problem solving in school example

10 Problem-Solving Scenarios for High School Students

It is certainly common to come across difficult situations including forgetting an assignment at home or overusing your phone only to miss an important project deadline. We are always surrounded by little difficulties that might become bigger problems if not addressed appropriately.

Whether it is saving your friend from the addiction to social media platforms or communicating your personal boundaries to relatives, problem-solving skills are one of the important skills you need to acquire throughout the journey of life.

Do you think these skills are in-built with other high school students? Certainly not.

It takes innovative learning methodologies just like problem-solving scenarios that help you immerse in the subject matter with precision. With problem-solving scenarios, you come across a range of problems that help you build critical thinking skills, logical reasoning, and analytical techniques.

The article will take you through scenarios that are a combination of various problems that need to be addressed strategically and carefully. As you read ahead, make sure to brainstorm solutions and choose the best one that fits the scenario. 

Helpful scenarios to build a problem-solving attitude in high schoolers

Learning through scenarios helps students look at situations from a completely analytical perspective. Problem-solving scenarios offer a combination of various situations that test the thinking skills and growth mindset of high school students. The below-mentioned scenarios are perfect for implementing problem-solving skills simply by allowing open discussions and contributions by students.

1. Uninvited Guests

You have arranged a party at your home after successfully winning the competition at the Science Fair. You invite everyone involved in the project however, one of your friends brings his cousin’s brother along. However, you have limited soft drink cans considering the number of invited people. How would you manage this situation without making anyone feel left out?

2. Communication Issues

A new teacher has joined the high school to teach about environmental conservation. She often involves students in different agriculture activities and workshops. However, one of your friends, John, is not able to understand the subject matter. He is unable to communicate his doubts to the teachers. How would you motivate him to talk to the teacher without the fear of judgment?

3. Friendship or Personal Choice?

The history teacher announced an exciting assignment opportunity that helps you explore ancient civilizations. You and your friend are pretty interested in doing the project as a team. One of your other friends, Jason, wants to join the team with limited knowledge and interest in the topic. Would you respect the friendship or deny him so you can score better on the assignment?

4. Peer Pressure 

It is common for high schoolers to follow what their friends do. However, lately, your friends have discovered different ways of showing off their skills. While they do all the fun things, there are certain activities you are not interested in doing. It often puts you in trouble whether to go with friends or take a stand for what is right. Would you take the help of peer mentoring activities in school or try to initiate a direct conversation with them?

5. Team Building 

Mr. Jason, the science teacher, assigns different projects and forms teams with random classmates. There are 7 people in each team who need to work towards project completion. As the group starts working, you notice that some members do not contribute at all. How will you ensure that everyone participates and coordinates with the team members?

6. Conflict Resolution 

The drama club and the English club are famous clubs in the school. Both clubs organize various events for the students. This time, both clubs have a tiff because of the event venue. Both clubs need the same auditorium for the venue on the same date. How would you mediate to solve the issue and even make sure that club members are on good terms with each other? 

7. Stress Management 

Your school often conducts different activities or asks students stress survey questions to ensure their happiness and well-being. However, one of your friends always misses them. He gets frustrated and seems stressed throughout the day. What would you do to ensure that your friend gets his issue acknowledged by teachers?

8. Time Management 

Your friend is always enthusiastic about new competitions in high school. He is running here and there to enroll and get certificates. In this case, he often misses important lectures and activities in class. Moreover, his parents complain that he misses swimming class too. How would you explain to him the importance of prioritizing and setting goals to solve this issue?

9. Educational Resources 

You and your friends are avid readers and often take advice from books. While most must-read books for bibliophiles are read by you, it is important to now look for other books. However, you witness that the school library lacks other important books on philosophy and the non-fiction category. How would you escalate this issue to the higher authorities by addressing the needs of students?

10. Financial Planning

Finance is an important factor and that is why your parents help you plan your pocket money and budgeting. Off lately, they have stopped doing so considering that you can manage on your own. However, after a few months, you have started spending more on games and high-end school supplies. You realize that your spending habits are leading to loss of money and reduced savings. How shall you overcome this situation?

Wrapping Up 

Involving students in different learning practices and innovative ways inspires them to think out of the box and make use of imagination skills. With the usage of different problem-solving scenarios, high school students get an opportunity to delve into realistic examples and consequences of different incidents.

Such scenarios offer an excellent way to promote understanding, critical thinking skills and enhance creativity. Ensure to use different activities and games for creating a comprehensive learning environment.

Sananda Bhattacharya, Chief Editor of TheHighSchooler, is dedicated to enhancing operations and growth. With degrees in Literature and Asian Studies from Presidency University, Kolkata, she leverages her educational and innovative background to shape TheHighSchooler into a pivotal resource hub. Providing valuable insights, practical activities, and guidance on school life, graduation, scholarships, and more, Sananda’s leadership enriches the journey of high school students.

Explore a plethora of invaluable resources and insights tailored for high schoolers at TheHighSchooler, under the guidance of Sananda Bhattacharya’s expertise. You can follow her on Linkedin

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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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15 Problem solving activities for students

In this guide

• 1. The detective game
• 2. Help ‘em out
• 3. What if…
• 4. Move IT!
• 5. The build
• 6. Just survive
• 7. Good old scavenger hunt maybe with a twist
• 9. Tower of terror
• 10. Community problem solving
• 11. Community problem solving documentary
• 12. Digital storytelling
• 13. Minefield/Lead the blind
• 14. Design sprints
• 15. Debates

Problem solving entails identifying, analyzing, and addressing challenges or obstacles using critical thinking, creativity, analytical skills, and reasoning. The World Economic Forum consistently ranks critical thinking and problem solving as top skills for the future in their list of essential abilities. 

Why is problem solving an important skill for students?

