why should students do problem solving in school

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.

why should students do problem solving in school

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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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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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.

Benefits of Problem-Solving in the K-12 Classroom

Posted October 5, 2022 by Miranda Marshall

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

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

Problem-solving is inherently student-centered.

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

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

Increases confidence and achievement across all school subjects.

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

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

Encourages collaboration and teamwork.

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

Increases metacognitive skills.

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

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

Helps with long-term knowledge retention.

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

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

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

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

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

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Study shows students in ‘active learning’ classrooms learn more than they think

For decades, there has been evidence that classroom techniques designed to get students to participate in the learning process produces better educational outcomes at virtually all levels.

And a new Harvard study suggests it may be important to let students know it.

The study , published Sept. 4 in the Proceedings of the National Academy of Sciences, shows that, though students felt as if they learned more through traditional lectures, they actually learned more when taking part in classrooms that employed so-called active-learning strategies.

Lead author Louis Deslauriers , the director of science teaching and learning and senior physics preceptor, knew that students would learn more from active learning. He published a key study in Science in 2011 that showed just that. But many students and faculty remained hesitant to switch to it.

“Often, students seemed genuinely to prefer smooth-as-silk traditional lectures,” Deslauriers said. “We wanted to take them at their word. Perhaps they actually felt like they learned more from lectures than they did from active learning.”

In addition to Deslauriers, the study is authored by director of sciences education and physics lecturer Logan McCarty , senior preceptor in applied physics Kelly Miller, preceptor in physics Greg Kestin , and Kristina Callaghan, now a physics lecturer at the University of California, Merced.

The question of whether students’ perceptions of their learning matches with how well they’re actually learning is particularly important, Deslauriers said, because while students eventually see the value of active learning, initially it can feel frustrating.

“Deep learning is hard work. The effort involved in active learning can be misinterpreted as a sign of poor learning,” he said. “On the other hand, a superstar lecturer can explain things in such a way as to make students feel like they are learning more than they actually are.”

To understand that dichotomy, Deslauriers and his co-authors designed an experiment that would expose students in an introductory physics class to both traditional lectures and active learning.

For the first 11 weeks of the 15-week class, students were taught using standard methods by an experienced instructor. In the 12th week, half the class was randomly assigned to a classroom that used active learning, while the other half attended highly polished lectures. In a subsequent class, the two groups were reversed. Notably, both groups used identical class content and only active engagement with the material was toggled on and off.

Following each class, students were surveyed on how much they agreed or disagreed with statements such as “I feel like I learned a lot from this lecture” and “I wish all my physics courses were taught this way.” Students were also tested on how much they learned in the class with 12 multiple-choice questions.

When the results were tallied, the authors found that students felt as if they learned more from the lectures, but in fact scored higher on tests following the active learning sessions. “Actual learning and feeling of learning were strongly anticorrelated,” Deslauriers said, “as shown through the robust statistical analysis by co-author Kelly Miller, who is an expert in educational statistics and active learning.”

Those results, the study authors are quick to point out, shouldn’t be interpreted as suggesting students dislike active learning. In fact, many studies have shown students quickly warm to the idea, once they begin to see the results. “In all the courses at Harvard that we’ve transformed to active learning,” Deslauriers said, “the overall course evaluations went up.”

Co-author Kestin, who in addition to being a physicist is a video producer with PBS’ NOVA, said, “It can be tempting to engage the class simply by folding lectures into a compelling ‘story,’ especially when that’s what students seem to like. I show my students the data from this study on the first day of class to help them appreciate the importance of their own involvement in active learning.”

McCarty, who oversees curricular efforts across the sciences, hopes this study will encourage more of his colleagues to embrace active learning.

“We want to make sure that other instructors are thinking hard about the way they’re teaching,” he said. “In our classes, we start each topic by asking students to gather in small groups to solve some problems. While they work, we walk around the room to observe them and answer questions. Then we come together and give a short lecture targeted specifically at the misconceptions and struggles we saw during the problem-solving activity. So far we’ve transformed over a dozen classes to use this kind of active-learning approach. It’s extremely efficient — we can cover just as much material as we would using lectures.”

A pioneer in work on active learning, Balkanski Professor of Physics and Applied Physics Eric Mazur hailed the study as debunking long-held beliefs about how students learn.

“This work unambiguously debunks the illusion of learning from lectures,” he said. “It also explains why instructors and students cling to the belief that listening to lectures constitutes learning. I recommend every lecturer reads this article.”

Dean of Science Christopher Stubbs , Samuel C. Moncher Professor of Physics and of Astronomy, was an early convert. “When I first switched to teaching using active learning, some students resisted that change. This research confirms that faculty should persist and encourage active learning. Active engagement in every classroom, led by our incredible science faculty, should be the hallmark of residential undergraduate education at Harvard.”

Ultimately, Deslauriers said, the study shows that it’s important to ensure that neither instructors nor students are fooled into thinking that lectures are the best learning option. “Students might give fabulous evaluations to an amazing lecturer based on this feeling of learning, even though their actual learning isn’t optimal,” he said. “This could help to explain why study after study shows that student evaluations seem to be completely uncorrelated with actual learning.”

This research was supported with funding from the Harvard FAS Division of Science.

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Center for Teaching

Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

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

Encourage Independence

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

Be sensitive

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

Encourage Thoroughness and Patience

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

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

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

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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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Collaborative Problem Solving in Schools »

Collaborative Problem Solving in Schools

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

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

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

Transform School Discipline

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

A Client’s Story

Collaborative Problem Solving and SEL

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

Collaborative Problem Solving and MTSS

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

The Results

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

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

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

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

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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 .

E ducational D esigner

Journal of the international society for design and development in education, introduction, the value of critiquing alternative problem solving strategies., development of the problem solving lessons: the designers’ remit, an example of a problem-solving lesson., sample and data collection, potential uses of “sample student work”, the design and form of sample student work, students needed exposure to a wide range of methods, difficulties in using sample student work in the classroom., discussion of the design issues raised, acknowledgements, about the authors.

Note: If you browse this site it will use temporary 'session cookies' to assist navigation and keep an anonymous record of page visits. More info…

Developing students’ strategies for problem solving in mathematics:

The role of pre-designed “sample student work”, sheila evans and malcolm swan centre for research in mathematics education university of nottingham, england.

This paper describes a design strategy that is intended to foster self and peer assessment and develop students’ ability to compare alternative problem solving strategies in mathematics lessons. This involves giving students, after they themselves have tackled a problem, simulated “sample student work” to discuss and critique. We describe the potential uses of this strategy and the issues that have arisen during trials in both US and UK classrooms. We consider how this approach has the potential to develop metacognitive acts in which students reflect on their own decisions and planning actions during mathematical problem solving.

An accompanying paper in this volume ( Swan & Burkhardt 2014 ) outlines the rationale, design and structure of the lesson materials developed in the Mathematics Assessment Project (MAP) [1] . In short, the MAP team has designed and developed over one hundred Formative Assessment Lessons (FALs) to support US Middle and High Schools in implementing the new Common Core State Standards for Mathematics. Each lesson consists of student resources and an extensive teacher guide. About one-third of these lessons involves the tackling of non-routine, problem-solving tasks. The aim of these lessons is to use formative assessment to develop students’ capacity to apply mathematics flexibly to unstructured problems, both from pure mathematics and from the real world. These non-routine lessons are freely available on the web: http://map.mathshell.org.uk

One challenge in designing the FALs was to incorporate aspects of self and peer-assessment, activities that have regularly been associated with significant learning gains ( Black & Wiliam 1998a ). These gains appear to be due to the reflective, self-monitoring or metacognitive habits of mind generated by such activity. As Schoenfeld ( 1983 , 1985, 1987, 1992 ) demonstrated, expert problem solvers frequently engage in metacognitive acts in which they step back and reflect on the approaches they are using. They ask themselves planning and monitoring questions, such as: ‘Is this going anywhere? Is there a helpful way I might represent this problem differently?’ They bring to mind alternative approaches and make selections based on prior experience. In contrast, novice problem solvers are often observed to become fixated on an approach and pursue it relentlessly, however unprofitably. Self and peer assessment appear to allow students to step back in a similar manner and allow ‘ working through tasks’ to be replaced by ‘ working on ideas’ . Our design challenge was therefore to incorporate opportunities into our lessons for students to develop the facility to engage in metacognitive acts in which they consider and evaluate alternative approaches to non-routine problems.

One of the practices from the Common Core State Standards that we sought to specifically address in this way, was: Construct viable arguments and critique the reasoning of others. Part of this standard reads as follows:

Mathematically proficient students are able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. ( NGA & CCSSO 2010 , p. 6)

A possible design strategy was to construct “sample student work” for students to discuss, critique and compare with their own ideas. In this paper we describe the reasons for this approach and the outcomes we have observed when this was used in classroom trials.

In a traditional classroom, a task is often used by the teacher to introduce a new technique, then students practice the technique using similar tasks. This is what some refer to as ‘Triple X’ teaching: ‘exposition, examples, exercises.’ There is no need for the teacher to connect or compare alternative approaches as it is predetermined that all students will solve each task using the same method. Any student difficulties are unlikely to surprise the teacher. This is not the case in a classroom where students employ different approaches to solve the same non-routine task; the teacher’s role is more demanding. Students may use unanticipated solution-methods and unforeseen difficulties may arise.

