we get here?

As a result of that work, it was determined the district will need to reduce approximately $25 million from the 2024-25 operating budget to comply with State of Michigan and Ann Arbor Public Schools Board of Education requirements. This represents approximately a 10% reduction to our district’s overall budget of more than $300 million. Our team is committed to navigating these challenges while continuing to provide our students with a world-class education.

Our budget challenges stem from three main historical factors:

Over the past four years, student enrollment has decreased by 1,123, which decreased the district’s revenue.
An increase in employees over the past decade.
Increases in operational costs.

I worked with our district leaders to identify immediate actions we could take to reduce costs and begin planning long-term solutions to ensure this does not happen again. We know some of these steps will be painful.

We are reducing central office and administrative staff positions, freezing hiring, conducting in-depth reviews of all central office, district and school budgets for efficiencies and cost savings and renegotiating contracts with vendors to identify cost savings on contracted services.

This will not solve the shortfall on its own given the magnitude of the budget challenges we face.

We know this has been a difficult process. We are committed to working together with staff and the AAPS community to ensure a comprehensive district budget plan is developed and implemented in a way that minimizes the impact on classrooms and student learning.

To build a thoughtful plan that moves us forward in a fiscally responsible way, we are seeking feedback from our valued staff and community members. As we continue to gather this feedback, we are hosting a virtual town hall meeting on Monday, April 15, that will allow us to share information and answer questions. It will be online at 6:30 p.m. Monday at access.live/annarborpublicschools . We also will host additional in-person venues for staff and community feedback and engagement.

Throughout this process, our district leadership team has remained steadfast in its commitment to transparency and openness. Together we can, and will, get through this challenging situation as a district and community.

Jazz Parks

The writer is interim superintendent of the Ann Arbor Public Schools

Submit a letter to the editor at freep.com/letters , and we may publish it online and in print.

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

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A guide to critical thinking: implications for dental education

Introduction

Data sources and search strategies

Eligibility criteria

Data coding design

Procedure for extracting and coding data

Publication bias test

Heterogeneity test

The analysis of the overall effect size

The analysis of moderator effect size

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

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

Suggestions for critical thinking teaching

Implications and limitations

Conclusions

Data availability

Acknowledgements

Author information

Corresponding authors

Ethics declarations

Ethical approval

Informed consent

Supplementary information

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Exploring the effects of digital technology on deep learning: a meta-analysis

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