In a 2020 report, the World Economic Forum emphasized the growing significance of critical thinking and problem-solving skills in the upcoming years ( Whiting, 2020 ). These skills are vital not only for academic success but also for navigating challenges beyond the classroom. Let’s explore four key benefits of problem-solving skills for students.

• Student centered learning: Problem solving encourages student engagement by encouraging hands-on exploration and discovery. Students fully engage with a topic, they are not expected to simply absorb and memorize information. It recognizes and honors students’ individual learning pace, as well as their unique strengths, interests, and motivations. 
• Enhanced critical thinking: By tackling problems from diverse perspectives and evaluating information from various sources and viewing the problem from various angles, students are able to develop improved critical thinking skills.  Problem solving also cultivates systems thinking, enabling students to grasp the interconnectedness of systems, complex issues, and devise holistic solutions. 
• Confidence building: Through regular practice, students gain confidence in their problem solving skills, equipping them to address challenges across a wide variety of subject areas and real-life scenarios. “The goal in teaching problem-solving is for it to become second nature, and for students to routinely express their curiosity, explore innovative solutions, and analyze the world around them to draw their own conclusions.” (Marshall, 2022)
• Teamwork and communication: Engaging in problem solving activities nurtures essential teamwork skills such as communication and collaboration. Students learn to actively listen, respect diverse perspectives, and resolve conflicts in a constructive manner. Moreover, they develop goal setting abilities, organization, and build a sense of personal accountability within a team environment. 

Problem solving activities for elementary

Problem solving activities can range from simple to complex and short to long.

1) The detective game

• Gather 5-10 clues about a person, place, historical event, pop culture phenomenon, animal, etc. these can be physical clues or images of clues. 
• Place the clues to a bag and have students draw one clue at a time. 
• Encourage students to work in small groups to solve the mystery. 
• Require a minimum number of clues to be drawn (2-3) before attempting their first guess. 

2) Help ‘em out

• Engage students in brainstorming sessions while reading about historical events or fictional characters.
• Encourage small group discussion and decision making. 
• Students can work at desks or on whiteboards. 
• Challenge the students to identify the problems faced and devise creative solutions to alter the outcomes. 

3) What if…

• Create a list of moral dilemmas for students to ponder, ChatGPT would be perfect for this.
• Cut them up and put them in a bag for students to pull out of or use an online randomizing tool like WheelPicker to make the selection. 
• Students then have to share how they would handle the situation using ethical reasoning and decision making skills.

Here are the prompts I used on ChatGPT:

I am looking for a list of 15 moral dilemmas for elementary students to try and solve.

And a follow-up prompt:

Could you give 10 more that are based around honesty, fairness, respect, and peer pressure?

And here are 10 dilemmas ChatGPT came up with in seconds: 

• Truth dilemma: Your friend breaks something and asks you not to tell anyone. Should you keep their secret or tell an adult what happened?
• Fairness dilemma: You’re playing a game and your friend keeps losing. Do you let them win to make them feel better or play your best?
• Respecting property dilemma: You find money on the ground. Do you keep it, try to find the owner, or turn it into a teacher?
• Honesty dilemma: You accidentally take something that belongs to someone else. Do you return it, keep it, or ignore what happened?
• Respect dilemma: Your friend likes a certain game, but you don’t. They invite you to play. Do you decline and risk hurting their feelings, or play to make them happy?
• Cheating dilemma: You notice someone cheating during a class assignment. Should you tell the teacher or keep quiet?
• Environment dilemma: You see someone littering in the park. Do you pick up the trash, ignore it, or say something to the person?
• Privacy dilemma: You find a diary belonging to your sibling or friend. Should you read it or respect their privacy?
• Homework dilemma: You finish your homework but notice that your friend forgot to complete theirs. They ask to copy your work. What do you do?
• Peer pressure dilemma: Your friends want to gossip about another classmate. Do you join in, stay silent, or change the subject?

4) Move IT!

In this activity students are required to move an object across the classroom while navigating various constraints. 

• Introduce limitations such as restrictions on carrying the object, it can’t touch the floor, limited steps, use of specific body parts, or communication limitations with team members. 
• Encourage collaborative problem solving and creative thinking to overcome the obstacles.

5) The build

Provide students with materials like straws, marshmallows, paper cups, etc. and challenge them to build. Challenges can be the tallest freestanding tower, a bridge that can hold a certain weight, or other structures following specific rules. Students must learn to think creatively, collaborate, and iterate. 

Problem solving activities for middle school

Middle school problem solving can also utilize those activities mentioned for elementary school with some slight tweaks. But, here are some more middle school style activities.

6) Just survive

Use survival scenarios to encourage small groups to employ critical thinking, collaboration, and creative problem solving skills. These scenarios immerse students in real-world situations and foster resilience and adaptability. 

Many scenarios can be found online. Here are a few:

• Survival Island (complete with Google Slides)
• Plane Crash (survival game with a Hatchet by Gary Paulsen feel)
• Moon Landing (space survival game)

7) Good old scavenger hunt maybe with a twist

Scavenger hunts require problem solving skills to solve clues, think critically, and collaborate to complete the hunt. A fun and innovative way to do this was created by a friend named Kathi Kersznowski, co-author of Sail the 7Cs with Microsoft Education, called FlipHunt: 

A Fliphunt is a video-based scavenger hunt that is completely organized and run in the AMAZING Flip (formerly Flipgrid) environment. It is a wonderfully fun way to get students up and moving while exploring new learning or documenting understanding using the most beloved edtech site for amplifying student voice and student engagement in ways never known before! https://kerszi.com

Escape rooms are an amazing way to promote problem solving and critical thinking with middle school students. Students are presented with a scenario or challenge within a controlled environment, such as a themed classroom or designated area, where they must work together to decipher puzzles, uncover clues, and solve challenges within a set time limit. Escape rooms provide immersive and engaging problem-solving experiences.