The benefits of learning mathematics by understanding, critiquing, comparing and discussing multiple approaches to a problem are well-known ( Pierce, et al. 2011 ; Silver, et al. 2005 ). Two approaches are commonly used: inviting students to solve each problem in more than one way, and allowing multiple methods to arise naturally within the classroom then having these discussed by the class. Both methods are difficult for teachers.

Instructional interventions intended to encourage students to produce alternative solutions have proved largely unsuccessful ( Silver, et al. 2005 ). It has been found that not only do students lack motivation to solve a problem in more than one way, but teachers are similarly reluctant to encourage them to do so ( Leikin & Levav-Waynberg 2007 ).

The second, perhaps more natural, approach is for students to share strategies within a whole class discussion. In Japanese classrooms, for example, lessons are often structured with four key components: Hatsumon (the teacher gives the class a problem to initiate discussion); Kikan-shido (the students tackle the problem in groups or individually); Neriage (a whole class discussion in which alternative strategies are compared and contrasted and through which consensus is sought) and finally the Matome , or summary ( Fernandez & Yoshida 2004 ; Shimizu 1999 ). Among these, the Neriage stage is considered to be the most crucial. This term, in Japanese refers to kneading or polishing in pottery, where different colours of clay are blended together. This serves as a metaphor for the considering and blending of students’ own approaches to solving a mathematics problem. It involves great skill on the part of the teacher, as she must select student work carefully during the Kikan-shido phase and sequence the work in a way that will elicit the most profitable discussions. In the Matome stage of the lesson, the Japanese teachers will tend to make a careful final comment on the mathematical sophistication of the approaches used. The process is described by Shimizu:

Based on the teacher’s observations during Kikan-shido, he or she carefully calls on students to present their solution methods on the chalkboard, selecting the students in a particular order. The order is quite important both for encouraging those students who found naive methods and for showing students’ ideas in relation to the mathematical connections among them. In some cases, even an incorrect method or error may be presented if the teacher thinks this would be beneficial to the class. Once students’ ideas are presented on the chalkboard, they are compared and contrasted orally. The teacher’s role is not to point out the best solution but to guide the discussion toward an integrated idea. ( Shimizu 1999 , p110)

In part, perhaps, influenced by the Japanese approaches, other researchers have also adopted similar models for structuring classroom activity. They too emphasize the importance of: anticipating student responses to cognitively demanding tasks; careful monitoring of student work; discerning the mathematical value of alternative approaches in order to scaffold learning; purposefully selecting solution-methods for whole class discussion; orchestrating this discussion to build on the collective sense-making of students by intentionally ordering the work to be shared; helping students make connections between and among different approaches and looking for generalizations; and recognizing and valuing students’ constructed solutions by comparing this with existing valued knowledge, so that they may be transformed into reusable knowledge ( Brousseau 1997 ; Chazan & Ball 1999 ; Lampert 2001 ; Stein, et al. 2008 ). However, this is demanding on teachers. The teachers’ concern that students participate in these discussions by sharing ideas with the whole class often becomes the main goal of the activity. Often researchers observe teachers sticking to a ‘show and tell’ approach rather than discussing the ideas behind the solutions in any depth. Student talk is often prioritized over peer learning ( Stein, et al. 2008 ). Merely accepting answers, without attempting to critique and synthesize individual contributions does guarantee participation, is less demanding on the teacher, but can constrain the development of mathematical thinking ( Mercer 1995 )

In our work prior to the Mathematics Assessment Project (MAP) project, however, we have found that approaches which rely on teachers selecting and discussing students’ own work are problematic when the mathematical problems are both non-routine and involve substantial chains of reasoning. Teachers have only limited time to spend with each group during the course of a lesson. They find it extremely difficult to monitor and interpret extended student reasoning as this can be poorly articulated or expressed. Most of the ‘problems’ discussed in the research literature are short and contain only a few steps, so the selection of student work is relatively straightforward. We have attempted to tackle this issue by suggesting teachers allow students time to work on the problems individually in advance of the lesson, and then collect in these early ideas and attempt to interpret the approaches before the formative assessment lesson itself. This time gap does allow teachers an opportunity to anticipate student responses in the lesson and prepare formative feedback in the form of written and oral questions. In addition, we have suggested that group work is undertaken using shared resources and is presented on posters so that student reasoning becomes more visible to the teacher as he or she is monitoring work. The selection and presentation of student approaches remains difficult however, partly because the responses are so complex that other students have difficulty understanding them. We often witness ‘show and tell’ events where the students present their approach only to be greeted with a silent incomprehension from their peers.

One possible solution we explore in the rest of this paper, is the use of pre-prepared “sample student work”. This is carefully designed, handwritten material that simulates how students may respond to a problem. The handwritten nature conveys to students that this work may contain errors and may be incomplete. The task for students is to critique each piece and compare the approaches used, with each other and with their own, before returning to improve their own work on the problem.

Here, we explore the use of sample student work in the classroom. We first describe how the sample student work fits into the design of a problem solving FALs; then consider its potential uses, its design and form and then the difficulties that have been observed as it has been used within the classroom. We conclude by discussing the design issues raised and possible directions for future research.

The design of the MAP lessons has been explained elsewhere in this volume ( Swan & Burkhardt 2014 ), so we refrain from repeating that here. The process was based on design research principles, involving theory-driven iterative cycles of design, enactment, analysis and redesign ( Barab & Squire 2004 ; Bereiter 2002 ; Cobb, et al. 2003 ; DBRC 2003 , p. 5; Kelly 2003 ; van den Akker, et al. 2006 ). Each lesson was developed, through two iterative design cycles, with each lesson being trialed in three or four US classrooms between each revision. Revisions were based on structured, detailed feedback from experienced observers of the materials in use in classrooms. The intention was to develop robust designs that may be used more widely by teachers, without further support.

The remit for the designers was to create lessons that had clarity of purpose and would maximize opportunities for students to make their reasoning visible to each other and their teacher. This was intended to ensure the alignment of teacher and student learning goals, to enable teachers to adapt and respond to student learning needs in the classroom, and to enable teachers to follow-up lessons appropriately ( Black & Wiliam 1998a , 1998b; Leahy, et al. 2005 ; Swan 2006 ). The lessons were designed to draw on a range of important mathematical content, be engaging and feature high-level cognitive challenges. They were intended to be accessible, allowing multiple entry points and solution strategies. This allowed students to approach the task in different ways based on their prior knowledge. The lessons were also designed to encourage decision-making, leading to a sense of student ownership. Opportunities for students to conjecture, review and make connections were embedded. Finally, the lessons were designed to provide opportunities for students to compare and critique multiple solution-methods ( Figure 1 Figure 1 ).

Research indicates that it is not sufficient for teachers to be simply handed non-routine tasks. Lessons such as these can proceed in unexpected ways and, without teacher guidance, can often result in teachers reducing the cognitive demands of the task and the corresponding learning opportunities ( Stein, et al. 1996 ). In order to support teachers in developing skills to successfully work with these lessons, detailed guides were written. The guides outline the structure of each lesson, clearly stating the designers’ intentions, suggestions for formative assessment, examples of issues students may face and offering detailed pedagogical guidance for the teacher.

In Figure 2 we offer one example of a problem-solving task [2] , and below outline a typical lesson structure:

An unscaffolded problem is tackled individually by students Students are given about 20 minutes to tackle the problem without help, and their initial attempts are collected in by the teacher.
Teachers assess a sample of the work The teacher reviews the sample and identifies the main issues that need addressing in the lesson. We describe the common issues ( Figure 3 ) that arise and suggest questions for the teacher to use to move students’ thinking forward. (In Having Kittens , these included: not developing a suitable representation, working unsystematically, not making assumptions explicit and so on).
Groups work on the problem The teacher asks students to work together, sharing their initial ideas and attempt to arrive at a joint, group solution, that they can present on a poster. The pre-prepared strategic questions are posed to students that seem to be struggling.
Students share different approaches Students visit each other’s posters and groups explain their approach. Alternatively a few group solutions may be displayed and discussed. This may help for example, to begin discussions on the assumptions made, and so on.

Students discuss sample student work Students are given a range of sample student work that illustrate a range of possible approaches ( Figure 4 ). They are asked to complete, correct and/or compare these. In the Kittens example, students are asked to comment on the correct aspects of each piece, the assumptions made, and how the work may be improved. The teacher’s guide contains a detailed commentary on each piece. For example, for Wayne’s solution, the guide says: Wayne has assumed that the mother has six kittens after 6 months, and has considered succeeding generations. He has, however, forgotten that each cat may have more than one litter. He has shown the timeline clearly. Wayne doesn’t explain where the 6-month gaps have come from.
Students improve their own solutions Students are given a further opportunity to act on what they have learned from each other and the sample student work.
Whole class discussion to review learning points in the lesson The teacher holds a class discussion focusing on some aspects of the learning. For example, he or she may focus on the role of assumptions, the representations used, and the mathematical structure of the problem. This may also involve further references to the sample student work.
Students complete a personal review questionnaire This simply invites students to reflect on how their understanding of the problem has evolved over the lesson andwhat they have learned from it.

