problem solving skills of students

Why Every Educator Needs to Teach Problem-Solving Skills

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

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

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

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

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

Problem-Solving Skills Help Students…

   develop resilience.

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

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

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

    Set and Achieve Goals

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

  Resolve Conflicts

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

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

    Achieve Success

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

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

Problem-Solving Skills Can Be Measured and Taught

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

What Are Performance-Based Assessments?

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

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

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

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

Preview a Performance-Based Assessment

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

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

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

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

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

Explore CAE’s Problem-Solving Assessments

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

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

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

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

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

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

Ready to Get Started?

Learn more about cae’s suite of products and let’s get started measuring and teaching students important higher-order skills like problem solving..

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Strategies to develop problem-solving skills in students.

• November 14, 2023

Students need the freedom to brainstorm, develop solutions and make mistakes — this is truly the only way to prepare them for life outside the classroom. When students are immersed in a learning environment that only offers them step-by-step guides and encourages them to focus solely on memorisation, they are not gaining the skills necessary to help them navigate in the complex, interconnected environment of the real world.

Choosing a school that emphasises the importance of future-focussed skills will ensure your child has the abilities they need to survive and thrive anywhere in the world. What are future-focussed skills? Students who are prepared for the future need to possess highly developed communication skills, self-management skills, research skills, thinking skills, social skills and problem-solving skills. In this blog, I would like to focus on problem-solving skills.

What Are Problem-Solving Skills?

The Forage defines problem-solving skills as those that allow an individual to identify a problem, come up with solutions, analyse the options and collaborate to find the best solution for the issue.

Importance of Problem-Solving in the Classroom Setting

Learning how to solve problems effectively and positively is a crucial part of child development. When children are allowed to solve problems in a classroom setting, they can test those skills in a safe and nurturing environment. Generally, when they face age-appropriate issues, they can begin building those skills in a healthy and positive manner.

Without exposure to challenging situations and scenarios, children will not be equipped with the foundational problem-solving skills needed to tackle complex issues in the real world. Experts predict that problem-solving skills will eventually be more sought after in job applicants than hard skills related to that specific profession. Students must be given opportunities in school to resolve conflicts, address complex problems and come up with their own solutions in order to develop these skills.

Benefits of Problem-Solving Skills for Students

Learning how to solve problems offers students many advantages, such as:

Improving Academic Results

When students have a well-developed set of problem-solving skills, they are often better critical and analytical thinkers as well. They are able to effectively use these 21st-century skills when completing their coursework, allowing them to become more successful in all academic areas. By prioritising problem-solving strategies in the classroom, teachers often find that academic performance improves.

Developing Confidence

Giving students the freedom to solve problems and create their own solutions is essentially permitting them to make their own choices. This sense of independence — and the natural resilience that comes with it — allows students to become confident learners who aren’t intimidated by new or challenging situations. Ultimately, this prepares them to take on more complex challenges in the future, both on a professional and social level.

Preparing Students for Real-World Challenges

The challenges we are facing today are only growing more complex, and by the time students have graduated, they are going to be facing issues that we may not even have imagined. By arming them with real-world problem-solving experience, they will not feel intimidated or stifled by those challenges; they will be excited and ready to address them. They will know how to discuss their ideas with others, respect various perspectives and collaborate to develop a solution that best benefits everyone involved.

The Best Problem-Solving Strategies for Students

No single approach or strategy will instil a set of problem-solving skills in students.  Every child is different, so educators should rely on a variety of strategies to develop this core competency in their students.  It is best if these skills are developed naturally.

These are some of the best strategies to support students problem-solving skills:

Project-Based Learning

By providing students with project-based learning experiences and allowing plenty of time for discussion, educators can watch students put their problem-solving skills into action inside their classrooms. This strategy is one of the most effective ways to fine-tune problem-solving skills in students.  During project-based learning, teachers may take notes on how the students approach a problem and then offer feedback to students for future development. Teachers can address their observations of interactions during project-based learning at the group level or they can work with students on an individual basis to help them become more effective problem-solvers.

Encourage Discussion and Collaboration in the Classroom Setting

Another strategy to encourage the development of problem-solving skills in students is to allow for plenty of discussion and collaboration in the classroom setting.  When students interact with one another, they are naturally developing problem solving skills.  Rather than the teacher delivering information and requiring the students to passively receive information, students can share thoughts and ideas with one another.  Getting students to generate their own discussion and communication requires thinking skills. 

Utilising an Inquiry-Based approach to Learning

Students should be presented with situations in which their curiosity is sparked and they are motivated to inquire further. Teachers should ask open-ended questions and encourage students to develop responses which require problem-solving. By providing students with complex questions for which a variety of answers may be correct, teachers get students to consider different perspectives and deal with potential disagreement, which requires problem-solving skills to resolve.

Model Appropriate Problem-Solving Skills

One of the simplest ways to instil effective problem-solving skills in students is to model appropriate and respectful strategies and behaviour when resolving a conflict or addressing an issue. Teachers can showcase their problem-solving skills by:

• Identifying a problem when they come across one for the class to see
• Brainstorming possible solutions with students
• Collaborating with students to decide on the best solution
• Testing that solution and examining the results with the students
• Adapting as necessary to improve results or achieve the desired goal

Prioritise Student Agency in Learning

Recent research shows that self-directed learning is one of the most effective ways to nurture 21st-century competency development in young learners. Learning experiences that encourage student agency often require problem-solving skills.  When creativity and innovation are needed, students often encounter unexpected problems along the way that must be solved. Through self-directed learning, students experience challenges in a natural situation and can fine-tune their problem-solving skills along the way.  Self-directed learning provides them with a foundation in problem-solving that they can build upon in the future, allowing them to eventually develop more advanced and impactful problem-solving skills for real life.

21st-Century Skill Development at OWIS Singapore

Problem-solving has been identified as one of the core competencies that young learners must develop to be prepared to meet the dynamic needs of a global environment.  At OWIS Singapore, we have implemented an inquiry-driven, skills-based curriculum that allows students to organically develop critical future-ready skills — including problem-solving.  Our hands-on approach to education enables students to collaborate, explore, innovate, face-challenges, make mistakes and adapt as necessary.  As such, they learn problem-solving skills in an authentic manner.

For more information about 21st-century skill development, schedule a campus tour today.

About Author

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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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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.

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Developing Problem-Solving Skills for Kids | Strategies & Tips

We've made teaching problem-solving skills for kids a whole lot easier! Keep reading and comment below with any other tips you have for your classroom!

Problem-Solving Skills for Kids: The Real Deal

Picture this: You've carefully created an assignment for your class. The step-by-step instructions are crystal clear. During class time, you walk through all the directions, and the response is awesome. Your students are ready! It's finally time for them to start working individually and then... 8 hands shoot up with questions. You hear one student mumble in the distance, "Wait, I don't get this" followed by the dreaded, "What are we supposed to be doing again?"

When I was a new computer science teacher, I would have this exact situation happen. As a result, I would end up scrambling to help each individual student with their problems until half the class period was eaten up. I assumed that in order for my students to learn best, I needed to be there to help answer questions immediately so they could move forward and complete the assignment.

Here's what I wish I had known when I started teaching coding to elementary students - the process of grappling with an assignment's content can be more important than completing the assignment's product. That said, not every student knows how to grapple, or struggle, in order to get to the "aha!" moment and solve a problem independently. The good news is, the ability to creatively solve problems is not a fixed skill. It can be learned by students, nurtured by teachers, and practiced by everyone!

Your students are absolutely capable of navigating and solving problems on their own. Here are some strategies, tips, and resources that can help:

Problem-Solving Skills for Kids: Student Strategies

These are strategies your students can use during independent work time to become creative problem solvers.

1. Go Step-By-Step Through The Problem-Solving Sequence 

Post problem-solving anchor charts and references on your classroom wall or pin them to your Google Classroom - anything to make them accessible to students. When they ask for help, invite them to reference the charts first.

2. Revisit Past Problems

If a student gets stuck, they should ask themself, "Have I ever seen a problem like this before? If so, how did I solve it?" Chances are, your students have tackled something similar already and can recycle the same strategies they used before to solve the problem this time around.

