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How to Inspire Students Through Problem Solving

Date October 24, 2024

Est. Reading Time 3 mins

Learning isn’t linear. It’s a dynamic, ongoing and intuitive process for students to think outside the box, arrive at new conclusions and cultivate effective solutions for real-world challenges.

Educators know there isn’t just one path to inspiring problem solving in the classroom. Because children are inherently creative, their limitless imagination gives them a greater likelihood of producing innovative ideas free from restriction or self-doubt. Teachers can help students achieve creative problem-solving skills by pairing their natural curiosity with hands-on STEM experiences.

Take a look at these helpful tips to inspire your students through problem solving and encourage independent, critical thinking.

Tips for Inspiring Student Problem Solving

1. ask open-ended questions.

Children are masters of making candid observations. By asking open-ended questions, educators empower students to arrive at their own conclusions.

For example, if a student presents a problem they haven’t yet solved, a thoughtful response might sound like, “What’s working well here? What if there was a different way to look at this problem? How could you carry this idea throughout your project?” Or perhaps best of all – “What will happen if you follow your instincts?” These types of open-ended questions create space for student ideation and support autonomous learning, giving children ownership over their ideas.

2. Promote Authentic Problem Solving

Educator Rich Lehrer says that creating an authentic approach to problem solving involves making real-world connections. While hypotheticals are great to consider, students respond well to challenges they can identify in their daily lives.

Authentic problem solving adds meaningful context to everyday challenges, making STEM topics less abstract and more relatable. By putting meaningful problem solving at the heart of using technology for good, Lehrer inspires the next generation of inventors to make positive changes in the world.

3. Build Persistence

“Mistakes are proof that you are trying!” Does this phrase sound familiar? Problem solving is often a trial-and-error process. When students are given project-based learning opportunities, they lean into the power of persistence. There’s nothing quite like the moment when a student brings their ideas to life.

Positive reinforcement from enthusiastic educators and peers is a sure way to build resilient, confident and competent creators. Another great way to demonstrate the power of perseverance is to introduce innovative role models. For instance, persistent innovators like National Inventors Hall of Fame ® Inductees are ideal role models who will spark inspiration!

4. Incorporate Invention Education

Invention education is an inspired approach to learning that fosters creative problem solving and builds confidence in STEM subjects through the hands-on act of invention. Students test prototypes, revise their designs and troubleshoot any existing flaws.

For more than 30 years, the National Inventors Hall of Fame has been developing invention education programs that provide unique experiential learning opportunities. These programs help students develop the I Can Invent ® Mindset – the same powerful mindset National Inventors Hall of Fame Inductees have used to develop world-changing solutions. The Hall of Fame’s approach to invention education creates an environment that welcomes innovative thinkers and supports collaboration as students design new and unique solutions for modern challenges.

Learn More Ways to Inspire and Empower Students

Teachers are often children’s biggest advocates because they see and know their potential. By engaging children with authentic problem solving and instilling the confidence to find solutions, early STEM experiences lead to tangible life skills. The more educators across the country strive to foster classroom environments where every idea is valued and each student feels inspired to problem solve, the better the academic outcomes! To learn more, explore our website .

Related Articles

3 ways invention education boosts engagement, what is invention education an inspired approach to learning, why is chronic absenteeism on the rise, supporting family engagement with invention education.

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Extracurriculars

Why Teaching Problem-Solving Skills is Essential for Student Success

Teaching the art of problem-solving is crucial for preparing students to thrive in an increasingly complex and interconnected world. Beyond the ability to find solutions, problem-solving fosters critical thinking, creativity, and resilience: qualities essential for academic success and lifelong learning. 

This article explores the importance of problem-solving skills, critical strategies for nurturing them in students, and practical approaches educators and parents can employ. 

By equipping students with these skills, we empower them to tackle challenges confidently, innovate effectively, and contribute meaningfully to their communities and future careers .