Collect students’ responses to the task. Make some notes on what their work reveals about their current levels of understanding, and their different problem solving approaches. The purpose of doing this is to forewarn you of issues that will arise during the lesson itself, so that you may prepare carefully. We suggest that you do not score students’ work. The research shows that this will be counterproductive, as it will encourage students to compare their scores and will distract their attention from what they can do to improve their mathematics To, help students to make further progress by summarizing their difficulties as a series of questions. Some suggestions for these are given on the next page. These have been drawn from common difficulties observed in trials of this lesson unit. (extract from the Teacher Guide)

By drawing attention to common issues, the contents of the table can also support teachers to scaffold students learning both during the collaborative activity and whole class discussions.

Altogether, these formative assessment lessons were trialed by over 100 teachers in over 50 US schools. During the third year of the project, many of the problem solving lessons were also taught in the UK by eight secondary school teachers, with first-hand observation by the lesson designers.

Although teachers in all of these trials were invited to teach the lesson as outlined in the guide, we also made it clear that teachers should feel able to adapt the materials to accommodate the needs, interests and previous attainment of students, as well as the teacher’s own preferred ways of working. We recognized that teachers play the central role in transforming the design intentions and, inevitably, that some of these transformations would surprise the designers .

We examined all available observer reports on the problem solving lessons and elicited all references to sample student work. These comments were then categorized under specific themes such as ‘Errors in Sample Student Work’ or ‘Questions for students to answer about sample student work’. Additionally, observers completed a questionnaire ( Figure 5 Figure 5 ) designed specifically to help designers better understand how teachers use the sample student work and the supporting guide, and how this use has evolved over the course of the project. This data forms the basis of the findings from the US lesson trials.

The analysis of the UK data is ongoing. Before and after each FAL teachers were interviewed using a questionnaire ( Figure 6 Figure 6 ) intended to help designers better comprehend key teacher behaviors and understandings, such as how the teacher prepared for the lesson, what she perceived as the ‘big mathematical ideas’ of the lesson, what she had learnt from the lesson. At the end of the one-year project, teachers were interviewed about their experiences. Again the questions asked were shaped by the literature and issues that had arisen over the course of the project. For example, how teachers used the guide and their opinions on the sample student work. At the time of writing, all the final interviews have been analyzed, as have the pre and post lesson responses made by two of the teachers. We have also developed a framework to analyze whole class discussions. Twelve class discussions have been analyzed. This data forms the basis of the findings from the UK lesson trials.

During the refinement of the lessons we have gradually become more aware that the purpose of sharing student approaches needs to be made explicit. By combining purposes inappropriately, we can undermine their effect. For example, if a sample approach is full of errors, the student may become so absorbed in working through the sample work that they fail to make comparisons between different pieces of work.

The following list describes some of the reasons we have designed sample student work:

To encourage a student that is stuck in one line of thinking to consider others If a student has struggled for some time with a particular approach, teachers are often tempted to suggest a specific approach. This can lead to subsequent imitative behavior by students. Alternatively the teacher may ask the student to consider other students’ attempts to solve the problem. This offers fresh insight and help without being directive.

“For students who have had trouble coming up with a solution, having the sample student work has helped them think of a way to organize or get started with the task. Since these students are having trouble getting a solution, they usually look over the various sample student work and pick one with which they feel most comfortable. Having Kittens was one task where students benefitted by seeing how other students organized their thinking”. (Observer comment from questionnaire)

To enable a student to make connections within mathematics Different approaches to a problem can facilitate connections between different elements of knowledge, thereby creating or strengthening networks of related ideas and enabling students to achieve ‘a coherent, comprehensive, flexible and more abstract knowledge structure’ ( Seufert, et al. 2007 ).

“I did not routinely, except perhaps at A level, make connections between topics and now I am trying to incorporate this into my practice at a much lower level. The sample student work highlighted how traditional my approach was and how I followed quite a linear route of mathematical progression” (UK teacher during end-of-project interview)

Figure 7 Figure 7 shows an example of sample solutions provided in the FALs that provide students with opportunities to connect and compare different representations.

To signal to students that mistakes are part of learning In so doing the stigma attached to being wrong may be reduced ( Staples 2007 ).
To draw attention to common mathematical misconceptions A sample piece of student work may be chosen or carefully designed to embody a particular mathematical misconception. Students may then be asked to analyse the line of reasoning embedded in the work, and explain its defects.
To compare alternative representations of a problem For modelling problems, many different representations are possible during the formulation stage. Typically these include verbal, diagrammatic, graphical, tabular and algebraic representations. Each has its own advantages and disadvantages, and through the comparison of these over a succession of problems, students may become more able to appreciate their power.
To compare hidden assumptions It is often helpful to offer students two correct responses to a problem that arrive at very different solutions solely because different modelling assumptions have been made. This draws attention to the sensitivity of the solution to the variables within the problem. An example of this is provided by the sample solutions in Figure 3 .
To draw students attention to valued criteria for assessment. Particularly when using tasks that involve problem solving and investigation, students often remain unsure of the educational purpose of the lesson and the criteria the teacher is using to judge the quality of their work ( Bell, et al. 1997 ). If they are asked, for example, to rank-order several pieces of sample student work according to given criteria (such as accuracy, quality of communication, elegance) they become more aware of such criteria. This can contribute significantly to the alignment of student and teacher objectives ( Leahy, et al. 2005 ). Also, engaging in another student’s thinking may strengthen students’ self-assessment skills.

Research suggests that students’ self-assessment capabilities may be enhanced if they are provided with existing solutions to work through and reflect upon. Carroll (1994) , for example, replaced students working through algebra problems with students studying worked examples. This was shown to be particularly effective with low-achievers because it reduced the cognitive load and allowed students to reflect on the processes involved.

In our work we have frequently found it necessary to design the ‘student work’ ourselves, rather than use examples taken straight from the classroom. This is often to ensure that the focus of students’ discussion will remain on those aspects of the work that we intend. For example, the work must be clear and accessible, if other students are to be able to follow the reasoning. If each piece of work is overlong, then students may find it difficult to apprehend the work as a whole, so that comparisons become difficult to make. If our created student work is too far removed (too easy or too difficult) from what the students themselves would or could do, then it loses credibility.

It was felt important to use handwritten work, as this communicates to students that the work is freshly created and has not been polished for publication. It reduces the perceived ‘authority’ of the mathematics presented, increases the likelihood that it may contain errors and introduces a third ‘person’ to the classroom who is unknown to the students. This anonymity can be advantageous; students do not know the mathematical prowess of the author. If it is known that a student with an established reputation for being ‘mathematically able’ has authored a solution then most will assume the solution is valid. Anonymity removes this danger. Making ‘student work’ anonymous also reduces the emotional aspects of peer review. Feedback from our early trials indicated that sometimes students were reserved and over-polite about one another’s work, reluctant to voice comments that could be perceived as negative. When outside work was introduced, they became more critical.

In the US trials, we found that, within a single class, the solution methods used by students were often similar in kind. This may be partly due to the common practice of US teachers to focus exclusively on each topic area for an extended period, thus making it likely that students will draw from that area when solving a problem. Alternatively, students may choose to use a solution method they assume is particularly valued, even when this might be inappropriate. The following observer comment would suggest that a numerical solution would be favored over a geometric one, for example:

Due to the ‘traditional’ approaches generally used here in the States, many teachers believe that ‘geometric’ solutions are NOT showing rigor or intelligence and that number is the best way. Students have internalized this… (Observer report)

In our experience, students are unlikely to draw autonomously on methods they are still unsure of or they have only just learned. The mathematics they choose to use will often relate back to mathematics used in earlier years. They may frequently resort, for example, to safe and inefficient ‘guess and check’ numerical methods, that they know they can rely on, rather than graphical or algebraic methods.

The difficulty of transferring methods from one context to another is a common theme in the research literature. For example, students may know how to figure out the gradient, intercept and the equation of a graph, but still find it challenging to recall and apply these concepts to a ‘real-world’ problem. One reason for the low degree of transfer is that students often recall concepts in a situation-specific manner, focusing mainly on surface features ( Gentner 1989 ; Medin & Ross 1989 ) rather than on the underlying mathematical principles. Our UK study supports these findings. On several occasions teachers taught a concept, in advance of the lesson, that they considered would help students to solve the problem and were subsequently surprised that students decided not to use it! Clearly, successful problem solving is not just about students’ knowledge - it is about how, when and whether they decide to use it ( Schoenfeld, 1992 , p. 44).

In the few cases where students did use a wide range of approaches, these rarely included strategies to match all the learning goals of the lesson. For example, students did not necessarily select different representations of the same concept, or use efficient, elegant or generalizable strategies. The mathematical learning opportunities were therefore limited.

For the above reasons we concluded that some fresh input of methods needed to be introduced into the classroom if students were to have opportunities to discuss alternative representations and powerful methods. This could perhaps come from the teacher, but that would then almost certainly remove the problem from students and result in students imitating the teacher’s method. Sample student work provides an alternative input that, as we have said, carries less authority.