3. Document What Doesn’t Work

Sometimes finding the answer to a problem requires the process of elimination. Have your students attempt to solve a problem at least two different ways before reaching out to you for help. Even better, encourage them write down their "Not-The-Answers" so you can see their thought process when you do step in to support. Cool thing is, you likely won't need to! By attempting to solve a problem in multiple different ways, students will often come across the answer on their own.

4. "3 Before Me"

Let's say your students have gone through the Problem Solving Process, revisited past problems, and documented what doesn't work. Now, they know it's time to ask someone for help. Great! But before you jump into save the day, practice "3 Before Me". This means students need to ask 3 other classmates their question before asking the teacher. By doing this, students practice helpful 21st century skills like collaboration and communication, and can usually find the info they're looking for on the way.

Problem-Solving Skills for Kids: Teacher Tips

These are tips that you, the teacher, can use to support students in developing creative problem-solving skills for kids.

1. Ask Open Ended Questions

When a student asks for help, it can be tempting to give them the answer they're looking for so you can both move on. But what this actually does is prevent the student from developing the skills needed to solve the problem on their own. Instead of giving answers, try using open-ended questions and prompts. Here are some examples:

2. Encourage Grappling

Grappling  is everything a student might do when faced with a problem that does not have a clear solution. As explained in this article from Edutopia , this doesn't just mean perseverance! Grappling is more than that - it includes critical thinking, asking questions, observing evidence, asking more questions, forming hypotheses, and constructing a deep understanding of an issue.

There are lots of ways to provide opportunities for grappling. Anything that includes the Engineering Design Process is a good one! Examples include:

• Engineering or Art Projects
• Design-thinking challenges
• Computer science projects
• Science experiments

3. Emphasize Process Over Product

For elementary students, reflecting on the process of solving a problem helps them develop a growth mindset . Getting an answer "wrong" doesn't need to be a bad thing! What matters most are the steps they took to get there and how they might change their approach next time. As a teacher, you can support students in learning this reflection process.

4. Model The Strategies Yourself! 

As creative problem-solving skills for kids are being learned, there will likely be moments where they are frustrated or unsure. Here are some easy ways you can model what creative problem-solving looks and sounds like.

• Ask clarifying questions if you don't understand something
• Admit when don't know the correct answer
• Talk through multiple possible outcomes for different situations 
• Verbalize how you’re feeling when you find a problem

Practicing these strategies with your students will help create a learning environment where grappling, failing, and growing is celebrated!

Problem-Solving Skill for Kids

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• Problem Solving in STEM

Solving problems is a key component of many science, math, and engineering classes.  If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer different types of problems.  Problem solving during section or class allows students to develop their confidence in these skills under your guidance, better preparing them to succeed on their homework and exams. This page offers advice about strategies for facilitating problem solving during class.

How do I decide which problems to cover in section or class?

In-class problem solving should reinforce the major concepts from the class and provide the opportunity for theoretical concepts to become more concrete. If students have a problem set for homework, then in-class problem solving should prepare students for the types of problems that they will see on their homework. You may wish to include some simpler problems both in the interest of time and to help students gain confidence, but it is ideal if the complexity of at least some of the in-class problems mirrors the level of difficulty of the homework. You may also want to ask your students ahead of time which skills or concepts they find confusing, and include some problems that are directly targeted to their concerns.

You have given your students a problem to solve in class. What are some strategies to work through it?

• Try to give your students a chance to grapple with the problems as much as possible.  Offering them the chance to do the problem themselves allows them to learn from their mistakes in the presence of your expertise as their teacher. (If time is limited, they may not be able to get all the way through multi-step problems, in which case it can help to prioritize giving them a chance to tackle the most challenging steps.)
• When you do want to teach by solving the problem yourself at the board, talk through the logic of how you choose to apply certain approaches to solve certain problems.  This way you can externalize the type of thinking you hope your students internalize when they solve similar problems themselves.
• Start by setting up the problem on the board (e.g you might write down key variables and equations; draw a figure illustrating the question).  Ask students to start solving the problem, either independently or in small groups.  As they are working on the problem, walk around to hear what they are saying and see what they are writing down. If several students seem stuck, it might be a good to collect the whole class again to clarify any confusion.  After students have made progress, bring the everyone back together and have students guide you as to what to write on the board.
• It can help to first ask students to work on the problem by themselves for a minute, and then get into small groups to work on the problem collaboratively.
• If you have ample board space, have students work in small groups at the board while solving the problem.  That way you can monitor their progress by standing back and watching what they put up on the board.
• If you have several problems you would like to have the students practice, but not enough time for everyone to do all of them, you can assign different groups of students to work on different – but related - problems.

When do you want students to work in groups to solve problems?

• Don’t ask students to work in groups for straightforward problems that most students could solve independently in a short amount of time.
• Do have students work in groups for thought-provoking problems, where students will benefit from meaningful collaboration.
• Even in cases where you plan to have students work in groups, it can be useful to give students some time to work on their own before collaborating with others.  This ensures that every student engages with the problem and is ready to contribute to a discussion.

What are some benefits of having students work in groups?

• Students bring different strengths, different knowledge, and different ideas for how to solve a problem; collaboration can help students work through problems that are more challenging than they might be able to tackle on their own.
• In working in a group, students might consider multiple ways to approach a problem, thus enriching their repertoire of strategies.
• Students who think they understand the material will gain a deeper understanding by explaining concepts to their peers.

What are some strategies for helping students to form groups?  

• Instruct students to work with the person (or people) sitting next to them.
• Count off.  (e.g. 1, 2, 3, 4; all the 1’s find each other and form a group, etc)
• Hand out playing cards; students need to find the person with the same number card. (There are many variants to this.  For example, you can print pictures of images that go together [rain and umbrella]; each person gets a card and needs to find their partner[s].)
• Based on what you know about the students, assign groups in advance. List the groups on the board.
• Note: Always have students take the time to introduce themselves to each other in a new group.

What should you do while your students are working on problems?

• Walk around and talk to students. Observing their work gives you a sense of what people understand and what they are struggling with. Answer students’ questions, and ask them questions that lead in a productive direction if they are stuck.
• If you discover that many people have the same question—or that someone has a misunderstanding that others might have—you might stop everyone and discuss a key idea with the entire class.

After students work on a problem during class, what are strategies to have them share their answers and their thinking?

• Ask for volunteers to share answers. Depending on the nature of the problem, student might provide answers verbally or by writing on the board. As a variant, for questions where a variety of answers are relevant, ask for at least three volunteers before anyone shares their ideas.
• Use online polling software for students to respond to a multiple-choice question anonymously.
• If students are working in groups, assign reporters ahead of time. For example, the person with the next birthday could be responsible for sharing their group’s work with the class.
• Cold call. To reduce student anxiety about cold calling, it can help to identify students who seem to have the correct answer as you were walking around the class and checking in on their progress solving the assigned problem. You may even want to warn the student ahead of time: "This is a great answer! Do you mind if I call on you when we come back together as a class?"
• Have students write an answer on a notecard that they turn in to you.  If your goal is to understand whether students in general solved a problem correctly, the notecards could be submitted anonymously; if you wish to assess individual students’ work, you would want to ask students to put their names on their notecard.  
• Use a jigsaw strategy, where you rearrange groups such that each new group is comprised of people who came from different initial groups and had solved different problems.  Students now are responsible for teaching the other students in their new group how to solve their problem.
• Have a representative from each group explain their problem to the class.
• Have a representative from each group draw or write the answer on the board.

What happens if a student gives a wrong answer?

• Ask for their reasoning so that you can understand where they went wrong.
• Ask if anyone else has other ideas. You can also ask this sometimes when an answer is right.
• Cultivate an environment where it’s okay to be wrong. Emphasize that you are all learning together, and that you learn through making mistakes.
• Do make sure that you clarify what the correct answer is before moving on.
• Once the correct answer is given, go through some answer-checking techniques that can distinguish between correct and incorrect answers. This can help prepare students to verify their future work.

How can you make your classroom inclusive?

• The goal is that everyone is thinking, talking, and sharing their ideas, and that everyone feels valued and respected. Use a variety of teaching strategies (independent work and group work; allow students to talk to each other before they talk to the class). Create an environment where it is normal to struggle and make mistakes.
• See Kimberly Tanner’s article on strategies to promoste student engagement and cultivate classroom equity. 