There are a number of places teachers can go to find escape rooms, some paid, some free or freemium, and some physical with locked boxes or digital using Google Sites or Google Forms.

• BreakoutEDU – Standards aligned Escape Room games.
• Digital Escape Rooms from Ditch That Textbook
• How to make your own digital escape room with Google Forms

9) Tower of terror

This is a “Red Solo Cup” cup stacking game. 

• Students are given 3 cups and 2 large index cards. 
• Cups are stacked with a card in between each cup. 
• Student teams have 3-10 minutes (be fluid with your time depending on the class) to pull the cards and get the cups to nest on top of each other, earning a point for each successful attempt. Check out this X (Twitter post) by Jonathan Alsheimer , Tower Of Terror . This quick, simple game encourages teamwork, communication, critical thinking, and collaboration in a fun fast paced way.

10) Community problem solving

Empower students to address real-world problems from the local community or your school community. Maybe it’s a dangerous intersection, food waste with school lunches, or single-use plastics in the cafeteria. Students can research, analyze data, and propose solutions, fostering civic engagement and social responsibility. This is an activity that can also be used for high school students. 

Problem solving activities for high school

High school problem-solving activities build on foundational skills while providing opportunities for deeper exploration and application. Here are some elevated ideas tailored to high school students:

11) Community problem solving documentary

Challenge students to create short documentaries using their phones as cameras about solving problems they see in the community, in school, or in the world. Students can edit directly on their phones, on sites like Canva , WeVideo , or Capcut . 

12) Digital storytelling

Encourage students to harness the power of Digital storytelling to promote problem solving. Whether through videos, graphics, podcasts, or interactive presentations, data visualization, or digital books ( BookCreator ), students can craft compelling narratives that inspire action and promote a problem-solving mindset.

Check out Michael Hernandez’s book Storytelling with Purpose Digital Projects to Ignite Student Curiosity and you can listen to Michael on the TeacherNerdz Podcast .

13) Minefield/Lead the blind

This is an outstanding activity created by Dr. Krista Welz & Melissa Welz which involves communication, collaboration, and planning. The “Minefield” activity is  where one student navigates through a “Minefield” guided only by verbal commands from their peers. This hands-on exercise promotes teamwork, planning, and effective communication skills. Here is a detailed Google Slides explanation by the creators.

14) Design sprints

Introduce students to the concept of design sprints, a structured process for solving complex problems through rapid prototyping and user feedback.  Small teams collaborate intensely over a short period, usually five days (can be shorter a class period or a few days), to ideate, prototype, and validate solutions. Here is a famous design sprint from IDEO shown on ABC’s Nightline, the shopping cart design sprint:

Here are a few ideas:

• Redesigning the school cafeteria menu: Students work collaboratively to identify issues with the current cafeteria menu, brainstorm innovative solutions, create prototypes of redesigned menus, and gather feedback through testing sessions to ultimately present improved menu designs to school administrators.
• Redesigning classroom layouts for enhanced learning: This sprint focuses on reimagining classroom setups to optimize student learning experiences. Students research, ideate, prototype, test, and present innovative classroom layouts designed to foster a more engaging and effective learning environment.
• Creating solutions for reducing school waste: Students address sustainability concerns by identifying sources of waste within the school, brainstorming eco-friendly solutions, prototyping waste reduction strategies, testing their effectiveness, and pitching refined solutions aimed at minimizing waste and promoting environmental stewardship.
• 11 Activities from IDEO’s d.school for educators: Link

15) Debates

Facilitate lively debates on contemporary issues to stimulate critical thinking and persuasive communication skills.  Topics could include:

• Establishing a universal basic income to address poverty.
• Social media regulation to address misinformation and hate speech on platforms. 
• Banning TikTok or any social media platform
• Animal testing for cosmetics and scientific purposes.
• Space exploration funding: Should governments invest more resources in space exploration and colonization efforts, or should these funds be allocated to other pressing issues on Earth? 

As we navigate an era of unprecedented change and uncertainty, the need for problem-solving skills has never been more pressing. Gone are the days of lifelong careers; instead, today’s students face a landscape where adaptability and innovation are key. By integrating problem-solving activities tailored to elementary, middle school, and high school students, educators play a pivotal role in equipping the next generation with the tools they need to thrive.

As educators, parents, and stakeholders, we must acknowledge the role of problem-solving skills in shaping resilient, creative, and adaptable individuals. Educators should prioritize the cultivation of these essential skills in our schools and communities, empowering students to confront challenges with confidence, innovation, and creativity. When we do,  we not only prepare them for the future but also foster a generation capable of shaping a brighter tomorrow.

*Many, if not all, of the activities above can be adapted up or down the grade levels. *

• Daneshgari, F. (2023, March 29). High School Problem-Solving: 6 Activities That Work . Safes Parental Control App. Retrieved April 7, 2024, from https://www.safes.so/blogs/problem-solving-activities-for-high-school-students/
• Educator Guides: Activities from d.school Books — Stanford d.school . (n.d.). Stanford d.school. Retrieved April 7, 2024, from https://dschool.stanford.edu/resources/educators-guides-books
• Engaging Problem Solving Activities for Middle School Students . (n.d.). Everyday Speech. Retrieved April 3, 2024, from https://everydayspeech.com/sel-implementation/engaging-problem-solving-activities-for-middle-school-students/
• 5 Problem-Solving Activities for the Classroom . (2013, February 14). Resilient Educator. Retrieved April 7, 2024, from https://resilienteducator.com/classroom-resources/5-problem-solving-activities-for-the-classroom/
• Foshay, W. R., & Kirkley, J. (1998). Principles for Teaching Problem Solving . PLATO Learning Inc. https://www.researchgate.net/publication/262798359_Principles_for_Teaching_Problem_Solving
• Khanna, B. (2023, September 29). World Economic Forum Warns of Skills Gap in the Future of Work . LinkedIn. Retrieved April 3, 2024, from https://www.linkedin.com/pulse/world-economic-forum-warns-skills-gap-future-work-bhupendra-khanna
• Marshall, M. (2022, October 5). Benefits of Problem-Solving in the K-12 Classroom – Institute of Competition Sciences . Institute of Competition Sciences. Retrieved April 3, 2024, from https://www.competitionsciences.org/2022/10/05/benefits-of-problem-solving-in-the-k-12-classroom/
• Understanding the Importance of Teaching Creative Problem-Solving in Elementary Schools . (n.d.). Everyday Speech. Retrieved April 3, 2024, from https://everydayspeech.com/sel-implementation/understanding-the-importance-of-teaching-creative-problem-solving-in-elementary-schools/
• Weil, Z. (2016). The World Becomes What We Teach: Educating a Generation of Solutionaries . Lantern Publishing & Media.
• Whiting, K. (2020, October 21). What are the top 10 job skills for the future? The World Economic Forum. Retrieved April 3, 2024, from https://www.weforum.org/agenda/2020/10/top-10-work-skills-of-tomorrow-how-long-it-takes-to-learn-them/