In this section we outline a few of the main difficulties we observed when sample student work was used in US and UK classrooms.

Students were analyzing work in superficial ways

In our first version of the teacher’s guide, we suggested that the teacher could introduce the sample work to the class by writing the following instructions on the board:

Imagine you are the teacher and have to assess this work. Correct the work and write comments on the accuracy and organization of each response. Make some specific suggestions as to how the work may be improved.

Feedback from the US trials indicated that these instructions were inadequate. Teachers and students were not clear on the purposes of the activity, and student responses were superficial. For example, observers reported US teachers asking:

What is the math we want to have a conversation about? Do we want students to explain the method? Do we want each piece to stand-alone or should students compare and contrast strategies?

Observers reported that students were not digging deeply enough into the mathematics of each sample and, unless asked a direct question by the teacher, they often worked in silence, looking for errors without evaluating the overall solution strategy. Some students mimicked the feedback they often received from their teacher, providing comments such as ‘Awesome’, ‘Good answer’ or ‘Show a little more work’. A clear message came from the observers; the prompts in the guide needed to be more explicit and focus on the mathematics of the problem; scaffolding was required. The decision was therefore made to include more specific questions, such as:

What piece of information has Danny forgotten to use? What is the purpose of Lydia’s graph? What is the point of figuring out the slope and intercept?

Such questions appeared to make the purpose more discernable to teachers. Feedback from the US observers to these changes was encouraging:

I think the questions or prompts about each piece of student work really focus the students on the thinking, bring out the key mathematics and are a great improvement to the original lesson…Last year students just made judgment statements, but this year the comments were focused on the mathematics.

Not all teachers shared this view, however. In the UK, one teacher commented:

Students are being forced along a certain path as a way to engage with the sample student work. Rather, they [the questions] should be more open and students are then able to comment in any way they like. …. I think sometimes they feel themselves kind of shoehorning in certain types of answer.

This teacher preferred to simply ask students to explain the approach; describe what the student had done well and suggest possible improvements. This practice did encourage engagement, and students’ assessment criteria were made visible to the teacher, but at times the learning goals of the lesson were only superficially attended to.

In both the US and UK, many students focused on the appearance of the work, rather than on its content, with comments on the neatness of diagrams and handwriting. Many commented that the sample work was poorly explained, but did not go on to say clearly how it should be improved. Sample comments were: ‘she needs to explain it better’; ‘the diagrams should not be all over the place’. We attempted to remedy this by suggesting that, rather than just making suggestions for improvement, students should actually make improvements. One teacher commented that this focus on effective mathematical communication had resulted in her students writing fuller explanations when solving problems for themselves.

Students were focused on correcting errors, while ignoring holistic issues

The feedback from observers on the use of errors in sample student work presented us with a more complex issue. Observers commented that when understandings were fragile, the errors often made ‘the most complicated ideas more complicated’. It also became apparent from US feedback that when errors were found in sample student work, some students dismissed the solutions as undeserving of further analysis. Similarly, in UK classrooms students and teachers often assumed the only goal of the activity was to locate and correct errors. One UK teacher commented that when the student work was error-free, students were more inclined to make holistic comparisons of strategic approach.

This led us to look carefully at our purposes in using errors. We had originally included two different kinds of errors: procedural and conceptual. Procedural errors are common arithmetic or algebraic mistakes. Conceptual errors are symptoms of incorrect reasoning and are often more structural in nature. In response to feedback from observers, we removed many of the procedural errors. In many cases, however, the design decision was taken to retain conceptual errors that encourage students to understand the solution-method and its purpose.

For example, Figure 10 shows a problem solving task and Figure 11 shows three samples of student work. Each sample contains a conceptual error. Included in the guide is an explanation of these errors:

Ella draws a sample space in the form of an organized table. Although Ella clearly presents her work, she makes the mistake of including the diagonals. This means the same ball is selected twice. This is not possible, as the balls are not replaced. (Teacher’s guide) Anna assumes that there are only two outcomes (that the two balls are the same color or that they are different colors), so that the probabilities are equal. Anna does not take into account the changes in probabilities when a ball is removed from the bag and not replaced. Jordan does not take into account that the first ball is not replaced. When selecting the second ball there are only 5 balls in the bag, so these probability fractions should all have a denominator of 5.

In some lessons we decide that, rather than including errors, we invited students to complete unfinished responses. For example, in the Testing a New Product task ( Figure 12 ) students’ were asked to complete the tables in Penny and Aran’s work and the final column in Harry’s graph ( Figure 13 ).

They were then asked to describe the advantages and disadvantages of each approach to the problem. Most students in a UK trial of the lesson were able to complete the work, they understood the processes, and were able to work out the correct answers. They did however encounter difficulties interpreting the resulting figures in the context of the real-world situation. This struggle prompted students to consider how far each approach is fit for purpose: how well it each one tackles the problem of working with the four variables of packaging, fragrance, gender and preference, and how far useful conclusions may be reached using each approach.

Students were not given time to consider a sufficient range of sample student work

Initial feedback from observers indicated the lessons were taking longer than had been anticipated; teachers were giving out all pieces of sample student work, but there was often insufficient time for students to successfully evaluate and compare the different approaches. In response to this, designers included the following generic text to all lessons guides:

There may not be time, and it is not essential, for all groups to look at all sample responses. If this is the case, be selective about what you hand out. For example, groups that have successfully completed the task using one method will benefit from looking at different approaches. Other groups that have struggled with a particular approach may benefit from seeing another student’s work that uses the same strategy.

These instructions encourage students to critique and reflect on unfamiliar approaches, to explicate a process and to compare their own work with a similar approach; this, in turn could serve as a catalyst to review and revise their own work. Differentiating the allocation of sample student work in this way may however create problems in the whole class discussion, as not all of the students will have worked on the piece of work under discussion. This instruction places pedagogical demands on teachers, however. They have to again make rapid decisions on which piece of work to allocate to each group. In US trials, however, the suggested approach was not followed:

We have some teachers who give all the sample student work and let students choose the order and the amount they do. This might be less common. Others are very controlling and hand out certain pieces to each group. Others like a certain method to solve problems and like to use that one to model. I think this is a function of the teacher’s comfort level with control and students expectations. (Observer report)

It turned out that very few students were allowed sufficient time to work on all the pieces of sample student work or time to evaluate unfamiliar methods.

These issues were also a concern for the UK teachers. At the start of the project some were reluctant to issue all of the sample student work at the same time, for fear that students would be overwhelmed. As one teacher commented:

At the beginning (of the project) it was too much for pupils to take on all the different methods at once. Even towards the end I didn’t always give them all to them. I believed they became unsettled because the task felt too great. I felt they needed to get used to just looking at one piece first. I also picked out pieces of work that I felt within their ability they could access. (Teacher report)

Students were not using the sample student work to improve their own solutions

Although the teachers clearly recognized that a prime purpose of sample student work was to serve as a catalyst for students to ultimately improve their own solutions, there was little evidence of students subsequently changing their work apart from when they noticed numerical errors. While most students acknowledged that their work needed improving, many did not take the next step and improve it. Only students that were stuck were likely to adapt or use a strategy from the sample student work.

The problem solving lessons were designed to involve cycles of refinement of students’ solutions. They attempted the task individually, before the lesson, then in groups, then considered the sample work and then again were urged to improve their work a third time. For teachers that were used to students working through a problem once, then moving on, this was a substantial new demand.

It is clear that communicating complex pedagogic intentions is not easy. It is made easier by having some common framework with reference points. A strategic goal of these lessons was to build this infrastructure in teachers’ minds

Students were often not invited to make comparisons between the sample approaches.

As mentioned earlier in the paper, the design intention is for students to compare alternative problem solving approaches. As such, all lessons include whole-class discussion instructions of the following kind:

Ask students to compare the different methods: Which method did you like best? Why? Which method did you find most difficult to understand? Why? How could the student improve his/her answer? Did anyone come up with a method different from these?

Feedback from both the US and UK classrooms indicate that teachers rarely encouraged students to make such comparisons. There appear to be multiple reasons for this.

Time pressure was a frequently raised issue. Students need sufficient time to identify and reflect on the similarities and differences between methods and connect these to the constraints and affordances of each method in terms of the context of the problem. The whole class discussion was held towards the end of the lesson. These discussions were often brief or non-existent, possibly reflecting how teachers value the activity. A common assumption was that the important learning had already happened, in the collaborative activity.

Another factor may be lack of adequate support in the guide. Research indicates it is not enough to simply suggest that sample student work should be compared, there need to be instructional prompts that draw students’ attention to the similarities and differences of methods ( Chazan & Ball 1999 ). Teachers and students need criteria for comparison to frame the discussion ( Gentner, et al. 2003 ; Rittle-Johnson & Star 2009 ). Furthermore, these prompts should occur prior to the whole-class discussion. Students need time to develop their own ideas before sharing them with the class.