A few final notes…

• Make sure that you have worked all of the problems and also thought about alternative approaches to solving them.
• Board work matters. You should have a plan beforehand of what you will write on the board, where, when, what needs to be added, and what can be erased when. If students are going to write their answers on the board, you need to also have a plan for making sure that everyone gets to the correct answer. Students will copy what is on the board and use it as their notes for later study, so correct and logical information must be written there.

For more information...

Tipsheet: Problem Solving in STEM Sections

Tanner, K. D. (2013). Structure matters: twenty-one teaching strategies to promote student engagement and cultivate classroom equity . CBE-Life Sciences Education, 12(3), 322-331.

• Designing Your Course
• A Teaching Timeline: From Pre-Term Planning to the Final Exam
• The First Day of Class
• Group Agreements
• Classroom Debate
• Flipped Classrooms
• Leading Discussions
• Polling & Clickers
• Teaching with Cases
• Engaged Scholarship
• Devices in the Classroom
• Beyond the Classroom
• On Professionalism
• Getting Feedback
• Equitable & Inclusive Teaching
• Advising and Mentoring
• Teaching and Your Career
• Teaching Remotely
• Tools and Platforms
• The Science of Learning
• Bok Publications
• Other Resources Around Campus

8 Chapter 6 Supporting Student Problem-Solving

Across content areas, the standards address problem-solving in the form of being able to improvise, decide, inquire, and research. In fact, math and science standards are premised almost completely on problem-solving and inquiry. According to the literature, however, problem-solving and inquiry are often overlooked or addressed only superficially in classrooms, and in some subject areas, are not attended to at all.

OVERVIEW OF PROBLEM-SOLVING AND INQUIRY IN K–12 CLASSROOMS

In keeping with a learning focus, this chapter first discusses problem-solving and inquiry to provide a basis from which teachers can provide support for these goals with technology.

What Is Problem-solving?

Whereas production is a process that focuses on an end-product, problem-solving is a process that centers on a problem. Students apply critical and creative thinking skills to prior knowledge during the problem-solving process. The end result of problem-solving is typically some kind of decision, in other words, choosing a solution and then evaluating it.

There are two general kinds of problems. Close-ended problems are those with known solutions to which students can apply a process similar to one that they have already used. For example, if a student understands the single-digit process in adding 2 plus 2 to make 4, she most likely will be able to solve a problem that asks her to add 1 plus 1. Open-ended or loosely structured problems, on the other hand, are those with many or unknown solutions rather than one correct answer. These types of problems require the ability to apply a variety of strategies and knowledge to finding a solution. For example, an open-ended problem statement might read:

A politician has just discovered information showing that a statement he made to the public earlier in the week was incorrect. If he corrects himself he will look like a fool, but if he doesn’t and someone finds out the truth, he will be in trouble. What should he do or say about this?

Obviously, there is no simple answer to this question, and there is a lot of information to consider.

Many textbooks, teachers, and tests present or ask only for the results of problem-solving and not the whole process that students must go through in thinking about how to arrive at a viable solution. As a result, according to the literature, most people use their personal understandings to try to solve open-ended problems, but the bias of limited experience makes it hard for people to understand the trade-offs or contradictions that these problems present. To solve such problems, students need to be able to use both problem-solving skills and an effective inquiry process.

What Is Inquiry?

Inquiry in education is also sometimes called research, investigation, or guided discovery. During inquiry, students ask questions and then search for answers to those questions. In doing so, they come to new understandings in content and language. Although inquiry is an instructional strategy in itself, it is also a central component of problem-solving when students apply their new understandings to the problem at hand. Each question that the problem raises must be addressed by thorough and systematic investigation to arrive at a well-grounded solution. Therefore, the term “problem-solving” can be considered to include inquiry.

For students to understand both the question and ways of looking at the answer(s), resources such as historical accounts, literature, art, and eyewitness experiences must be used. In addition, each resource must be examined in light of what each different type of material contributes to the solution. Critical literacy, or reading beyond the text, then, is a fundamental aspect of inquiry and so of problem-solving. Search for critical literacy resources by using “critical literacy” and your grade level, and be sure to look at the tools provided in this text’s Teacher Toolbox.

What Is Problem-Based Learning?

Problem-based learning (PBL) is a teaching approach that combines critical thinking, problem- solving skills, and inquiry as students explore real-world problems. It is based on unstructured, complex, and authentic problems that are often presented as part of a project. PBL addresses many of the learning goals presented in this text and across the standards, including communication, creativity, and often production.

Research is being conducted in every area from business to education to see how we solve problems, what guides us, what information we have and use during problem-solving, and how we can become more efficient problem solvers. There are competing theories of how people learn to and do solve problems, and much more research needs to be done. However, we do know several things. First, problem-solving can depend on the context, the participants, and the stakeholders. In addition, studies show that content appears to be covered better by “traditional” instruction, but students retain better after problem-solving. PBL has been found effective at teaching content and problem-solving, and the use of technology can make those gains even higher (Chauhan, 2017). Research clearly shows that the more parts of a problem there are, the less successful students will be at solving it. However, effective scaffolding can help to support students’ problem-solving and overcomes some of the potential issues with it (Belland, Walker, Kim, & Lefler, 2017).

The PBL literature points out that both content knowledge and problem-solving skills are necessary to arrive at solutions, but individual differences among students affect their success, too. For example, field-independent students in general do better than field-dependent students in tasks. In addition, students from some cultures will not be familiar with this kind of learning, and others may not have the language to work with it. Teachers must consider all of these ideas and challenges in supporting student problem-solving.

Characteristics of effective technology-enhanced problem-based learning tasks

PBL tasks share many of the same characteristics of other tasks in this book, but some are specific to PBL. Generally, PBL tasks:

Involve learners in gaining and organizing knowledge of content. Inspiration and other concept-mapping tools like the app Popplet are useful for this.

Help learners link school activities to life, providing the “why” for doing the activity.

Give students control of their learning.

Have built-in and just-in-time scaffolding to help students. Tutorials are available all over the Web for content, language, and technology help.

Are fun and interesting.

Contain specific objectives for students to meet along the way to a larger goal.

Have guidance for the use of tools, especially computer technologies.

Include communication and collaboration (described in chapter 3).

Emphasize the process and the content.

Are central to the curriculum, not peripheral or time fillers.

Lead to additional content learning.

Have a measurable, although not necessarily correct, outcome.

More specifically, PBL tasks:

Use a problem that “appeals to human desire for resolution/stasis/harmony” and “sets up need for and context of learning which follows” (IMSA, 2005, p. 2).

Help students understand the range of problem-solving mechanisms available.

Focus on the merits of the question, the concepts involved, and student research plans.

Provide opportunities for students to examine the process of getting the answer (for example, looking back at the arguments).

Lead to additional “transfer” problems that use the knowledge gained in a different context.

Not every task necessarily exhibits all of these characteristics completely, but these lists can serve as guidelines for creating and evaluating tasks.

Student benefits of problem-solving

There are many potential benefits of using PBL in classrooms at all levels; however, the benefits depend on how well this strategy is employed. With effective PBL, students can become more engaged in their learning and empowered to become more autonomous in classroom work. This, in turn, may lead to improved attitudes about the classroom and thus to other gains such as increased abilities for social-problem solving. Students can gain a deeper understanding of concepts, acquire skills necessary in the real world, and transfer skills to become independent and self-directed learners and thinkers outside of school. For example, when students are encouraged to practice using problem-solving skills across a variety of situations, they gain experience in discovering not only different methods but which method to apply to what kind of problem. Furthermore, students can become more confident when their self-esteem and grade does not depend only on the specific answer that the teacher wants. In addition, during the problem-solving process students can develop better critical and creative thinking skills.

Students can also develop better language skills (both knowledge and communication) through problems that require a high level of interaction with others (Verga & Kotz, 2013). This is important for all learners, but especially for ELLs and others who do not have grade-level language skills. For students who may not understand the language or content or a specific question, the focus on process gives them more opportunities to access information and express their knowledge.