Why Teaching Problem-Solving Skills is Important

Problem-solving is a crucial skill that empowers students to tackle challenges with confidence and creativity . In an educational context, problem-solving is not just about finding solutions; it involves critical thinking, analysis, and application of knowledge. Students who excel in problem-solving can understand complex problems, break them down into manageable parts, and develop effective strategies to solve them. This skill is applicable across all subjects, from math and science to language arts and social studies, fostering a more profound understanding and retention of material .

Beyond academics, problem-solving is a cornerstone of success in life. Successful people across various fields possess strong problem-solving abilities. They can navigate obstacles, innovate solutions, and adapt to changing circumstances. In engineering and business management careers, problem solvers are highly valued for their ability to find efficient and creative solutions to complex issues.

Educators prepare students for future challenges and opportunities by teaching problem-solving in schools. They learn to think critically , work collaboratively, and persist in facing difficulties, all essential lifelong learning and achievement skills. Thus, nurturing problem-solving skills in students enhances their academic performance and equips them for success in their future careers and personal lives.

Aspects of Problem Solving

Developing problem-solving skills is crucial for preparing students to navigate the complexities of the modern world. Critical thinking, project-based learning, and volunteering enhance academic learning and empower students to address real-world challenges effectively. By focusing on these aspects, students can develop the skills they need to innovate, collaborate, and positively impact their communities.

Critical Thinking

Critical thinking is a fundamental skill for problem-solving as it involves analysing and evaluating information to make reasoned judgments and decisions. It enables students to approach problems systematically, consider multiple perspectives, and identify underlying issues.

Critical thinking allows students to:

• Analyse information : Students can assess the relevance and reliability of information to determine its impact on problem-solving. For example, in a science project, critical thinking helps students evaluate experimental results to draw valid conclusions.
• Develop solutions : Students can choose the most effective solution by critically evaluating different approaches. In a group project, critical thinking enables students to compare and refine ideas to solve a problem creatively.

Project-Based Learning

Project-based learning (PBL) is an instructional approach where students learn by actively engaging in real-world and personally meaningful projects. It allows students to explore complex problems and develop essential skills such as collaboration and communication.

Here is how project-based learning helps students develop problem-solving skills.

• Apply knowledge : Students apply academic concepts to real-world problems by working on projects. For instance, in designing a community garden, students use math to plan the layout and science to understand plant growth.
• Develop skills : PBL fosters problem-solving by challenging students to address authentic problems. For example, in a history project, students might analyse primary sources to understand the causes of historical events and propose solutions to prevent similar conflicts.

Volunteering

Volunteering allows students to contribute to their communities while developing empathy, leadership , and problem-solving skills. It provides practical experiences that enhance learning and help students understand and address community needs.

Volunteering is important because it allows students to:

• Identify needs : Students can identify community needs and consider solutions by working in diverse settings. For example, volunteering at a food bank can inspire students to address food insecurity by organising donation drives.
• Collaborate : Volunteering encourages teamwork and collaboration to solve problems. Students learn to coordinate tasks and resources to achieve common goals when organising a charity event.

The Problem-Solving Process

Problem-solving involves a systematic approach to understanding, analysing, and solving problems. Here are the critical steps in the problem-solving process:

• Identify the problem : The first step is clearly defining and understanding the problem. This involves identifying the specific issue or challenge that needs to be addressed.
• Define goals : Once the problem is identified, it's essential to establish clear and measurable goals. This helps focus efforts and guide the problem-solving process.
• Explore possible solutions : The next step is brainstorming and exploring various solutions. This involves generating ideas and considering different approaches to solving the problem.
• Evaluate options : After generating potential solutions, evaluate each option based on its feasibility, effectiveness, and possible outcomes.
• Choose the best solution : Select the most appropriate solution that best meets the defined goals and addresses the root cause of the problem.
• Implement the solution : Once a solution is chosen, it must be implemented. This step involves planning the implementation process and taking necessary actions to execute the solution.
• Monitor progress : After implementing the solution, monitor its progress and evaluate its effectiveness. This step helps ensure that the problem is being resolved as expected.
• Reflect and adjust : Reflect on the problem-solving process, identify any lessons learned, and make adjustments if necessary. This continuous improvement cycle helps refine solutions and develop better problem-solving skills.