Rather than compare the different pieces of sample student work, UK students were consistently given the opportunity to compare one piece with their own. Students often used the sample to figure out errors either in their own or in the sample itself. One UK teacher noted that when groups were given the sample student work that most closely reflected their own solution-method, their comments appeared to be more thoughtful, whereas with unfamiliar solution-methods students often focused on the correctness of the result or the neatness of the drawing and did not perceive it as a solution-method they would use.

Most of the teachers involved in the trials had never before attempted to ask students to critique work in the ways described above. They reported that ‘getting inside another person’s head’ proved challenging and students learned to do this only gradually.

I think it has taken most of the year to get the kids to actually be able to look at a piece of work and follow it through to see what that person has done …..

One of the profound difficulties for designers is in trying to increase the possibilities for reflective activity in classrooms. The etymology of the word curriculum is from the Latin word for a race or a racecourse, which in turn is derived from the verb currere meaning to run. Perhaps unfortunately, that is precisely what it feels like for most students. The introduction of problem solving in general, and of analyzing sample student work in particular are seen by many as time-consuming activities that detract from the primary goal of improving procedural fluency or ‘learning more stuff’.

We are encouraged, however to see that the new Common Core State Standards place explicit value on the development of problem solving, mathematical practices and, in particular, on students being able to critique reasoning. Most students, we suspect, are not aware of this new agenda. Some years ago, we conducted an experiment to see whether students could identify the purposes of a number of different kinds of mathematics lesson. It became clear that students’ and teachers’ perceptions of the purposes of the lessons were only aligned for procedural mathematics. The mismatch between teacher and student perceptions was more pronounced as lessons became progressively more practices-oriented ( Swan, et al. 2000 ). There was some empirical evidence, however, that by introducing metacognitive activities into the classroom that this mismatch could be reduced. These included such activities as discussing key conceptual obstacles and common errors, explaining errors in sample student work – and orally reviewing the purpose of each lesson.

In this paper, we have seen that, left to themselves, students are unlikely to produce a wide range of qualitatively different solutions for comparison, and therefore it may be helpful to create samples of work to stimulate such reflective discussion. We have, however also noted that we have found it necessary to:

discourage superficial analysis, by stating explicitly the purpose of the sample student work, and by asking specific questions that relate to this purpose;
encourage holistic comparisons by making the sample student work short, accessible and clear, and by not including arithmetic and other low-level errors that distract the students’ attention away from the identified purpose;
make the distribution of the sample student work more effective, by perhaps sequencing it so that successive pairwise comparisons of approaches can be made;
offer students explicit opportunities to incorporate what they have learned from the sample work into their own solutions;
offer the teachers support for the whole class discussion so that they can identify and draw out criteria for the comparison of alternative approaches.

From a designers’ perspective, it is natural to focus on the challenges in creating a design that may be used effectively by the target audiences. We may thus have given the impression that the lessons have been unsuccessful in achieving their goals. This, however, is far from the truth. These lessons are proving extremely popular with teachers and are currently being used as professional development tools across the US. They are also forming the basis for ‘lesson studies’ in both the US and the UK. In the lesson studies, they are viewed as ‘research proposals’ rather than ‘lesson plans’.

Teachers and observers have described on many occasions the learning they have gained from comparing student work in these lessons; teacher comments include:

I now think pupils can learn more from working with many different solutions to one problem rather than solving many different problems, each in only one way.

It moves away from students chasing the answer.

I can now see how much easier it is for a student to recognize that, say a trial and improvement method is inefficient, when it is compared to a sleek geometrical method rather than when simply looking at the solution on its’ own.

To our knowledge, there are no major studies that focus on how teachers work with a range of pre-written solution-methods for a range of non-routine problems. This study raises many issues and in so doing acts as a launch pad for further more detailed studies. More exploration is required into how the use of sample student work affects pupils’ capacity to solve problems. One might expect to see, for example, that students increase their repertoire of available methods when solving problems. So far, however, we have no evidence of this. We do, however, have some early indications that students are beginning to write clearer and fuller explanations as a result of critiquing sample student work.

We would like to acknowledge the support for the study, the Bill and Melinda Gates Foundation, our co-researchers at the University of Berkeley, California and the observer team.

[1] The Maths Assessment Project, based at UC Berkeley, was directed by Alan Schoenfeld, Hugh Burkhardt, Daniel Pead, Phil Daro and Malcolm Swan, who led the lesson design team which included at various stages Nichola Clarke, Rita Crust, Clare Dawson, Sheila Evans, Colin Foster and Marie Joubert. The work was supported by the Bill & Melinda Gates Foundation; their program officer was Jamie McKee. The US observers who provided the feedback from US classrooms were led by David Foster, Mary Bouck and Diane Schaefer, working with Sally Keyes, Linda Fisher, Joe Liberato and Judy Keeley.

[2] The Having Kittens task used in this lesson was originally designed by Acumina Ltd. ( http://www.acumina.co.uk/ ) for Bowland Maths ( http://www.bowlandmaths.org.uk ) and appears courtesy of the Bowland Charitable Trust.

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Sheila Evans is a member of the Mathematics Assessment Project team in the Centre for Research in Mathematical Education at the University of Nottingham. For the last four years she has worked designing, observing, teaching, revising and providing professional development for the MAP Formative Assessment Lessons. She is currently working on a doctorate using teaching resources that have been shaped by this project. Before that, she taught for fifteen years in secondary schools in the UK and Africa, and wrote a textbook Access to Maths aimed at students without traditional qualifications who wished to study at University .

Malcolm Swan is Director of the Centre for Research in Mathematical Education at the University of Nottingham, which incorporates the Shell Centre for Mathematical Education team. He has led the design teams in a sequence of research and development projects. He led the diagnostic teaching research program that established many of the design principles set out in this paper. In 2008 he was awarded the first ISDDE Prize for educational design, for The Language of Functions and Graphs.

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14 fascinating teacher interview questions for principals, tips for success if you have a master’s degree and can’t find a job, 14 ways young teachers can get that professional look, which teacher supplies are worth the splurge, 8 business books every teacher should read, conditional admission: everything you need to know, college majors: everything you need to know, 7 things principals can do to make a teacher observation valuable, 3 easy teacher outfits to tackle parent-teacher conferences, strategies and methods to teach students problem solving and critical thinking skills.

The ability to problem solve and think critically are two of the most important skills that PreK-12 students can learn. Why? Because students need these skills to succeed in their academics and in life in general. It allows them to find a solution to issues and complex situations that are thrown there way, even if this is the first time they are faced with the predicament.

Okay, we know that these are essential skills that are also difficult to master. So how can we teach our students problem solve and think critically? I am glad you asked. In this piece will list and discuss strategies and methods that you can use to teach your students to do just that.

Direct Analogy Method

A method of problem-solving in which a problem is compared to similar problems in nature or other settings, providing solutions that could potentially be applied.

Attribute Listing

A technique used to encourage creative thinking in which the parts of a subject, problem, or task are listed, and then ways to change those component parts are examined.

Attribute Modifying

A technique used to encourage creative thinking in which the parts of a subject, problem, or task are listed, and then options for changing or improving each part are considered.

Attribute Transferring

A technique used to encourage creative thinking in which the parts of a subject, problem or task listed and then the problem solver uses analogies to other contexts to generate and consider potential solutions.

Morphological Synthesis

A technique used to encourage creative problem solving which extends on attribute transferring. A matrix is created, listing concrete attributes along the x-axis, and the ideas from a second attribute along with the y-axis, yielding a long list of idea combinations.

SCAMPER stands for Substitute, Combine, Adapt, Modify-Magnify-Minify, Put to other uses, and Reverse or Rearrange. It is an idea checklist for solving design problems.

Direct Analogy

A problem-solving technique in which an individual is asked to consider the ways problems of this type are solved in nature.

Personal Analogy

A problem-solving technique in which an individual is challenged to become part of the problem to view it from a new perspective and identify possible solutions.

Fantasy Analogy

A problem-solving process in which participants are asked to consider outlandish, fantastic or bizarre solutions which may lead to original and ground-breaking ideas.

Symbolic Analogy

A problem-solving technique in which participants are challenged to generate a two-word phrase related to the design problem being considered and that appears self-contradictory. The process of brainstorming this phrase can stimulate design ideas.

Implementation Charting

An activity in which problem solvers are asked to identify the next steps to implement their creative ideas. This step follows the idea generation stage and the narrowing of ideas to one or more feasible solutions. The process helps participants to view implementation as a viable next step.

Thinking Skills

Skills aimed at aiding students to be critical, logical, and evaluative thinkers. They include analysis, comparison, classification, synthesis, generalization, discrimination, inference, planning, predicting, and identifying cause-effect relationships.

Can you think of any additional problems solving techniques that teachers use to improve their student’s problem-solving skills?

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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.

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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] .

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21st Century Skills: Why is problem-solving the need of the hour for school students?

The 21st century is about new challenges and problems which require a new set of skills. The world around us is evolving rapidly, and children need to learn essential skills such as critical reasoning , problem solving and critical thinking . Many studies have shown that children today need to develop these skills to solve key real-world problems . Even the honorable Prime Minister of India, Shri Narendra Modi, talked about the importance of 21st-century skills and the addition of these skills in the school curriculum according to New Education Policy 2020. Because of the importance of these skills, many education institutes are trying to incorporate these skills into their curriculum. However, there are still many areas that need to be developed in this field.