The problem-solving process

The use of PBL requires different processes for students and teachers. The teacher’s process involves careful planning. There are many ways for this to happen, but a general outline that can be adapted includes the following steps:

After students bring up a question, put it in the greater context of a problem to solve (using the format of an essential question; see chapter 4) and decide what the outcome should be–a recommendation, a summary, a process?

Develop objectives that represent both the goal and the specific content, language, and skills toward which students will work.

List background information and possible materials and content that will need to be addressed. Get access to materials and tools and prepare resource lists if necessary.

Write the specific problem. Make sure students know what their role is and what they are expected to do. Then go back and check that the problem and task meet the objectives and characteristics of effective PBL and the relevant standards. Reevaluate materials and tools.

Develop scaffolds that will be needed.

Evaluate and prepare to meet individual students’ needs for language, assistive tools, content review, and thinking skills and strategies

Present the problem to students, assess their understanding, and provide appropriate feedback as they plan and carry out their process.

The student process focuses more on the specific problem-solving task. PBL sources list different terms to describe each step, but the process is more or less the same. Students:

Define and frame the problem: Describe it, recognize what is being asked for, look at it from all sides, and say why they need to solve it.

Plan: Present prior knowledge that affects the problem, decide what further information and concepts are needed, and map what resources will be consulted and why.

Inquire: Gather and analyze the data, build and test hypotheses.

Look back: Review and evaluate the process and content. Ask “What do I understand from this result? What does it tell me?”

These steps are summarized in Figure 6.1.

Problem-solving strategies that teachers can demonstrate, model, and teach directly include trial and error, process of elimination, making a model, using a formula, acting out the problem, using graphics or drawing the problem, discovering patterns, and simplifying the problem (e.g., rewording, changing the setting, dividing it into simpler tasks). Even the popular KWL (Know, Want to Know, Learned) chart can help students frame questions. A KWL for a project asking whether a superstore should be built in the community might look like the one in Figure 6.2. Find out more about these strategies at http://literacy.kent.edu/eureka/strategies/discuss-prob.html .

Teaching problem-solving in groups involves the use of planning and other technologies. Using these tools, students post, discuss, and reflect on their joint problem-solving process using visual cues that they create. This helps students focus on both their process and the content. Throughout the teacher and student processes, participants should continue to examine cultural, emotional, intellectual, and other possible barriers to problem-solving.

Teachers and Problem-solving

The teacher’s role in PBL

During the teacher’s process of creating the problem context, the teacher must consider what levels of authenticity, complexity, uncertainty, and self-direction students can access and work within. Gordon (1998) broke loosely structured problems into three general types with increasing levels of these aspects. Still in use today, these are:

Academic challenges. An academic challenge is student work structured as a problem arising directly from an area of study. It is used primarily to promote greater understanding of selected subject matter. The academic challenge is crafted by transforming existing curricular material into a problem format.

Scenario challenges. These challenges cast students in real-life roles and ask them to perform these roles in the context of a reality-based or fictional scenario.

Real-life problems. These are actual problems in need of real solutions by real people or organizations. They involve students directly and deeply in the exploration of an area of study. And the solutions have the potential for actual implementation at the classroom, school, community, regional, national, or global level. (p. 3)

To demonstrate the application of this simple categorization, the learning activities presented later in this chapter follow this outline.

As discussed in other chapters in this book, during student work the teacher’s role can vary from director to shepherd, but when the teacher is a co-learner rather than a taskmaster, learners become experts. An often-used term for the teacher’s role in the literature about problem-solving is “coach.” As a coach, the teacher works to facilitate thinking skills and process, including working out group dynamics, keeping students on task and making sure they are participating, assessing their progress and process, and adjusting levels of challenge as students’ needs change. Teachers can provide hints and resources and work on a gradual release of responsibility to learners.

Challenges for teachers

For many teachers, the roles suggested above are easier said than done. To use a PBL approach, teachers must break out of the content-dissemination mode and help their students to do the same. Even when this happens, in many classrooms students have been trained to think that problem-solving is getting the one right answer, and it takes time, practice, and patience for them to understand otherwise. Some teachers feel that they are obligated to cover too much in the curriculum to spend time on PBL or that using real-world problems does not mesh well with the content, materials, and context of the classroom. However, twenty years ago Gordon (1998) noted, “whether it’s a relatively simple matter of deciding what to eat for breakfast or a more complex one such as figuring out how to reduce pollution in one’s community, in life we make decisions and do things that have concrete results. Very few of us do worksheets” (p. 2). He adds that not every aspect of students’ schoolwork needs to be real, but that connections should be made from the classroom to the real world. Educators around the world are still working toward making school more like life.

In addition, many standardized district and statewide tests do not measure process, so students do not want to spend time on it. However, teachers can overcome this thinking by demonstrating to students the ways in which they need to solve problems every day and how these strategies may transfer to testing situations.

Furthermore, PBL tasks and projects may take longer to develop and assess than traditional instruction. However, teachers can start slowly by helping students practice PBL in controlled environments with structure, then gradually release them to working independently. The guidelines in this chapter address some of these challenges.

GUIDELINES FOR TECHNOLOGY-SUPPORTED PROBLEM-SOLVING

Obviously, PBL is more than simply giving students a problem and asking them to solve it. The following guidelines describe other issues in PBL.

Designing Problem-Solving Opportunities

The guidelines described here can assist students in developing a PBL opportunity.

Guideline #1: Integrate reading and writing. Although an important part of solving problems, discussion alone is not enough for students to develop and practice problem-solving skills. Effective problem-solving and inquiry require students to think clearly and deeply about content, language, and process. Reading and writing tasks can encourage students to take time to think about these issues and to contextualize their thinking practice. They can also provide vehicles for teachers to understand student progress and to provide concrete feedback. Students who have strengths in these areas will be encouraged and those who need help can learn from their stronger partners, just as those who have strengths in speaking can model for and assist their peers during discussion. Even in courses that do not stress reading and writing, integrating these skills into tasks and projects can promote successful learning.

Guideline #2: Avoid plagiarism. The Internet is a great resource for student inquiry and problem-solving. However, when students read and write using Internet resources, they often cut and paste directly from the source. Sometimes this is an innocent mistake; students may be uneducated about the use of resources, perhaps they come from a culture where the concept of ownership is completely different than in the United States, or maybe their language skills are weak and they want to be able to express themselves better. In either case, two strategies can help avoid plagiarism: 1) The teacher can teach directly about plagiarism and copyright issues. Strategies including helping students learn how to cite sources, paraphrase, summarize, and restate; 2) The teacher can be as familiar as possible with the resources that students will use and check for plagiarism when it is suspected. To do so, the teacher can enter a sentence or phrase into any Web browser with quote marks around it and if the entry is exact, the original source will come up in the browser window. Essay checkers such as Turnitin (http://turnitin.com/) are also available online that will check a passage or an entire essay.

Guideline #3: Do not do what students can do. Teaching, and particularly teaching with technology, is often a difficult job, due in part to the time it takes teachers to prepare effective learning experiences. Planning, developing, directing, and assessing do not have to be solely the teacher’s domain, however. Students should take on many of these responsibilities, and at the same time gain in problem-solving, language, content, critical thinking, creativity, and other crucial skills. Teachers do not always need to click the mouse, write on the whiteboard, decide

criteria for a rubric, develop questions, decorate the classroom, or perform many classroom and learning tasks. Students can take ownership and feel responsibility. Although it is often difficult for teachers to give up some of their power, the benefits of having more time and shared responsibility can be transformational. Teachers can train themselves to ask, “Is this something students can do?”

Guideline #4: Make mistakes okay. Problem-solving often involves coming to dead ends, having to revisit data and reformulate ideas, and working with uncertainty. For students used to striving for correct answers and looking to the teacher as a final authority, the messiness of problem-solving can be disconcerting, frustrating, and even scary. Teachers can create environments of acceptance where reasoned, even if wrong, answers are recognized, acknowledged, and given appropriate feedback by the teacher and peers. Teachers already know that students come to the task with a variety of beliefs and information. In working with students’ prior knowledge, they can model how to be supportive of students’ faulty ideas and suggestions. They can also ask positive questions to get the students thinking about what they still need to know and how they can come to know it. They can both encourage and directly teach students to be supportive of mistakes and trials as part of their team-building and leadership skills.