Ronald M. Nober

Technology/STEAM Teacher

Ron Nober is a technology/STEAM teacher and co-host of the TeacherNerdz Podcast. He has a focus on using the United Nations Sustainable Development Goals (SDGs) in the classroom as well as connecting technology to social good.

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20 Problem-Solving Activities for Middle School Students

• Middle School Education

Introduction:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Conclusion:

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

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Classroom problem-solving activities teach children how to engage problems rather than to become frustrated with them. Teachers have the opportunity to teach children the proper methods for dealing with stressful situations, complex problems, and fast decision-making. While a teacher is unlikely to actually put the child into a difficult or otherwise harmful situation, he or she can use activities to teach the child how to handle such situations later on in life.

Teach the problems

To solve any problem, students must go through a process to do so. The teacher can explore this process with students as a group. The first step is to fully understand the problem. To teach this, ask students to describe the problem in their own words. This ensures the student is able to comprehend and express the concern at hand. Then, they must describe and understand the barriers presented. At this point, it’s a good idea to provide ways for the student to find a solution. That’s where activities come into play.

The following are five activities elementary teachers can use to teach problem-solving to students. Teaching students to identify the possible solutions requires approaching the problem in various ways.

No. 1 – Create a visual image

One option is to teach children to create a visual image of the situation. Many times, this is an effective problem-solving skill. They are able to close their eyes and create a mind picture of the problem. For younger students, it may be helpful to draw out the problem they see on a piece of paper.

Ask the child to then discuss possible solutions to the problem. This could be done by visualizing what would happen if one action is taken or if another action is taken. By creating these mental images, the student is fully engaged and can map out any potential complications to their proposed solution.

No. 2 – Use manipulatives

Another activity that is ideal for children is to use manipulatives. In a situation where the problem is space-related, for example the children can move their desks around in various ways to create a pattern or to better visualize the problem. It’s also possible to use simple objects on a table, such as blocks, to create patterns or to set up a problem. This is an ideal way to teach problem-solving skills for math.

By doing this, it takes a problem, often a word problem that’s hard for some students to visualize, and places it in front of the student in a new way. The child is then able to organize the situation into something he or she understands.

No. 3 – Make a guess

Guessing is a very effective problem-solving skill. For those children who are unlikely to actually take action but are likely to sit and ponder until the right answer hits them, guessing is a critical step in problem-solving. This approach involves trial and error.

Rather than approaching guessing as a solution to problems (you do not want children to think they can always guess), teach that it is a way to gather more data. If, for example, they do not know enough about the situation to make a full decision, by guessing, they can gather more facts from the outcome and use that to find the right answer.

No. 4 – Patterns

No matter if the problem relates to social situations or if it is something that has to do with science, patterns are present. By teaching children to look for patterns, they can see what is happening more fully.

For example, define what a pattern is. Then, have the child look for any type of pattern in the context. If the children are solving a mystery, for example, they can look for patterns in time, place or people to better gather facts.

No. 5 – Making a list

Another effective tool is list making. Teach children how to make a list of all of the ideas they come up with right away. Brainstorming is a fun activity in any subject. Then, the child is able to work through the list to determine which options are problems or not.

Classroom problem-solving activities like these engage a group or a single student. They teach not what the answer is, but how the student can find that answer.

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By Jeff Heyck-Williams, the director of curriculum and instruction for Two Rivers Public Charter School

When I visited a 5th grade class recently, the students were tackling the following problem:

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

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

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

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

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

The Problem-Solving Routine

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

Problem Solving from Two Rivers Public Charter School on Vimeo .

Before Problem-Solving: The KWI

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

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

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

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

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

During Problem-Solving: The Metacognitive Moment

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

After Problem-Solving: Evaluating Solutions

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

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

The opinions expressed in Next Gen Learning in Action are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.

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Problem Solving Skills for Students: Top 8 Proven Strategies

Table of Contents

1. Follow the Problem Solving Process Step-by-Step

2. review previous challenges, 3. “3 before me” rule, 4. enhance problem solving elements, 5. apply proven methods from established theories, 6. create an open, non-critical setting, 7. be a good role model, 8. observe, evaluate, and share feedback, ishcmc – nurturing future problem solvers, faqs on problem solving skills for students.

This article explores eight proven strategies that enhance problem solving capabilities in students, gives problem solving skills examples for students , and provides a guide on how to improve problem solving skills in students .

Educators who use these strategies with their students can give them the knowledge and abilities to approach challenges bravely and creatively, establishing the foundation for lifelong learning and adaptability.