HCL, a $10.1 bn global enterprise has launched a program HCL Jigsaw – India’s Premier Critical Reasoning Platform, which assesses students on key 21st-century skills with a focus on solving real world problems using problem-solving and critical thinking . HCL Jigsaw believes that the best age to learn these basic skills is during school time, when children are open to new challenges and opportunities. Therefore, the program is explicitly targeting students in grades 6-9.

This article highlights the importance of problem-solving as the need of the hour for school students , tips to improve problem-solving skills and a few creative problem-solving activities for kids.

Why is Problem-Solving The Need of The Hour for Students?

In the past, students followed a mechanical progression in education. Every year posed new challenges and concepts for them as they undertook a standardized, one-size-fits-all curriculum and examinations. Education was concerned with getting the correct answer and scoring high grades, to reach the next level. There was little room for out of the box thinking that considered innovative solutions. The more information students could retain and regurgitate, the better equipped they were for an exam, ultimately translating to their real-life success. As a result, students were kept astray from practical skills and complex real-world problems they would eventually face after finishing their formative years in school and college.

The 21st-century problems require both theoretical as well as practical knowledge to be solved. students need to think out of the box to find suitable solutions to new and upcoming challenges. Before we talk about the importance of problem-solving skills for students, let us understand what exactly 21st-century problem-solving skill means.

Problem-solving is a systematic process that involves critical reasoning and thinking to find a suitable solution to problems to achieve desired objectives. Following are the reasons why problem-solving is essential for school students:

It helps students distinguish between solvable issues and problems that cannot be solved.
It is necessary for preparing school students to face complex interpersonal and academic problems.
Students who learn problem-solving skills often have a deeper understanding of causality.
When children solve problems individually or in a group, they become more resilient. They learn to look at problems from a new perspective. Therefore, it makes them capable of taking more calculated risks.
Problem-solving is essential to a child’s development because confident and productive children usually grow up as successful and confident adults.
When students practice problem solving consistently, they can develop better social and situational awareness. They will also learn to manage time properly and develop patience.
Students who learn to solve problems from childhood are curious, resourceful, and determined.
Employers always demand individuals who can work in a group and can jump out of their inherent thinking mode, especially since many of the challenges that the world faces today are unique and new.

The World Economic Forum has also recognized problem-solving skills as one of the ten essential 21st-century skills . A focus on problem-solving during the school years helps students be more resourceful, confident, and think methodically. It enables students to find constructive and unique solutions to the problems of current times. Parents and teachers need to focus on these skills for their child’s overall development

Some Creative Problem-Solving Activities for Children

Impromptu Skits: Thisactivity involves creating slips for different real-world situations like angry customers, fraud in the company, etc., and then ask the kids to pick any slip and enact a skit on the given situation.

Tower Building: This group activity requires the group to make the tallest tower using building blocks within the given time.

Alphabet Animal Game: Ask the kids to make a big circle and shout various animal names alphabetically one by one. If any kid takes more than 5 seconds, then that kid is out, and the circle gets smaller in size.

Tips to Improve Problem Solving, Creative Thinking and Critical Reasoning Skills

Following are a few tips of improve the problem-solving skills of school studentsand make them more resourceful and competent individuals to solve 21st-century problems:

Let children think outside the box and find unique and creative solutions to challenging problems.
Encourage decision-making by empowering them to handle different situations.
Explain the benefits of group work and invite them to participate in group activities.
Let children express their opinions and ideas in public and avoid intervening as it might hamper their confidence.
Try asking students open-ended questions and problems as it helps children learn creative thinking skills.
Enroll with HCL Jigsaw to teach children essential group activity problem-solving, critical reasoning, and creative thinking skills. This will help prepare confident and competent individuals who are ready to face real-world 21st-century problems.

HCL Jigsaw aspires to build a community of young problem-solvers from Grades 6–9 through a pan-India problem-solving assessment program. Students are judged on three core competencies within problem-solving: how well they define a problem, communicate it, and think critically about synthesizing information, drawing conclusions, and proposing solutions. Learn more about the exciting learning journey offered by HCL Jigsaw and Enroll now before July 31, 2022 for this unique opportunity.

10 Tips for Enhancing Your Child’s Critical Reasoning Skills

What teachers and parents must know about the hcl jigsaw platform.

HCL Jigsaw is a competitive platform aimed at helping you assess critical reasoning skills and putting them on an exciting lifelong learning journey. Designed by the industry’s best minds, the program includes opportunities to win exciting prizes and creating innovative solutions.

6 Ways Schools Are Managing Students’ Cellphone Use

A flurry of school districts across the country are tightening cellphone restrictions, because they believe students’ misuse of the devices has negatively affected their behavior and ability to learn.

In 2015, 66 percent of schools in the United States prohibited non-academic use of cellphones during school hours, according to the National Center for Education Statistics . By 2020, that percentage had jumped to 77 percent.

Many educators blame students’ cellphone use for being the top distraction in schools and classrooms . The constant use of the devices has also been linked to students’ worsening mental health .

The issue has caught the attention of federal and state policymakers, too. Some states—such as California, Florida, Indiana, and Tennessee—have passed laws allowing schools to restrict cellphone use. A handful of other states are considering passing similar laws. Congressional lawmakers have also introduced legislation that would require a federal study on the effects of cellphone use on students’ mental health and academic performance.

Liz Kolb, a clinical professor of education technologies and teacher education at the University of Michigan, said it’s unlikely that all 50 states will pass laws restricting students’ cellphone use, “but we’re seeing a lot more [movement] at the individual school level, where they’re trying to figure out policies that make sense [for their communities].”

At the district level, these restrictions vary widely. Some districts restrict student cellphone use anywhere and any time during the school day. Some allow use of the devices during lunch and in the hallways. And others haven’t placed any restrictions at all, often because of parent and student pushback.

Even in districts where there’s a ban, “there’s a lot of nuance” in how schools are addressing it, Kolb said. “In order for a full school ban to be effective, you really have to have strong leadership supporting the staff in enforcing it.”

Some of those nuances include exceptions for students who have a documented need to have their digital devices for health reasons, such as checking blood glucose levels if a student has diabetes. Teachers also have the flexibility to allow students to use their cellphones in class if they are needed for instructional purposes.

Here are six different policy approaches districts are putting in place to address concerns about student cellphone use:

1. Cellphones are restricted for all students, regardless of grade level

In Florida’s Orange County district , all students are prohibited from using their cellphones and other wireless communication devices, such as smartwatches, during school hours—meaning from the first bell to the dismissal bell, these devices must be silenced and put away in their bags. If a student is caught using a phone during the school day, the device will be confiscated and returned to the student at the end of the day. Depending on the circumstances of the violation, a student could also get detention or be suspended.

Flint schools in Michigan also prohibit all students, regardless of grade level, from using cellphones or other personal electronic devices. If a student is caught using a phone, it will be confiscated and returned to the student’s parent or caretaker.

Some districts provide technological solutions, such as pouches, to lock and store students’ phones during the school day. In other districts, educators have found creative ways to separate students from their phones, such as using over-the-door shoe holders where students place their phones during class.

2. Cellphones restricted only for elementary students, more flexible for middle and high school students

While restrictions on the use of cellphones and other two-way communication devices exist for all students in the Wauwatosa district in Wisconsin , there are more flexible rules for middle and high school students. Cellphones are prohibited all day for elementary students, but middle and high school students can use their phones before and after school, between class periods, during lunch, and in free periods. Teachers and principals have discretion for imposing consequences for misuse.

Close up of elementary or middle school white girl using a mobile phone in the classroom.

3. Cellphones are prohibited for elementary and middle school students, but more flexible for high school students

Elementary and middle school students in Virginia’s Rockingham district are prohibited from using personal electronic devices during the school day, while high school students may use their devices during lunch, study hall, advisory periods if permitted by a teacher and principal, and in between classes.

4. Cellphones are restricted only in classrooms, locker rooms, and bathrooms

Other districts, such as Richmond schools in Wisconsin, have restrictions on cellphone use only in certain areas of schools, such as classrooms, locker rooms, and bathrooms—to prevent bullying or sharing of inappropriate images, according to some district policies.

5. Cellphones restricted only in classrooms

Some restrictions are centered around classroom time only and allow students to use their phones outside of the classroom. In the Brush school district in Colorado , for instance, students aren’t allowed to have their phones out during instructional hours but can use them any other time. If a student is caught with a phone when they’re not allowed to have it, parents can either come to school to collect the phone or they can let the school keep the phone until the end of the day.

Students' cell phones are collected by school administration before the start of spring break at California City Middle School in California City, Calif., on March 11, 2022.

6. Cellphone restrictions are left up to each school

There are also districts, such as Meriden in Connecticut and Minnetonka in Minnesota, that don’t have districtwide restrictions, but instead have guidelines that schools can choose to follow.

For instance, in Meriden, the guidelines recommend elementary students keep their phones in their bags the whole school day; middle school students keep their phones in their lockers but can use them during lunch; and to let high school students have access to their phones all day but they must be turned off and out of sight during class time.