How to Become a General Problem Solver

Parents play a crucial role in nurturing their children's problem-solving skills. Here are some ways parents can help their children become effective problem solvers.

• Encourage critical thinking : Encourage children to ask questions, analyse information, and consider different perspectives. Engage them in discussions that challenge their thinking and promote reasoning.
• Support independence : Allow children to tackle challenges on their own. Offer guidance and encouragement without immediately providing solutions. This helps build confidence and resilience.
• Provide opportunities for problem-solving : Create opportunities for children to solve real-life problems, such as planning a family event, organising their room, or resolving conflicts with siblings or friends.
• Foster creativity : Encourage creative thinking and brainstorming. Provide materials and activities that stimulate imagination and innovation.
• Model problem-solving behaviours : Demonstrate problem-solving skills in your own life and involve children in decision-making processes. Show them how to approach challenges calmly and methodically.

How Online Schooling Encourages Problem-Solving

Online schooling encourages problem-solving skills by requiring students to navigate digital platforms, manage their time effectively , and troubleshoot technical issues independently. 

Students often engage in interactive assignments and projects that promote critical thinking and creativity. They learn to adapt to different learning environments and collaborate virtually, fostering innovative solutions. 

Online schooling also encourages self-directed learning , where students must identify and address their own learning gaps. This enhances problem-solving abilities and prepares them for the complexities of the digital age.

To find out more about online learning, click here . 

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Why Every Educator Needs to Teach Problem-Solving Skills

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

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

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

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

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

Problem-Solving Skills Help Students…

   develop resilience.

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

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

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

    Set and Achieve Goals

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

  Resolve Conflicts

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

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

    Achieve Success

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

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

Problem-Solving Skills Can Be Measured and Taught

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

What Are Performance-Based Assessments?

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

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

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

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

Preview a Performance-Based Assessment

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

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

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

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

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

Explore CAE’s Problem-Solving Assessments

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

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

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

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

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

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

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

Using Games and Design Challenges to Teach Students About Managing Conflict

By introducing students to activities that scaffold conflict, teachers can provide low-stakes lessons to prepare kids to navigate it in healthy ways.

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As second-grade teachers, we know that our students are exploring new relationships, changing social dynamics, and feeling the emotional weight that these interactions can have. Our students often encounter conflict as we ask them to take risks, stand up for what they believe in, and share their thoughts and opinions. With this in mind, we created and piloted a three-pronged hands-on approach to building both comfort and skills around managing conflict.

Our approach includes cooperative games and design challenges as well as good-to-know and problem jars. Each part is designed to allow our students to encounter consistent developmentally appropriate and varying types of conflict in order to build problem-solving skills. Throughout each activity, students are put in a variety of mixed groupings where they are confronted with increasingly complex challenges, last-minute changes, and peer leadership opportunities that shift the social dynamics. We are excited to share our approach and help other teachers implement these ideas.

The first few weeks of the year are all about community-building, developing routines, and getting to know our students better as people and learners. Cooperative games are a fantastic way to help students build relationships and begin to collaborate together as a group. As we thought through where we wanted to start, we knew that we wanted to focus on cooperative games that were easy to prepare, low cost, and easy to introduce and play quickly as either a whole or partial group. We wanted students to practice thinking flexibly, shifting roles, and finding success and failure collectively.

Some of our favorite games are the balloon challenge, the colored dots game, and the airplane game. While we introduced many of these games throughout the first semester, we revisited more complex versions, adjusted group sizes, and pushed our students to work through challenges with increasing independence as the year progressed.

Having had some experience with design challenges in the past, we knew that we could use them to push students in unique ways, and these activities tend to be excellent breeding grounds for conflict. We also love that they provide students an opportunity to work in small, fluid groupings and complete a challenge together using varying materials that are low cost and common.

Starting Point

To begin, students are introduced to the challenge and have a five-minute brainstorming period in which they create a plan as a group. After five minutes have lapsed, students then get their materials and begin creating for 10 to 20 minutes, depending on the challenge. There is never a winner who is celebrated or recognized; instead, we commend students for working together. Once the timer has ended, students reflect upon the process through both a group discussion and independently as part of an exit ticket.