In addition, teachers may need to help students to understand that even a well-reasoned argument or answer can meet with opposition. Students must not feel that they have made a bad decision just because everyone else, particularly the teacher, does not agree. Teachers can model for students that they are part of the learning process and they are impartial as to the outcome when the student’s position has been well defended.

PROBLEM-SOLVING AND INQUIRY TECHNOLOGIES

As with all the goals in this book, the focus of technology in problem-solving is not on the technology itself but on the learning experiences that the technology affords. Different tools exist to support different parts of the process. Some are as simple as handouts that students can print and complete, others as complex as modeling and visualization software. Many software tools that support problem-solving are made for experts in the field and are relatively difficult to learn and use. Examples of these more complicated programs include many types of computer-aided design software, advanced authoring tools, and complex expert systems. In the past there were few software tools for K–12 students that addressed the problem-solving process directly and completely, but more apps are being created all the time that do so. See the Teacher Tools for this text for examples.

Simple inquiry tools that help students perform their investigations during PBL are much more prevalent. The standard word processor, database, concept mapping/graphics and spreadsheet software can all assist students in answering questions and organizing and presenting data, but there are other tools more specifically designed to support inquiry. Software programs that can be used within the PBL framework are mentioned in other chapters in this text. These programs, such as the Tom Snyder Productions/Scholastic programs mentioned in chapter 2 address the overlapping goals of collaboration, production, critical thinking, creativity, and problem-solving. Interestingly, even video games might be used as problem-solving tools. Many of these games require users to puzzle out directions, to find missing artifacts, or to follow clues that are increasingly difficult to find and understand. One common tool with which students at all levels might be familiar is Minecraft (Mojang; https://minecraft.net/en-us/). The Internet has as many resources as teachers might need to use Minecraft across the disciplines to teach whole units and even gamify the classroom.

The following section presents brief descriptions of tools that can support the PBL process. The examples are divided into stand-alone tools that can be used on one or more desktops and Web-based tools.

Stand-Alone Tools

Example 1: Fizz and Martina’s Math Adventures (Tom Snyder Productions/Scholastic)

Students help Fizz and Martina, animated characters in this software, to solve problems by figuring out which data is relevant, performing appropriate calculations, and presenting their solutions. The five titles in this series are perfect for a one-computer classroom. Each software package combines computer-based video, easy navigation, and handouts and other resources as scaffolds. This software is useful in classrooms with ELLs because of the combination of visual, audio, and text-based reinforcement of input. It is also accessible to students with physical disabilities because it can run on one computer; students do not have to actually perform the mouse clicks to run the software themselves.

This software is much more than math. It includes a lot of language, focuses on cooperation and collaboration in teams, and promotes critical thinking as part of problem-solving. Equally important, it helps students to communicate mathematical ideas orally and in writing. See Figure 6.6 for the “getting started” screen from Fizz and Martina to view some of the choices that teachers and students have in using this package.

Example 2: I Spy Treasure Hunt, I Spy School Days, I Spy Spooky Mansion (Scholastic)

The language in these fun simulations consists of isolated, discrete words and phrases, making these programs useful for word study but not for overall concept learning. School Days, for example, focuses on both objects and words related to school. However, students work on extrapolation, trial and error, process of elimination, and other problem-solving strategies. It is difficult to get students away from the computer once they start working on any of the simulations in this series. Each software package has several separate hunts with a large number of riddles that, when solved, allow the user to put together a map or other clues to find the surprise at the end. Some of the riddles involve simply finding an item on the screen, but others require more thought such as figuring out an alternative representation for the item sought or using a process of elimination to figure out where to find it. All of the riddles are presented in both text and audio and can be repeated as many times as the student requires, making it easier for language learners, less literate students, and students with varied learning preferences to access the information. Younger students can also work with older students or an aide for close support so that students are focused. Free versions of the commercial software and similar types of programs such as escape rooms (e.g., escapes at 365 Escape {http://www.365escape.com/Room-Escape-Games.html] and www.primarygames.com) can be found across the Web.

There are many more software packages like these that can be part of a PBL task. See the Teacher Toolbox for ideas.

Example 3: Science Court (Tom Snyder Productions/Scholastic)

Twelve different titles in this series present humorous court cases that students must help to resolve. Whether the focus is on the water cycle, soil, or gravity, students use animated computer-based video, hands-on science activities, and group work to learn and practice science and the inquiry process. As students work toward solving the case, they examine not only the facts but also their reasoning processes. Like Fizz and Martina and much of TSP’s software, Science Court uses multimedia and can be used in the one-computer classroom (as described in chapter 2), making it accessible to diverse students.

Example 4: Geographic Information Systems (GIS)

The use of GIS to track threatened species, map hazardous waste or wetlands in the community, or propose solutions for other environmental problems supports student “spatial literacy and geographic competence” (Baker, 2005, n.p.), in addition to experimental and inquiry techniques, understanding of scale and resolution, and verification skills. Popular desktop-based GIS that students can access include Geodesy and ArcVoyager; many Web-based versions also exist. A GIS is not necessarily an easy tool to learn or use, but it can lead to real-world involvement and language, concept, and thinking skills development.

Web-Based Tools

Many technology-enhanced lessons and tools on the Web come premade. In other words, they were created for someone else’s students and context. Teachers must adapt these tools to fit their own teaching styles, student needs, goals, resources, and contextual variables. Teachers must learn to modify these resources to make them their own and help them to work effectively in their unique teaching situation. With this in mind, teachers can take advantage of the great ideas in the Web-based tools described below.

Example 1: WebQuest

A WebQuest is a Web-based inquiry activity that is highly structured in a preset format. Most teachers are aware of WebQuests—a Web search finds them mentioned in every state, subject area, and grade level, and they are popular topics at conferences and workshops. Created by Bernie Dodge and Tom March in 1995 (see http://webquest.org/), this activity has proliferated wildly.

Each WebQuest has six parts. The Quest starts with an introduction to excite student interest. The task description then explains to students the purpose of the Quest and what the outcome will be. Next, the process includes clear steps and the scaffolds, including resources, that students will need to accomplish the steps. The evaluation section provides rubrics and assessment guidelines, and the conclusion section provides closure. Finally, the teacher section includes hints and tips for other teachers to use the WebQuest.

Advantages to using WebQuests as inquiry and problem-solving tools include:

Students are focused on a specific topic and content and have a great deal of scaffolding.

Students focus on using information rather than looking for it, because resources are preselected.

Students use collaboration, critical thinking, and other important skills to complete their Quest.

Teachers across the United States have reported significant successes for students participating in Quests. However, because Quests can be created and posted by anyone, many found on the Web do not meet standards for inquiry and do not allow students autonomy to work in authentic settings and to solve problems. Teachers who want to use a WebQuest to meet specific goals should examine carefully both the content and the process of the Quest to make sure that they offer real problems as discussed in this chapter. A matrix of wonderful Quests that have been evaluated as outstanding by experts is available on the site.

Although very popular, WebQuests are also very structured. This is fine for students who have not moved to more open-ended problems, but to support a higher level of student thinking, independence, and concept learning, teachers can have students work in teams on Web Inquiry Projects ( http://webinquiry.org/ ).

Example 2: Virtual Field Trips

Virtual field trips are great for concept learning, especially for students who need extra support from photos, text, animation, video, and audio. Content for field trips includes virtual walks through museums, underwater explorations, house tours, and much more (see online field trips suggested by Steele-Carlin [2014] at http://www.educationworld.com/a_tech/tech/tech071.shtml ). However, the format of virtual field trips ranges from simple postcard-like displays to interactive video simulations, and teachers must review the sites before using them to make sure that they meet needs and goals.

With a virtual reality headset (now available for sale cheaply even at major department stores), teachers and students can go on Google Expeditions ( https://edu.google.com/expeditions/ ), 3D immersive field trips from Nearpod ( http://nearpod.com ), and even create their using resources from Larry Ferlazzo’s “Best Resources for Finding and Creating Virtual Field Trips” at http://larryferlazzo.edublogs.org/2009/08/11/the-best-resources-for-finding-and-creating-virtual-field-trips/.