Other districts, such as Pawtucket in Rhode Island , allow principals or teachers to implement their own school or classroom rules around cellphones, as long as there’s a clear plan for allowing students to use them in case of emergencies.

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What is 'school refusal' and what can I do if my child struggles to get to school?

A composite of three images, of a young girl in a school uniform, clinging to school gates or lying on steps.

Chances are you've heard about or have a child who struggles to attend school.

A growing number of Aussie kids are missing school — for the last decade attendance rates have been dropping according to the national attendance authority, ACARA.

One of the reasons experts say some kids are not going is "school refusal". It's a term that refers to kids who experience emotional distress around school.

Many experts and families argue the more accurate term is "school can't", as it's not a deliberate choice by the child.

The issue — the subject of this week's Four Corners, 'The Kids Who Can't' — has largely been a hidden struggle for families. But last year a Senate inquiry brought new attention and some recommendations.

Desperate parents though, are still searching for answers.

There's no easy solution, and every kid's situation is different, but here are some resources and options that might help you.

What is school refusal and who is at risk?

The reasons children struggle to attend school can be complex. Research suggests that risk factors can include psychological problems, socio-economic disadvantage and school environment problems like bullying.

While school refusal can be caused by problems at home or school, it's often associated with autism, ADHD and anxiety disorders.

Some of the ways experts and education departments say it can present are:

Reluctance to get up on school mornings
Tantrums or outbursts
Repeated pleas to go home
Frequent lateness or skipping of school
Frequent requests to go to the sick bay
Threats to harm themselves

Fundamentally it's where a child has trouble attending or remaining at school due to varying underlying stressors.

Sydney mum Alice says her eight-year-old daughter Frieda, who is autistic, struggles to get to school full-time.

"Some days we couldn't even get out of the house. Some days we would get as far as the footpath and then she couldn't go in … then sometimes [she'd] just run away," she says.

Experts say school refusal can impact anyone, but certain groups are more at risk.

"They may be autistic, they may have learning difficulties, ADHD. They may have anxiety or some other mood disorder," says Lisa McKay-Brown, an education researcher at the University of Melbourne.

A close up of coloured pencils in a bucket.

Isn't it just wagging?

Truancy involves children who typically conceal their absence from their parents and may show antisocial behaviours.

School refusal, on the other hand, is when parents know about their child's absence from school and have tried to get them to attend. The attendance issue is often due to distress.

What can my child's current school do?

Your child's school should be your first point of contact to seek help.

This may mean collaborating with the school to come up with any adjustments to assist your child and make them feel safe. As education is a state-run system – schools can advise what support options are available in your area.

For example:

In New South Wales, extra support may be sought by your child's school. They may apply for integration funding support (IFS) to fund a teaching and support officer for your child or other support if that is additionally required.

Your school may also explore the option of a transfer to a school for specific purposes (SSPs) that provide targeted and specialist programs. As part of the referral process, it may be required that students have a confirmed disability that meets the department's disability criteria.

Are there any government programs focusing on school refusers?

Each state has different resources available for families dealing with school refusal.

In Victoria, the education department runs programs to re-engage youth in their schooling (there's a similar program in NSW). In one of them, called the "Navigator", Victorian kids aged 12 to 17 can be referred if their attendance is below 30 per cent.

In Queensland, families can call the Regional Youth Engagement Service for help and assistance if their child is refusing to go to school. They can put parents in touch with guidance counsellors and other professionals to provide support.

Two children's backpacks hang on hooks in a classroom. One is a Jurassic Park backpack.

There are no other government schools in my catchment zone, what are my options?

There are a number of independent schools that cater for young people who are disengaged from education and whose needs are not being met by the mainstream system.

But they're not everywhere, and there's high demand to secure a place. The waitlist at one school, MacKillop Education Geelong, was up to 100 people long.

Ethan, a 12-year-old from Geelong waited six months to get a spot at the school.

When he did get in, he flourished.

"When he came here, he couldn't read, couldn't write, couldn't do anything, and now, he's taking on board the learning … to the point where he can go back to mainstream school next year," says his mother Sam.

A woman and her son laugh sitting at a table. He is holding a pen and has a sheet of paper in front of him.

The school has 80 students enrolled and keeps class sizes limited to eight kids. It has chill-out areas for students who need emotional regulation, and made adjustments like allowing kids to choose what they wear.

Distance education programs are also available at some schools for children and youth who may be geographically isolated or whose special circumstances prevent them from attending a school.

Are there other options?

Some parents homeschool in order to meet their child's education needs themselves. It is a legally recognised alternative to enrolment in a school.

For some, it's a last resort they feel they must take on, even if it means sacrificing work and other commitments. But for many, it's just not financially feasible.

Each state and territory has different registration and monitoring requirements for parents who homeschool their kids.

Home Education Association, a not-for-profit community support group, has some resources on what each state and territory requires .

How many families is this affecting?

It's really hard to tell.

Deakin University researcher, Associate Professor Glenn Melvin, says one of the biggest issues with addressing school refusal is that we don't know how many young people it's impacting.

There is no comprehensive national data on school refusal because most states and territories are not tracking the reason kids are absent from school

"Departments of Education don't routinely collect this data, but this is critical data. It might be that the problem is much larger than we expect," Dr Melvin says.

Victoria is the only state that tracks school refusal numbers.

In 2021, 11,825 students were affected – but the Victorian government says this is a conservative estimate.

a classroom environment with a table and a few chairs.

What's being done?

The Senate inquiry into school refusal made 14 recommendations to the federal, state and territory governments.

They include:

A nationally agreed definition of school refusal and a consistent approach to recording school absences
funding a support network for parents and schools
An expansion of subsidised student mental health care visits

This month, the federal government agreed or supported in principle two of the inquiry's 14 recommendations.

They include commissioning the Australian Education Research Organisation to analyse what's driving the problem and possible interventions as well as disseminating school refusal training for teachers.

Greens senator Penny Allman-Payne, who helped instigate the inquiry, says some solutions could be integrated into mainstream schools.

"We know that there are things that work: early intervention, smaller class sizes, flexible campuses, interest-led learning," she says.

How can I understand the issue better as a parent?

While no national resource exists to help parents dealing with school refusal, most state education departments have information available online.

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Campus protests over the Gaza war

Top companies are on students' divest list. but does it really work.

A demonstrator protests outside the encampment established in support of Palestinians in Gaza at Columbia University on April 29, 2024. Columbia protesters are demanding their university sell off investments in a number of companies with business ties to Israel. Alex Kent/Getty Images hide caption

It's become a common mantra by protesters at universities across the country: "Disclose, divest, we will not stop, we will not rest."

Broadly, the protesters want their universities to sell off their investments in companies that have businesses or investments in Israel because of the country's invasion of Gaza. That's where the term divest comes from.

Police enter Columbia University's Hamilton Hall amid pro-Palestinian protests

College antiwar protests grow as students take over buildings on campuses

As student protesters get arrested, they risk being banned from campus too

The calls on campuses vary. Columbia University protesters, for example, have a broad list of divestment targets, demanding the Ivy League college disclose and unload investments in a broad set of companies with ties to Israel, including Google, Amazon and Airbnb .

Other protesters at universities are targeting defense-related companies and weapon manufacturers. Cornell University protesters are calling for divestments from companies including Boeing and Lockheed Martin.

Here's a look at what divestment means.

Why there's a call for divestments

Protests against university investments have a long history.

During the 1970s and 1980s, students at Columbia and other universities successfully pressed administrators to sell off investments in companies doing business with South Africa over the country's apartheid policies.

Since the 2010s, students have successfully called for some universities to divest themselves from companies tied to fossil fuels or to freeze their investments in that sector, including at Syracuse University.

Do divestments actually work?

Not really. Divesting by universities doesn't change corporate behavior, but it can provide a big moral and symbolic victory for protesters.

Most analysts agree that divestments don't usually punish the companies targeted. And some analysts argue divestments actually are worse in the long run. By staying invested, the reasoning goes, universities can have more of a say about a company's operations. Selling off their investments would likely be scooped up by other investors who are less likely to speak up.

For universities, divesting from companies that do business in Israel could also risk blowback from students, faculty or alumni who support Israel.

The University of California, for example, said it was opposed to "calls for boycott against and divestments from Israel."

"While the University affirms the right of our community members to express diverse viewpoints, a boycott of this sort impinges on the academic freedom of our students and faculty and the unfettered exchange of ideas on our campuses" the university said last week.

These are big reasons why almost no university has yet agreed to divest from investments tied to Israel, though a few have been willing to hold talks with protesters.

Protesters are pressing on, however. That's because getting a university to divest from companies with ties to Israel would not only achieve their goals, it would also likely serve as a moral victory by sparking a lot of headlines and debate.

"Divestment itself doesn't really influence the companies or the industries being targeted directly," said Prof. Todd Ely from the School of Public Affairs at the University of Colorado Denver. "It's more the stigma created and drawing attention to the issue more broadly."