• Follow the Problem Solving Process Step-by-Step
• Review Previous Challenges
• “3 Before Me” Rule
• Enhance Problem Solving Elements
• Apply Proven Methods from Established Theories
• Create an Open, Non-Critical Setting
• Be a Good Role Model
• Observe, Evaluate, And Share Feedback

The problem solving process is a structured approach that systematically guides students to tackle challenges. It involves:

• Identifying the Problem: Clearly state the problem. What are you trying to solve? Be specific about the issue(s).
• Considering Different Perspectives: Practice active listening to understand various viewpoints.
• Brainstorming: Generate potential solutions without evaluation.
• Evaluating Options: Assess the pros and cons of each solution.
• Selecting the Best Solution: Choose the option with the highest potential for success and consider its consequences.
• Implementing the Decision: Develop a plan and execute it.
• Monitoring Progress: Track the implementation and adjust as necessary.

Encourage students to reflect on past experiences when they encountered similar problems. Students can draw from their previous solutions by asking themselves, “Have I ever seen a problem like this before?”. Self-reflection can promote self-reliance and build confidence in problem solving skills for students . When instructors have pupils journal their challenges and solutions, it can help speed up the process.

Additionally, discussing case studies or real-life examples in class allows students to apply their knowledge to new situations . Reviewing past challenges strengthens students’ problem solving abilities and helps them better understand how to approach various problem types.

Implementing the “3 Before Me” rule can foster a collaborative learning environment where students support each other in problem solving endeavors. Educators promote autonomy, resourcefulness, active peer learning, and communication by encouraging students to seek peer help with 3 classmates before approaching the teacher.

During class activities, teachers might model the application of this rule and explain its rationale.  Through the practice of “3 Before Me,” students can use their peers’ combined knowledge and experience, which improves their problem solving skills and builds a sense of support and community.

Provide kids with options in various circumstances to encourage them to make judgments . Let them weigh their advantages and disadvantages, stimulating critical thinking and decision-making skills.

Incorporate decision-making opportunities into everyday activities, such as selecting food or planning leisure activities. Students who participate in these exercises can improve their analytical skills and learn to predict the effects of their decisions.

Furthermore, educators can introduce structured decision-making frameworks, such as cost-benefit analysis or SWOT analysis, to provide students with a systematic approach to evaluating options. Only when educators empower students with these tools and methods can the students make informed decisions and efficiently overcome complicated challenges.

Integrating psychological theories into problem solving approaches can broaden students’ perspectives and enhance problem solving skills . For instance, the “psychological distancing” theory suggests detaching emotions from problem solving to facilitate objective analysis.

Educators can assist students in getting a better knowledge of underlying issues, seeking potential solutions, and eliminating the chances of biases or preferences by encouraging them to approach situations objectively.

Similarly, the “ heuristic framework ” can help students break down complex problems into manageable components, facilitating strategic planning and problem decomposition .

Educators can incorporate components of this framework, such as backward planning, into classroom activities to encourage students to approach problems systematically. By applying these theories in practical contexts, students can develop adaptable problem solving strategies across various domains and situations

Furthermore, educators can leverage established pedagogical frameworks, such as the International Baccalaureate (IB) programme of ISHCMC, to promote critical thinking and problem solving skills for students . ISHCMC’s IB curriculum emphasizes inquiry-based learning, encouraging students to explore complex issues, ask probing questions, and develop analytical reasoning skills.

ISHCMC educators promote active learning by engaging students in inquiry-based activities, helping them develop a thorough comprehension of essential topics. The IB’s holistic approach to education also prioritizes the entire student body’s academic, emotional, and social growth.

Creating a supportive environment for students to express ideas freely fosters problem solving skills . Educators achieve this through open communication , risk-taking encouragement , and valuing diverse perspectives . With constructive comments and positive reinforcement, educators assist students in developing resilience and self-assurance when confronting obstacles.

Additionally, incorporating collaborative learning activities, such as group discussions and peer feedback sessions, can enhance problem solving skills by encouraging students to engage with different viewpoints and approaches . Educators create an open, non-critical setting to empower students to explore innovative solutions and develop creative problem solving strategies.

Educators, as role models, can significantly shape students’ problem solving skills through their behaviors and attitudes . By demonstrating effective techniques and decision-making processes, teachers offer effective guidance to students. Involving students in discussions and activities allows them to practice critical thinking and problemsolving in real-world scenarios.

For instance, educators can create opportunities for students to observe problem solving in action, such as case studies or simulations. By modeling structured problem solving approaches and offering feedback and encouragement, educators inspire students to develop their problem solving abilities and become confident, independent learners.

Educators should observe students’ problem solving processes, offer timely feedback , and encourage continuous reflection and improvement to identify strategies, specify areas for growth, and provide support.

Constructive feedback that highlights students’ strengths and areas for improvement helps refine their problem solving skills . A culture of ongoing feedback and reflection enables students to take responsibility for their education and develop the resilience and adaptability to navigate challenging situations effectively.

Through observation, assessment, and feedback, educators help students become competent and self-assured problem solvers.

How to teach problem solving skills for students is paramount in preparing them for the challenges they will encounter academically and in their future careers. By implementing proven strategies such as following a structured problem solving process, reviewing previous challenges , and encouraging an open and collaborative learning environment , educators can empower students to become confident and adept problem solvers.

At ISHCMC, we strive to nurture future problem solvers through our rigorous academic standards and holistic approach to education .

As the first fully authorized IB World School in Ho Chi Minh City , we provide students opportunities to develop their problem solving skills through inquiry-based learning, collaborative projects, and real-world applications .

Apply to ISHCMC today to nurture your children for success in a rapidly changing world!

Besides how to assess problem solving skills in students , and examples of problem solving skills for students , we will delve into other common questions about students’ problem solving skills for academic and personal growth.

1. What are problem solving skills for students?

Problem solving skills for students involve more than just applying learned procedures. entail understanding the environment, identifying complex problems, reviewing information, developing and evaluating strategies, and implementing solutions to achieve desired outcomes. True problem solving involves applying a method to a specific problem under certain conditions that the solver hasn’t encountered before.