Example 3: Raw Data Sites

Raw data sites abound on the Web, from the U.S. Census to the National Climatic Data Center, from databases full of language data to the Library of Congress. These sites can be used for content learning and other learning goals. Some amazing sites can be found where students can collect their own data. These include sites like John Walker’s (2003) Your Sky (www.fourmilab.to/yoursky) and Water on the Web (2005, waterontheweb.org). When working with raw data students have to draw their own conclusions based on evidence. This is another important problem-solving skill. Note that teachers must supervise and verify that data being entered for students across the world is accurate or

Example 4: Filamentality

Filamentality (https://keithstanger.com/filamentality.html) presents an open-ended problem with a lot of scaffolding. Students and/or teachers start with a goal and then create a Web site in one of five formats that range in level of inquiry and problem-solving from treasure hunts to WebQuests. The site provides lots of help and hints for those who need it, including “Mentality Tips” to help accomplish goals. It is free and easy to use, making it accessible to any teacher (or student) with an Internet connection.

Example 5: Problem Sites

Many education sites offer opportunities for students to solve problems. Some focus on language (e.g., why do we say “when pigs fly”?) or global history (e.g., what’s the real story behind Tut’s tomb?); see, for example, the resources and questions in The Ultimate STEM Guide for Students at http://www.mastersindatascience.org/blog/the-ultimate-stem-guide-for-kids-239-cool-sites-about-science-technology-engineering-and-math/. These problems range in level from very structured, academic problems to real-world unsolved mysteries.

The NASA SciFiles present problems in a format similar to WebQuests at https://knowitall.org/series/nasa-scifiles. In other parts of the Web site there are video cases, quizzes, and tools for problem-solving.

There is an amazing number of tools, both stand-alone and Web-based, to support problem-solving and inquiry, but no tool can provide all the features that meet the needs of all students. Most important in tool choice is that it meets the language, content, and skills goals of the project and students and that there is a caring and supportive teacher guiding the students in their choice and use of the tool.

Teacher Tools

There are many Web sites addressed specifically to teachers who are concerned that they are not familiar enough with PBL or that they do not have the tools to implement this instructional strategy. For example, from Now On at http://www.fno.org/ toolbox.html provides specific suggestions for how to integrate technology and inquiry. Search “problem-solving” on the amazing Edutopia site ( https://www.edutopia.org/ ) for ideas, guidelines, examples, and more.

LEARNING ACTIVITIES: PROBLEM-SOLVING AND INQUIRY

In addition to using the tools described in the previous section to teach problem-solving and inquiry, teachers can develop their own problems according to the guidelines throughout this chapter. Gordon’s (1998) scheme of problem-solving levels (described previously)—academic, scenario, and real life—is a simple and useful one. Teachers can refer to it to make sure that they are providing appropriate structure and guidance and helping students become independent thinkers and learners. This section uses Gordon’s levels to demonstrate the variety of problem-solving and inquiry activities in which students can participate. Each example is presented with the question/problem to be answered or solved, a suggestion of a process that students might follow, and some of the possible electronic tools that might help students to solve the problem.

Academic problems

Example 1: What Will Harry Do? (Literature)

Problem: At the end of the chapter, Harry Potter is faced with a decision to make. What will he do?

Process: Discuss the choices and consequences. Choose the most likely, based on past experience and an understanding of the story line. Make a short video to present the solution. Test it against Harry’s decision and evaluate both the proposed solution and the real one.

Tools: Video camera and video editing software.

Example 2: Treasure Hunt (History)

Problem: Students need resources to learn about the Civil War.

Process: Teacher provides a set of 10 questions to find specific resources online.

Tools: Web browser.

Example 3: Problem of the Week (Math)

Problem: Students should solve the math problem of the week.

Process: Students simplify the problem, write out their solution, post it to the site for feedback, then revise as necessary.

Tools: Current problems from the Math Forum@Drexel, http://mathforum.org/pow/

Example 1: World’s Best Problem Solver

Problem: You are a member of a committee that is going to give a prestigious international award for the world’s best problem-solver. You must nominate someone and defend your position to the committee, as the other committee members must do.

Process: Consult and list possible nominees. Use the process of elimination to determine possible nominees. Research the nominees using several different resources. Weigh the evidence and make a choice. Prepare a statement and support.

Tools: Biography.com has over 25,000 biographies, and Infoplease (infoplease.com) and the Biographical Dictionary (http://www.s9.com/) provide biographies divided into categories for easy searching.

Example 2: Curator

Problem: Students are a committee of curators deciding what to hang in a new community art center. They have access to any painting in the world but can only hang 15 pieces in their preset space. Their goals are to enrich art appreciation in the community, make a name for their museum, and make money.

Process: Students frame the problem, research and review art from around the world, consider characteristics of the community and other relevant factors, choose their pieces, and lay them out for presentation to the community.

Tools: Art museum Web sites, books, and field trips for research and painting clips; computer-aided design, graphics, or word processing software to lay out the gallery for viewing.

Example 3: A New National Anthem

Problem: Congress has decided that the national anthem is too difficult to remember and sing and wants to adopt a new, easier song before the next Congress convenes. They want input from musicians across the United States. Students play the roles of musicians of all types.

Process: Students define the problem (e.g., is it that “The Star-Spangled Banner” is too difficult or that Congress needs to be convinced that it is not?). They either research and choose new songs or research and defend the current national anthem. They prepare presentations for members of Congress.

Tools: Music sites and software, information sites on the national anthem.

Real-life problems

Example 1: Racism in School

Problem: There have been several incidents in our school recently that seem to have been racially motivated. The principal is asking students to consider how to make our school a safe learning environment for all students.

Process: Determine what is being asked—the principal wants help. Explore the incidents and related issues. Weigh the pros and cons of different solutions. Prepare solutions to present to the principal.

Tools: Web sites and other resources about racism and solutions, graphic organizers to organize the information, word processor or presentation software for results. Find excellent free tools for teachers and students at the Southern Poverty Law Center’s Teaching Tolerance Web site at www.tolerance.org.

Example 2: Homelessness vs. Education

Problem: The state legislature is asking for public input on the next budget. Because of a projected deficit, political leaders are deciding which social programs, including education and funding for the homeless, should be cut and to what extent. They are interested in hearing about the effects of these programs on participants and on where cuts could most effectively be made.

Process: Decide what the question is (e.g., how to deal with the deficit? How to cut education or funding for the homeless? Which programs are more important? Something else?). Perform a cost-benefit analysis using state data. Collect other data by interviewing and researching. Propose and weigh different solution schemes and propose a suggestion. Use feedback to improve or revise.

Tools: Spreadsheet for calculations, word processor for written solution, various Web sites and databases for costs, electronic discussion list or email for interviews.

Example 3: Cleaning Up

Problem: Visitors and residents in our town have been complaining about the smell from the university’s experimental cattle farms drifting across the highway to restaurants and stores in the shopping center across the street. They claim that it makes both eating and shopping unpleasant and that something must be done.

Process: Conduct onsite interviews and investigation. Determine the source of the odor. Measure times and places where the odor is discernible. Test a variety of solutions. Choose the most effective solution and write a proposal supported by a poster for evidence.

Tools: Online and offline sources of information on cows, farming, odor; database to organize and record data; word processing and presentation software for describing the solution.

These activities can all be adapted and different tools and processes used. As stated previously, the focus must be both on the content to be learned and the skills to be practiced and acquired. More problem-solving activity suggestions and examples can be found at site at http://www.2learn.ca/.

ASSESSING LEARNER PROBLEM-SOLVING AND INQUIRY

Many of the assessments described in other chapters of this text, for example, rubrics, performance assessments, observation, and student self-reflection, can also be employed to assess problem-solving and inquiry. Most experts on problem-solving and inquiry agree that schools need to get away from testing that does not involve showing process or allowing students to problem-solve; rather, teachers should evaluate problem-solving tasks as if they were someone in the real-world context of the problem. For example, if students are studying an environmental issue, teachers can evaluate their work throughout the project from the standpoint of someone in the field, being careful that their own biases do not cloud their judgment on controversial issues. Rubrics, multiple-choice tests, and other assessment tools mentioned in other chapters of this text can account for the multiple outcomes that are possible in content, language, and skills learning. These resources can be used as models for assessing problem-solving skills in a variety of tasks. Find hundreds of problem-solving rubrics by searching the Web for “problem-solving rubrics” or check Pinterest for teacher-created rubrics.