Examples of design challenges that our students love are cup stacking, the Play-Doh–and–toothpick building challenge, and the egg-drop challenge . We found that both assigning leadership roles within their groups and increasing the difficulty level pushed students to overcome new challenges and discomfort. Feel free to be inspired by these activities, but change them as you see fit.

We know that effective assessment tools help drive instruction and build our understanding of our students’ feelings and needs. To this end, we created multiple types of both formal and informal assessments that can be completed quickly and easily to help maintain consistency and encourage our students to be reflective about themselves as problem solvers.

Our students fill out an exit ticket based on the Likert scale that allows us to track how their understanding of conflict has changed over time after engaging in both cooperative games and design challenges.

Checking In

Finally, we know that students love their teachers, seek their approval, and enjoy sharing what is going on in their own lives. The good-to-know jar and problem jar offer students a space where they can check in with their own emotional experiences, identities, and culture, and use their real-life problems to share what is on their mind and help them navigate tricky feelings that they may feel uncomfortable sharing verbally.

The two jars are accessible to students throughout the week. Students contribute to these jars anonymously, and each student is encouraged to submit either a good-to-know or a problem throughout the week. On Fridays, we read through the problem jar as a class and talk through possible solutions or just acknowledge that some problems can’t be solved right away but that by talking about them, we are communicating that we will work harder to figure out a plan together.

Giving students a space to see that we, as their teachers, take their thoughts and opinions seriously and then connect their problems with real, immediate action is important in encouraging our students to be problem solvers. We also ask our students to consider how they naturally approach and respond to conflict. Providing them with this opportunity for self-reflection allows them to identify their personal strengths and challenges. The better we know each other, the more comfortable we’ll be with sharing how we feel and engaging in productive conflict.

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

The positive impact of an innovative UC San Diego problem-solving educational curriculum continues to grow

• Daniel Kane - [email protected]

Published Date

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Problem solving is a critical skill for technical education and technical careers of all types. But what are best practices for teaching problem solving to high school and college students? 

The University of California San Diego Jacobs School of Engineering is on the forefront of efforts to improve how problem solving is taught. This UC San Diego approach puts hands-on problem-identification and problem-solving techniques front and center. Over 1,500 students across the San Diego region have already benefited over the last three years from this program. In the 2023-2024 academic year, approximately 1,000 upper-level high school students will be taking the problem solving course in four different school districts in the San Diego region. Based on the positive results with college students, as well as high school juniors and seniors in the San Diego region, the project is getting attention from educators across the state of California, and around the nation and the world.

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In Summer 2023, th e 27 community college students who took the unique problem-solving course developed at the UC San Diego Jacobs School of Engineering thrived, according to Alex Phan PhD, the Executive Director of Student Success at the UC San Diego Jacobs School of Engineering. Phan oversees the project. 

Over the course of three weeks, these students from Southwestern College and San Diego City College poured their enthusiasm into problem solving through hands-on team engineering challenges. The students brimmed with positive energy as they worked together. 

What was noticeably absent from this laboratory classroom: frustration.

“In school, we often tell students to brainstorm, but they don’t often know where to start. This curriculum gives students direct strategies for brainstorming, for identifying problems, for solving problems,” sai d Jennifer Ogo, a teacher from Kearny High School who taught the problem-solving course in summer 2023 at UC San Diego. Ogo was part of group of educators who took the course themselves last summer.

The curriculum has been created, refined and administered over the last three years through a collaboration between the UC San Diego Jacobs School of Engineering and the UC San Diego Division of Extended Studies. The project kicked off in 2020 with a generous gift from a local philanthropist.

Not getting stuck

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

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

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

What does it mean to explicitly teach problem solving? 

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

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

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

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

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

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

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

Portrait of the Problem-Solving Curriculum

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

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

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

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

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

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

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

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

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

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

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

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

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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
• Artificial Intelligence
• Advising and Mentoring
• Teaching and Your Career
• Teaching Remotely
• Tools and Platforms
• The Science of Learning
• Bok Publications
• Other Resources Around Campus