Teaching problem solving should involve modeling effective methods, contextualizing skills within specific subjects, aiding students in problem understanding, allocating sufficient time for practice, and prompting analytical thinking through questions and suggestions while linking errors to misconceptions for learning.

This approach promotes critical thinking and decision-making abilities crucial for addressing genuine challenges.

2. At what age do children start developing problem solving skills?

Problem solving skills begin to develop around the age of 2 to 3 . By age three, children start to apply problem solving skills in particular situations. However, very young children’s problem solving skills are constrained by three factors: a short attention span, challenges in understanding cause-and-effect relationships, and lack of experience in tackling problems independently.

Such foundational skills continue to develop and become more sophisticated throughout childhood and adolescence. Influences such as education, personal experiences, and overall cognitive development shape and enhance problem solving abilities.

By adolescence, individuals usually have a more developed capacity to handle problems at a higher level of complexity, think critically, and come up with innovative solutions.

3. What are the benefits of problem solving skills for students?

Problem solving skills offer numerous benefits for students:

• Improved Academic Performance: Enhance critical and analytical thinking, improving academic results across subjects.
• Increased Confidence: Encourage independence, fostering resilient learners unafraid of challenges, preparing them for future complexities.
• Real-World Preparedness: Equip students to tackle evolving challenges by fostering collaboration, respect for diverse perspectives, and innovative problem solving approaches.
• Distinguishing Between Issues: Help differentiate solvable problems from unsolvable ones, promoting effective decision-making.
• Enhanced Understanding: Encourage deeper comprehension of causality, fostering resilience and adaptability.
• Social and Situational Awareness: Promote better time management, patience, curiosity, resourcefulness, and determination.
• Employability: Develop essential skills for working in teams, adapting to new and unique challenges, and meeting employer demands.

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20 Problem-Solving Activities For Middle School: Discussions, Games, Strategies, And Resources

November 20, 2023 //  by  Lesa M.K. Bullins, EdS

Problem-solving skills are important to the building of critical thinking, which in turn strengthens student executive function. Good problem solvers can build stronger cognitive flexibility, a critical component of executive functioning.

The teenage years are a crucial time for neuroplasticity, so it is a prime time for learning and developing important cognitive skills along with critical information. Bring problem-solving to life in your middle school classroom with these 20 activities.

1. Feelings Expression Scenarios

A huge part of problem-solving is properly expressing your own feelings. Students often struggle to state how they feel without combative, aggressive, or accusatory language; therefore opportunities to practice with realistic situations is a key problem-solving component. You can create scenario task cards to support students in realistic applications for relatable situations, or use pre-made cards.

Learn More:  Pinterest

2. Empathy Empowered Discussions

In addition to being able to calmly and kindly express one's feelings, empathy is a key problem-solving component. Teens can often struggle to express empathy as they have difficulty recognizing and interpreting due to the teenage brain functioning.

Teenage brains are still developing, so different areas of the brain are controlling different functions than we see in adult brains; furthermore, since teens are still figuring out what they think and feel about a variety of things, it can be difficult for them to recognize and consider the feelings and thoughts of others. You can instigate empathy discussions through relatable content like this short video.

Learn More:  Austin Wideman

3. Model, Model, Model...and then Model Some More!

Students learn more from what they see you do than what they hear you say! This means you have to be an active and purposeful model of what you expect. So make sure you are aware of your actions and words in front of your students!

Learn More:  Education World

4. Get Out of the Way

We need to allow students the time and space to solve problems. We cannot intervene every time they struggle to find the answer right away. Constant intervention hinders critical thinking and decision-making skills.

Make sure to leave some room for students to figure out solutions. Keep safe proximity so students have the comfort to know you are there if they cannot find a solution, but resist the urge to jump in as soon as you see them struggling.

Learn More:  Brookings

5. Plan a Road Trip

Engage problem-solving skills within context while reinforcing math, research, geography, and communication skills, too! Students can plan a road trip from start to finish in small groups. As an added bonus, you can let students travel virtually to the places they planned for their trip using Google Earth.

If time allows, they can even take screenshots and stage selfies for a presentation to share their trip with the class! This is a really great cross-curricular activity for the digital classroom, too!

6. Escape the Room

Escape rooms were made for problem-solving, so what better way to build these skills for students in an exciting way! Create different challenge activities surrounding a variety of subjects and skills to reinforce while lettings students put problem-solving to use finding practical solutions to escape the room!

Divide kids into teams and get on this engaging problem-solving activity!

7. Teach Explicit Strategies for Reflection

Students can build analytical skills by reflecting on their problem-solving process. Teach explicit skills to help students recognize and reflect on how they solve problems to reinforce future use and strengthen overall critical thinking abilities. Check out how Ellie from Cognitive Cardio made it work even in the time constraints of middle school schedules!

Learn More:  Cognitive Cardio With MSMM

8. Daily Practice

Give students short, interesting, and challenging problems to solve during the morning and afternoon transition times. Daily practice solving challenges is important for cognitive development and reinforces academic skills! You can find tons of daily challenges online or create your own.

9. Build Something

Let students work together in teams to build something from simple building materials. Increase the challenge by limiting resources or requiring students to pick their own resources for building blocks from a variety of random items. You can check out the marshmallow toothpick tower-building activity!

Learn more: Wow Sci

10. Blind Drawing Partners

Students can work in partner pairs or small groups to develop a vast array of abilities through this problem-solving activity. Blind team-building activities are excellent, low-prep ways to engage students' critical thinking and communication!

There are different ways you can implement this, but check out this video for an example of one application of the blind drawing game.

Learn more: Philip Barry

11. Laser Maze

Create a laser maze for students to get active in problem-solving. Create and implement different time durations to increase the challenge. Do not have lasers? No budget for lasers? Don't worry, red painter's tape will do the job!