In addition to the techniques mentioned above, many teachers suggest keeping a weekly problem-solving notebook (also known as a math journal or science journal), in which students record problem solutions, strategies they used, similarities with other problems, extensions of the problem, and an investigation of one or more of the extensions. Using this notebook to assess students’ location and progress in problem-solving could be very effective, and it could even be convenient if learners can keep them online as a blog or in a share cloud space.

FROM THE CLASSROOM

Research and Plagiarism

We’ve been working on summaries all year and the idea that copying word for word is plagiarism. When they come to me (sixth grade) they continue to struggle with putting things in their own words so [Microsoft Encarta] Researcher not only provides a visual (a reference in APA format) that this is someone else’s work, but allows me to see the information they used to create their report as Researcher is an electronic filing system. It’s as if students were printing out the information and keeping it in a file that they will use to create their report. But instead of having them print everything as they go to each individual site they can copy and paste until later. When they finish their research they come back to their file, decide what information they want to use, and can print it out all at once. This has made it easier for me because the students turn this in with their report. So, I would say it not only allows students to learn goals of summarizing, interpreting, or synthesizing, it helps me to address them in greater depth and it’s easier on me! (April, middle school teacher)

I evaluated a WebQuest for middle elementary (third–fourth grades), although it seems a little complicated for that age group. The quest divides students into groups and each person in the group is given a role to play (a botanist, museum curator, ethnobotanist, etc.). The task is for students to find out how plants were used for medicinal purposes in the Southwest many years ago. Students then present their findings, in a format that they can give to a national museum. Weird. It was a little complicated and not well done. I liked the topic and thought it was interesting, but a lot of work would need to be done to modify it so that all students could participate. (Jennie, first-grade teacher).

CHAPTER REVIEW

Define problem-solving and inquiry.

The element that distinguishes problem-solving or problem-based learning from other strategies is that the focal point is a problem that students must work toward solving. A proposed solution is typically the outcome of problem-solving. During the inquiry part of the process, students ask questions and then search for answers to those questions.

Understand the interaction between problem-solving and other instructional goals. Although inquiry is also an important instructional strategy and can stand alone, it is also a central component of problem-solving because students must ask questions and investigate the answers to solve the problem. In addition, students apply critical and creative thinking skills to prior knowledge during the problem-solving process, and they communicate, collaborate, and often produce some kind of concrete artifact.

Discuss guidelines and tools for encouraging effective student problem-solving.

It is often difficult for teachers to not do what students can do, but empowering students in this way can lead to a string of benefits. Other guidelines, such as avoiding plagiarism, integrating reading and writing, and making it okay for students to make mistakes, keep the problem-solving process on track. Tools to assist in this process range from word processing to specially designed inquiry tools.

Create and adapt effective technology-enhanced tasks to support problem-solving. Teachers can design their own tasks following guidelines from any number of sources, but they can also find ready-made problems in books, on the Web, and in some software pack-ages. Teachers who do design their own have plenty of resources available to help. A key to task development is connecting classroom learning to the world outside of the classroom.

Assess student technology-supported problem-solving.

In many ways the assessment of problem-solving and inquiry tasks is similar to the assessment of other goals in this text. Matching goals and objectives to assessment and ensuring that students receive formative feedback throughout the process will make success more likely.

Baker, T. (2005). The history and application of GIS in education. KANGIS: K12 GIS Community. Available from http://kangis.org/learning/ed_docs/gisNed1.cfm.

Belland, B., Walker, A., Kim, N., & Lefler, M. (2017). Synthesizing results from empirical research on computer-based scaffolding in STEM education: A meta-analysis. Review of Educational Research, 87(2), pp. 309-344.

Chauhan, S. (2017). A meta-analysis of the impact of technology on learning effectiveness of elementary students. Computers & Education, 105, pp. 14-30.

Dooly, M. (2005, March/April). The Internet and language teaching: A sure way to interculturality? ESL Magazine, 44, 8–10.

Gordon, R. (1998, January).Balancing real-world problems with real-world results. Phi Delta Kappan, 79(5), 390–393. [electronic version]

IMSA (2005). How does PBL compare with other instructional approaches? Available: http://www2 .imsa.edu/programs/pbln/tutorials/intro/intro7.php.

Molebash, P., & Dodge, B. (2003). Kickstarting inquiry with WebQuests and web inquiry projects. Social Education, 671(3), 158–162.

Verga, L., & Kotz, S. A. (2013). How relevant is social interaction in second language learning? Frontiers in Human Neuroscience, 7, 550. http://doi.org/10.3389/fnhum.2013.00550

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Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

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College Minor: Everything You Need to Know

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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Reimagining Assessment Assessing the Transfer of Critical Thinking and Problem Solving Skills

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

Educators are rethinking the purposes, forms, and nature of assessment. Beyond testing mastery of traditional content knowledge—an essential task, but not nearly sufficient—educators are designing assessment for learning as an integral part of the learning process.

Two Rivers embarked on a multi-year project to define and assess critical thinking and problem solving in project-based learning expeditions.

Two Rivers Public Charter School in Washington, D.C., is a network of EL Education schools serving over 700 students in preschool through 8th grade. Throughout our twelve-year history, we have continued to champion the importance of embracing a broader definition of student success than what has been handed to us by state and national policy. While we believe that it is essential for all students to be proficient in math, literacy, and the sciences, we believe that that is not enough. Students also need a rich set of social and cognitive skills that span beyond any given discipline.

Furthermore, we believe that we can best teach students these skills through hands-on interdisciplinary project-based learning. As EL Education schools, our projects are defined as expeditions lasting 10 to 12 weeks in which students tackle messy, real world problems that don’t have easy paths to solutions nor do they have one clear right answer. Through intentional design of these projects, teachers address the core content and basic skills defined by literacy and content standards; the social skills of collaboration and communication; the intrapersonal skills defined by character; and the broadly applicable cognitive skills of critical thinking and problem solving.

In the life of our schools, we have seen the powerful way that our students through project-based learning have embraced deeper learning outcomes, and exhibited the habits of effective critical thinking, collaboration, and personal character. However, our evidence that this is working is only found in anecdotes and in the quality of student work. We have been unable to demonstrate neither the degree to which students are developing these skills within projects nor their ability to transfer the skills beyond the context of the current project.

Focusing just on the dimensions of critical thinking and problem solving, our teachers expressed frustration at not knowing in concrete terms what those cognitive skills looked like when students exhibited them. Building on our understanding of the essential role that assessment for learning plays in the learning process and the very practical consideration of how we help teachers and students define and work towards developing these skills, we have embarked on a multi-year project to define and assess critical thinking and problem solving.

Critical thinking and problem solving, as we define it, are the set of non-discipline specific cognitive skills people use to analyze vast amounts of information and creatively solve problems. We have broken those skills down into these five core components:

• Schema Development: The ability to learn vast amounts of information and organize it in ways that are useful for understanding
• Metacognition and Evaluation: The ability to think critically about what one is doing and evaluate many potential choices
• Effective Reasoning: The ability to create claims and support them with logical evidence
• Problem Solving: The ability to identify the key questions in a problem, develop possible paths to a solution, and follow through with a solution
• Creativity and Innovation: The ability to formulate new ideas that are useful within a particular context

Our project is working to create learning progressions in each of these core components with accompanying rubrics. The progressions of learning and rubrics will both help define for students and teachers the skills that all students should be developing as well as function as evaluative tools to provide a picture where each student sits in the development of these skills and what are the next steps for further learning.

However, we believe it is not enough for students to be able to develop these skills within the highly scaffolded context of our expeditions. If they have truly learned the skills, they should have the ability to transfer them. With this in mind, we are working to create short content-neutral performance tasks that will give teachers and students valuable information about each of the five core components listed above. Our hypothesis is that through having students tackle short novel tasks, we will be able to draw clear conclusions about their learning of critical thinking and problem solving skills.