A person stands among tents at an encampment set up by pro-Palestinian protesters on the campus of Columbia University on April 25, 2024. Leonardo Munoz/AFP via Getty Images hide caption

A person stands among tents at an encampment set up by pro-Palestinian protesters on the campus of Columbia University on April 25, 2024.

Can universities actually do it?

Yes, but it can be complicated.

Endowments at the nation's top universities have grown into multi-billion dollar chests, with investments in all kind of investment funds, including specialized private funds that prevent people from cashing out for a number of years.

More broadly, endowments have become a vital source of financing for universities. They allow for investments and scholarships while securing the university's financial future.

What a 1968 Columbia University protester makes of today's pro-Palestinian encampment

Some endowment chiefs have even become well known figures in finance, including the late David Swensen who served as Yale's chief investment officer and grew the university's funds massively.

Endowments "are intended to kind of preserve and grow the resources available to colleges and universities. And the number one use of those funds is to support students and student financial aid," says Prof. Ely. "So it's a complex situation where calls to change the way these funds are invested by students and other interested parties do end up kind of in a circular way going back to support the students themselves."

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What is behind US college protests over Israel-Gaza war?

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WHAT ARE THE PROTESTERS DEMANDING?

Who are the protesters, what has been the response from authorities.

Columbia, US colleges on edge in face of growing protests

WHAT HAS BEEN THE IMPACT ON REGULAR CAMPUS LIFE?

How are political leaders responding.

Reporting by Julia Harte in New York, Kanishka Singh in Washington, Brendan O'Brien in Chicago, and Andrew Hay in Albuquerque, New Mexico, Editing by Rosalba O'Brien

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What We Know About the Protests and Arrests at Columbia University

After nearly two weeks of protests, demonstrators seized Hamilton Hall. By the end of the night, the police moved into to arrest them.

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Tents are set up on campus at night, with Palestinian flags and students walking around.

By Alan Blinder

Columbia University is grappling with the fallout from its president’s promise to Congress that she would crack down on unsanctioned protests, and her decision to ask the police to clear an encampment on campus, resulting in the arrests of more than 100 students earlier this month.

On Tuesday, after protesters seized Hamilton Hall overnight, Columbia called in the police again and asked officers to remain on campus until May 17, after commencement.

“The events on campus last night have left us no choice,” Nemat Shafik, Columbia’s president, said in a letter to a New York Police Department official on Tuesday.

Police officers in riot gear made dozens of arrests and removed banners from Hamilton Hall’s facade overnight. An encampment near the building was cleared, leaving behind square indents on the grass on Wednesday morning. The campus was still closed on Wednesday to everyone but students who lived there and employees who provided essential services.

Dr. Shafik’s plea for the police presence came after almost two weeks of protests rocked the university, with demonstrators building (and rebuilding) an encampment, recriminations over the initial summoning of the police to campus on April 18, and accusations that Columbia has effectively allowed protesters, in some instances, to celebrate Hamas and target Jewish students for intimidation.

Last week, the university started offering hybrid classes, an acknowledgment that the disputes at the center of campus tension were unlikely to be resolved before the end of the school year. Commencement is scheduled for May 15.

On Friday, university leaders signaled that they were not eager to call in the police again.

“We called on N.Y.P.D. to clear an encampment once, but we all share the view, based on discussions within our community and with outside experts, that to bring back the N.Y.P.D. at this time would be counterproductive, further inflaming what is happening on campus, and drawing thousands to our doorstep who would threaten our community,” Columbia leaders, including Dr. Shafik, wrote. “Having said that, we also need to continue to enforce our own rules and ensure that those who violate the norms of our community face consequences.”

Columbia said Monday evening that it had started to suspend students who remained in the encampment, after they effectively declined an offer from the university to limit discipline. The Hamilton Hall occupation began hours later.

At around 9 p.m. on Tuesday, the police returned to Columbia and began arresting protesters.

How Columbia got here

Since the Oct. 7 attack by Hamas on Israel, American college campuses have been hubs of increased protest and debate. The scene at Columbia has been particularly contentious, with protests drawing hundreds of demonstrators, and some faculty members drawing attention for statements that critics considered to be antisemitic.

Columbia administrators, like their counterparts on campuses across the country, have struggled to fine-tune a response that balances discipline, free speech, academic freedom and institutional and national politics. For example, Columbia suspended two pro-Palestinian student groups after a walkout, and it has rewritten its protest policies, suspended some students and moved to cut or reduce ties to some faculty members.

The university’s approach was the focus of a congressional committee hearing on April 17. Over more than three hours in Washington, Dr. Shafik and other Columbia leaders tried to placate Republican lawmakers by acknowledging that they had been unprepared for the tensions of recent months and promising new crackdowns.

Although their answers appeared to please some lawmakers on Capitol Hill, they stirred unrest on campus, where protesters had built an encampment in the hours before Dr. Shafik’s testimony.

Columbia called in the police twice in April.

Less than 24 hours after the hearing adjourned, New York City police officers in riot gear entered the private campus at the request of Dr. Shafik and Columbia leaders. The police swept into the encampment to arrest defiant protesters and dismantle the demonstration, which was calling for the university to eliminate its financial ties to Israel. The authorities reported more than 100 arrests .

Many people welcomed the decision to call in the police to remove the tent protest in mid-April, and said that Dr. Shafik was well within her power to shut down unauthorized protests on private property. But the decision also provoked fresh outcry from students, faculty members, free-speech groups and critics of Israel, who argued that it was counterproductive to shut down a peaceful protest, particularly on a campus that is supposed to be a marketplace of ideas.

By the time many of the critiques rolled in, protesters had already started gathering again, chanting some of the same slogans — “We don’t want no Zionists here” and “Israel is a racist state” — that Dr. Shafik had suggested were creating “a harassing and intimidating environment for many of our students.”

Protesters pitched tents again, but this time the administration sought to negotiate with them.

Within two weeks, however, the negotiations broke down and protesters took over Hamilton Hall, an administrative building that has a long history of student takeovers. Columbia lost patience and brought the police back to campus. Dr. Shafik, in her letter to the Police Department on Tuesday evening, said the university had made its decision “with the utmost regret.”

Some protests unnerved Jewish students

Columbia cannot control what happens off its property, and the neighborhood around its campus has drawn significant attention in the aftermath of the arrests, with some reports of antisemitic harassment. School officials have said much of the incendiary language has come from outside protesters.

“Go back to Poland!” one masked protester who clutched a Palestinian flag shouted outside the Columbia campus gates, according to a video posted on X . Elsewhere online, a Columbia student said protesters had stolen, and then tried to burn, an Israeli flag, and that Jewish students had been splashed with water.

The Columbia chapter of Chabad, an international Orthodox Jewish movement, said that protesters targeted Jewish students with expletives as they left campus.

The White House condemned the episodes of antisemitic protest. A spokesman, Andrew Bates, said that “calls for violence and physical intimidation targeting Jewish students and the Jewish community are blatantly antisemitic, unconscionable and dangerous.”

Elie Buechler, an Orthodox rabbi who works at Columbia, said that campus and city police officers had failed to guarantee the safety of Jewish students “in the face of extreme antisemitism and anarchy" and suggested that the students return home “until the reality in and around campus has dramatically improved.”

That view was not universally shared. Hillel, the Jewish student organization on campus, called for increased security and said it was not urging Jewish students to leave.

Some on-campus activists distanced themselves from the agitators.

“There’s so many young Jewish people who are, like, a vital part” of the protests, said Grant Miner, a Jewish graduate student at Columbia who belongs to a student coalition calling on Columbia to divest from companies connected to Israel.

That group said in a statement, “We are frustrated by media distractions focusing on inflammatory individuals who do not represent us,” and added that the group’s members “firmly reject any form of hate or bigotry.”

Reporting was contributed by Liset Cruz , Colbi Edmonds , Luis Ferré-Sadurní , Erin Nolan , Sharon Otterman and Lola Fadulu .

Alan Blinder is a national correspondent for The Times, covering education. More about Alan Blinder

Our Coverage of the U.S. Campus Protests

News and Analysis

President Biden broke days of silence to finally speak out on the unrest disrupting campuses across the United States, denouncing violence and antisemitism even as he defended the right to peaceful dissent.

At the University of California, Los Angeles, police officers dismantled a pro-Palestinian encampment and made arrests after a tense hourslong standoff with demonstrators.

Police officers in riot gear arrested pro-Palestinian demonstrators at Fordham University’s Manhattan campus , the third university in New York City to face mass arrests.

Choosing Anonymity: In an online world, doxxing and other consequences have led many student protesters to obscure their identities by wearing masks and scarves. That choice has been polarizing .

Seeing Links to a Global Struggle: In many student protesters’ eyes, the war in Gaza is linked to other issues , such as policing, mistreatment of Indigenous people, racism and climate change.

Ending the Unrest: Across the nation, universities are looking for ways to quell the protests . Columbia has taken the spotlight after calling in the police twice , while Brown chose a different path .

A 63-Year-Old Career Activist: Videos show Lisa Fithian, whom the police called a “professional agitator,” working alongside protesters at Columbia who stormed Hamilton Hall.

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Why Every Educator Needs to Teach Problem-Solving Skills

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