Learn More:  That Phillips Family

12. Shared Story Puzzles

Creating story puzzles that force students to work in groups together to put together, add on, and create a cohesive story that is meaningful is another challenging task to engage in collaborative problem-solving.

Learn More:  Secondary English Coffee Shop

13. Yarn Webs

This social-skill-building collaborative problem-solving activity is fun for any age. Organize students into teams then let them choose a color of yarn, build a team web, and see who can navigate. There are so many ways this activity can be adapted, but you can watch a video of one interpretation here .

Learn More:  KEYSAmeriCorps

14. Scavenger Hunt

Create a series of clues that students must solve to progress through the game. Working in groups can help build conflict resolution and social skills as well. Check out how to create scavenger hunts for the classroom in this video by Learning Life.

Learn more: Learning Life

15. Boom! Math!

An excellent way to build advanced problem-solving skills, as well as mathematical analysis, is to create math Boom Cards with word problems like these from Math in the Middle. Boom cards are a great activity for students to practice and build skills!

Learn more: Boom Learning

16. Wheel of Solutions

Give students practice in exercising a number of different kinds of problem-solving skills by spinning and communicating a solution using the skills on which they land. You can make one in the classroom with a posterboard or create a digital wheel. Such a fun interactive resource! Use this great pre-made digital activity from Resource Haven on Boom Learning or create your own!

Learn More:  Boom Learning

17. Collaborative Math

Another activity for team building that supports mathematical concept reinforcement is students working together to collaboratively solve math problems. Check out how Runde's Room made sure everyone is engaged in working on solving parts of the problem through the sticky-note collaborative math activity.

18. Get Mysterious

Math Mysteries are a fun activity that builds out-of-the-box thinking and creates an inquisitive environment. Problem-solving develops through the process of inquisition! You can create your own or use Lee and Miller's 40 Fabulous Math Mysteries Kid's Can't Resist Scholastic book found here.

19. Logic Puzzles and Games

In addition to logic-building games like Chess, you can provide logic puzzles for morning and afternoon transitions, during downtime, or for early finishers. Logic puzzles help students think critically. You can make your own or get some prefabricated resources like the ones found in this book by Chris King .

Learn More:  Brainzilla

20. Lead Number Talks

Number talks are important to building problem-solving. Number talks allow students to build on one another in a collaborative way, discuss how they have solved problems before, consider how those solutions may be applicable to new skills they are about to learn, and build depth in math concepts.

So instead of getting quiet, get them talking!

Learn More:  North Dakota Teaching Kayla Durkin

Problem Solving Activities: 7 Strategies

• Critical Thinking

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

Shametria Routt Banks

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2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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39 Best Problem-Solving Examples

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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Problem-solving is a process where you’re tasked with identifying an issue and coming up with the most practical and effective solution.

This indispensable skill is necessary in several aspects of life, from personal relationships to education to business decisions.

Problem-solving aptitude boosts rational thinking, creativity, and the ability to cooperate with others. It’s also considered essential in 21st Century workplaces.

If explaining your problem-solving skills in an interview, remember that the employer is trying to determine your ability to handle difficulties. Focus on explaining exactly how you solve problems, including by introducing your thoughts on some of the following frameworks and how you’ve applied them in the past.

Problem-Solving Examples

1. divergent thinking.

Divergent thinking refers to the process of coming up with multiple different answers to a single problem. It’s the opposite of convergent thinking, which would involve coming up with a singular answer .

The benefit of a divergent thinking approach is that it can help us achieve blue skies thinking – it lets us generate several possible solutions that we can then critique and analyze .

In the realm of problem-solving, divergent thinking acts as the initial spark. You’re working to create an array of potential solutions, even those that seem outwardly unrelated or unconventional, to get your brain turning and unlock out-of-the-box ideas.

This process paves the way for the decision-making stage, where the most promising ideas are selected and refined.

Go Deeper: Divervent Thinking Examples

2. Convergent Thinking

Next comes convergent thinking, the process of narrowing down multiple possibilities to arrive at a single solution.

This involves using your analytical skills to identify the best, most practical, or most economical solution from the pool of ideas that you generated in the divergent thinking stage.

In a way, convergent thinking shapes the “roadmap” to solve a problem after divergent thinking has supplied the “destinations.”

Have a think about which of these problem-solving skills you’re more adept at: divergent or convergent thinking?

Go Deeper: Convergent Thinking Examples

3. Brainstorming

Brainstorming is a group activity designed to generate a multitude of ideas regarding a specific problem. It’s divergent thinking as a group , which helps unlock even more possibilities.

A typical brainstorming session involves uninhibited and spontaneous ideation, encouraging participants to voice any possible solutions, no matter how unconventional they might appear.

It’s important in a brainstorming session to suspend judgment and be as inclusive as possible, allowing all participants to get involved.

By widening the scope of potential solutions, brainstorming allows better problem definition, more creative solutions, and helps to avoid thinking “traps” that might limit your perspective.

Go Deeper: Brainstorming Examples

4. Thinking Outside the Box

The concept of “thinking outside the box” encourages a shift in perspective, urging you to approach problems from an entirely new angle.

Rather than sticking to traditional methods and processes, it involves breaking away from conventional norms to cultivate unique solutions.

In problem-solving, this mindset can bypass established hurdles and bring you to fresh ideas that might otherwise remain undiscovered.

Think of it as going off the beaten track when regular routes present roadblocks to effective resolution.

5. Case Study Analysis

Analyzing case studies involves a detailed examination of real-life situations that bear relevance to the current problem at hand.

For example, if you’re facing a problem, you could go to another environment that has faced a similar problem and examine how they solved it. You’d then bring the insights from that case study back to your own problem.

This approach provides a practical backdrop against which theories and assumptions can be tested, offering valuable insights into how similar problems have been approached and resolved in the past.