Through the course of this work, we hope that our process will be useful to other educators interested in achieving deeper learning outcomes for their students. We realize that deeper learning will not become a reality in most schools until teachers and leaders have a clear vision for what it looks like on a day-to-day basis and how we can clearly demonstrate student growth in these essential skills. We hope that our work will help to inform how to make deeper learning a concrete reality. It is a work in progress, and we invite you to share your thoughts and follow our progress at our website  https://learn.tworiverspcs.org .

Learn more about Two Rivers' Assessment for Learning Project on their grantee page .

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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Development of physics worksheet with discovery learning-stem to improve student problem solving skills

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Ahmad Risal Patappa , Zuhdan Kun Prasetyo , Toni Rahmanto; Development of physics worksheet with discovery learning-stem to improve student problem solving skills. AIP Conf. Proc. 29 April 2024; 2622 (1): 020010. https://doi.org/10.1063/5.0133572

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This paper aims to develop a student worksheet with a discovery learning-STEM model on dynamic electric material to build on students’ problem-solving skills in YAPPI Wonosari Vocational High school. The method used is R&D with a 4-D model that includes defining, designing, developing, and disseminating. The instruments used include validation sheets and tests—data in a physics worksheet to improve students’ problem-solving skills. This study’s data collection methods contain expert validation, observation, pre-test, and post-test—the data analysis using the sign test. The results showed that 1) the development of student worksheets with discovery learning-STEM on dynamic electric material was feasible in terms of the validation results. This can be seen from the results of validation that show the feasibility of physics worksheets for improving problem-solving skills is in the excellent category, and 2) the effectiveness of using physics worksheet with discovery learning-STEM based on data obtained from the pre-test and post-test results can improve problem-solving skills as a problem in the implementation class. Thus, student worksheet developed with discovery learning STEM is compatible with improving problem-solving skills.

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6 crucial soft skills every student needs to master in the 21st century

T hriving in this ever-changing world not only requires a breadth of skills rooted in academic competencies for children but also abilities like teamwork, critical thinking, communication, persistence, and creativity amongst others. These skills are in fact interconnected.

We live in an era when students require these diverse sets of skills to survive and be successful. It is no longer enough to rely on conventional skill sets like the power of memory and recall, rote, and repetition.

Schools are aware of the evolution of society and the economy and hence are equipping teachers in terms of upskilling and adapting curriculum to ensure conceptual understanding, development of competencies, and growth in character, to ensure that students are nurtured, challenged, and empowered to achieve their academic and personal goals.

What skills then would be useful to students who have to shape their lives in tune with the rapidly changing world?

Here are six crucial soft skills every student needs to master in the 21 st century as listed by Shweta Sastri, Managing Director, Canadian International School, Bangalore:

1. ADAPTABILITY AND CREATIVITY

In the digital age, things are changing very rapidly. By the time students learn one set of skills, a newer version is already emerging.

Students will need to adapt to changing conditions and learn things quickly and efficiently and mentors will have to ensure that students are aware of the best methods to learn new things. Learning how to learn is an important skill that cannot be overemphasised!

2. COLLABORATION SKILLS ARE VITAL

It's quite possible that traditional classrooms may encourage competition and independence compared to collaboration and teamwork. Schools have to keep pace with changing scenarios and bring in a culture of collaboration which are crucial to achieving collective goals.

Every professional today works collaboratively with others in some capacity.  From engineers to artists, learning how to work in a group setting or leading a team that needs motivation requires practice.  What better way to foster these lifelong skills than in a classroom?

3. COMMUNICATION SKILLS

In the new digital age, there is great emphasis on the ability to communicate; hence, students have to be familiar with emerging technologies used in communication. In the current era, technology is omnipresent and schools need to adapt to new communication changes.

In addition to conceptual understanding, students should have the opportunity to grow in character to become well-rounded global citizens who have the confidence to impact a remarkable and sustainable future.

4. CRITICAL THINKING AND PROBLEM-SOLVING

Creating an environment that focuses on conceptual understanding and application of that knowledge to real-world skills leads to lifelong learning and retention of knowledge. 

Building an environment that fosters critical thinking, risk-taking, creativity, and the courage to make mistakes and move beyond them should be a priority.  

Focusing on learning to understand rather than learning to test should be a high priority for educators.

The ability to think critically is not easy and needs instruction and support. However once this skill is mastered, it will help develop analytical capabilities that will help students be competitive in an ever-changing global market.

5. CULTURAL UNDERSTANDING

Growing and learning in a multicultural environment gives children a greater understanding of others' beliefs, attitudes, and behaviours. As globalisation continues to bring cultures together, it is imperative to equip students with the continued experience to be citizens of a global future.

These experiences come from an education model that includes diverse narratives, qualities, and viewpoints, which facilitate an understanding of social pluralism. Multiculturalism promotes principles of inclusion, democracy, and a sense of togetherness, among many other positive traits.

6. UPSKILLING AND ALWAYS BEING AT THE CUTTING EDGE IN TECH 

Technology has shaped human history over the years and will undoubtedly continue to do so. Today, the digital revolution is spreading across the globe, creating connections never before thought of and students will have to have a breadth of broad technological skills.

Whether it is called the Second Machine Age, the Digital Revolution, or the 4th Industrial Revolution, technologists, economists and academics are all concerned with recent rapid technological advances and their implications for the future.

The world is constantly changing and the pace at which the economy is progressing makes agility a great value and in the modern world, there is no one better placed than those who can multitask in a quick time.

Recognising the nature of these changes is vital in understanding the current context in which we live, and the changes to be expected in the future. This, in turn, helps us determine how we view education and the need for the breadth of skills approach.

It is now central that we explore how to align these aspirations in the context of the educational environment.

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Committee for real-life Problem-solving skills of Students

01 May 2024

Committee for real-life problem-solving skills of students 

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10 Signs of Mentally Strong Students

​Mentally strong students bounce back from setbacks and failures with a positive attitude. They view challenges as opportunities for growth rather than insurmountable obstacles.​

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Emotional Regulation

​They have a strong ability to manage their emotions effectively, which helps them stay focused and composed even in stressful situations.​

Self-Motivation​

​Mentally strong students are intrinsically motivated and set high standards for themselves. They don't rely solely on external rewards or validation to drive their actions.​

Adaptability​

​They are flexible and adaptable, able to adjust to changes in their environment or circumstances without losing sight of their goals.​

​Despite facing difficulties, mentally strong students maintain a positive outlook and believe in their ability to overcome challenges through effort and perseverance.​

Problem-Solving Skills​

​They are adept at analyzing problems, identifying potential solutions, and taking decisive action to resolve issues they encounter.​

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Healthy boundaries​.

​Mentally strong students know how to establish and maintain healthy boundaries in their relationships, prioritizing their own well-being while still being empathetic towards others.​

Self-Confidence​

​They have a strong sense of self-confidence and believe in their own abilities to succeed academically and in other areas of life.​

Effective Communication​

​Mentally strong students communicate assertively and respectfully, expressing their thoughts and feelings clearly while also being receptive to feedback from others.​

Self-Discipline​

​They exhibit self-discipline in managing their time and resources efficiently, prioritizing tasks, and staying focused on their long-term goals even when faced with distractions or temptations.​

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6 Tips for Teaching Math Problem-Solving Skills

Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

A growing concern with students is the ability to problem-solve, especially with complex, multistep problems. Data shows that students struggle more when solving word problems than they do with computation , and so problem-solving should be considered separately from computation. Why?

Consider this. When we’re on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don’t have to do the thinking. I can think about what I’m going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn’t be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution. 

1. Link problem-solving to reading

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing . Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, “Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?” Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that “how many more” means to subtract, we’re taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it. 

3. Revisit ‘representation’

The word “representation” can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what’s actually happening in the problem first.

Using an anchor chart like one of these ( lower grade , upper grade ) can help students to choose a representation that most closely matches what they’re visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: “Varush went on a trip with his family to his grandmother’s house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?”

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what’s happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn’t necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process. 

4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that’s required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks. 

5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, “Good readers and mathematicians reread.” 

6. Spiral concepts so students frequently use problem-solving skills

When students don’t have to switch gears in between concepts, they’re not truly using deep problem-solving skills. They already kind of know what operation it might be or that it’s something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process. 

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.