See a Broader Range of Analysis Examples Here

6. Action Research

Action research involves a repetitive process of identifying a problem, formulating a plan to address it, implementing the plan, and then analyzing the results. It’s common in educational research contexts.

The objective is to promote continuous learning and improvement through reflection and action. You conduct research into your problem, attempt to apply a solution, then assess how well the solution worked. This becomes an iterative process of continual improvement over time.

For problem-solving, this method offers a way to test solutions in real-time and allows for changes and refinements along the way, based on feedback or observed outcomes. It’s a form of active problem-solving that integrates lessons learned into the next cycle of action.

Go Deeper: Action Research Examples

7. Information Gathering

Fundamental to solving any problem is the process of information gathering.

This involves collecting relevant data , facts, and details about the issue at hand, significantly aiding in the understanding and conceptualization of the problem.

In problem-solving, information gathering underpins every decision you make.

This process ensures your actions are based on concrete information and evidence, allowing for an informed approach to tackle the problem effectively.

8. Seeking Advice

Seeking advice implies turning to knowledgeable and experienced individuals or entities to gain insights on problem-solving.

It could include mentors, industry experts, peers, or even specialized literature.

The value in this process lies in leveraging different perspectives and proven strategies when dealing with a problem. Moreover, it aids you in avoiding pitfalls, saving time, and learning from others’ experiences.

9. Creative Thinking

Creative thinking refers to the ability to perceive a problem in a new way, identify unconventional patterns, or produce original solutions.

It encourages innovation and uniqueness, often leading to the most effective results.

When applied to problem-solving, creative thinking can help you break free from traditional constraints, ideal for potentially complex or unusual problems.

Go Deeper: Creative Thinking Examples

10. Conflict Resolution

Conflict resolution is a strategy developed to resolve disagreements and arguments, often involving communication, negotiation, and compromise.

When employed as a problem-solving technique, it can diffuse tension, clear bottlenecks, and create a collaborative environment.

Effective conflict resolution ensures that differing views or disagreements do not become roadblocks in the process of problem-solving.

Go Deeper: Conflict Resolution Examples

11. Addressing Bottlenecks

Bottlenecks refer to obstacles or hindrances that slow down or even halt a process.

In problem-solving, addressing bottlenecks involves identifying these impediments and finding ways to eliminate them.

This effort not only smooths the path to resolution but also enhances the overall efficiency of the problem-solving process.

For example, if your workflow is not working well, you’d go to the bottleneck – that one point that is most time consuming – and focus on that. Once you ‘break’ this bottleneck, the entire process will run more smoothly.

12. Market Research

Market research involves gathering and analyzing information about target markets, consumers, and competitors.

In sales and marketing, this is one of the most effective problem-solving methods. The research collected from your market (e.g. from consumer surveys) generates data that can help identify market trends, customer preferences, and competitor strategies.

In this sense, it allows a company to make informed decisions, solve existing problems, and even predict and prevent future ones.

13. Root Cause Analysis

Root cause analysis is a method used to identify the origin or the fundamental reason for a problem.

Once the root cause is determined, you can implement corrective actions to prevent the problem from recurring.

As a problem-solving procedure, root cause analysis helps you to tackle the problem at its source, rather than dealing with its surface symptoms.

Go Deeper: Root Cause Analysis Examples

14. Mind Mapping

Mind mapping is a visual tool used to structure information, helping you better analyze, comprehend and generate new ideas.

By laying out your thoughts visually, it can lead you to solutions that might not have been apparent with linear thinking.

In problem-solving, mind mapping helps in organizing ideas and identifying connections between them, providing a holistic view of the situation and potential solutions.

15. Trial and Error

The trial and error method involves attempting various solutions until you find one that resolves the problem.

It’s an empirical technique that relies on practical actions instead of theories or rules.

In the context of problem-solving, trial and error allows you the flexibility to test different strategies in real situations, gaining insights about what works and what doesn’t.

16. SWOT Analysis

SWOT is an acronym standing for Strengths, Weaknesses, Opportunities, and Threats.

It’s an analytic framework used to evaluate these aspects in relation to a particular objective or problem.

In problem-solving, SWOT Analysis helps you to identify favorable and unfavorable internal and external factors. It helps to craft strategies that make best use of your strengths and opportunities, whilst addressing weaknesses and threats.

Go Deeper: SWOT Analysis Examples

17. Scenario Planning

Scenario planning is a strategic planning method used to make flexible long-term plans.

It involves imagining, and then planning for, multiple likely future scenarios.

By forecasting various directions a problem could take, scenario planning helps manage uncertainty and is an effective tool for problem-solving in volatile conditions.

18. Six Thinking Hats

The Six Thinking Hats is a concept devised by Edward de Bono that proposes six different directions or modes of thinking, symbolized by six different hat colors.

Each hat signifies a different perspective, encouraging you to switch ‘thinking modes’ as you switch hats. This method can help remove bias and broaden perspectives when dealing with a problem.

19. Decision Matrix Analysis

Decision Matrix Analysis is a technique that allows you to weigh different factors when faced with several possible solutions.

After listing down the options and determining the factors of importance, each option is scored based on each factor.

Revealing a clear winner that both serves your objectives and reflects your values, Decision Matrix Analysis grounds your problem-solving process in objectivity and comprehensiveness.

20. Pareto Analysis

Also known as the 80/20 rule, Pareto Analysis is a decision-making technique.

It’s based on the principle that 80% of problems are typically caused by 20% of the causes, making it a handy tool for identifying the most significant issues in a situation.

Using this analysis, you’re likely to direct your problem-solving efforts more effectively, tackling the root causes producing most of the problem’s impact.

21. Critical Thinking

Critical thinking refers to the ability to analyze facts to form a judgment objectively.

It involves logical, disciplined thinking that is clear, rational, open-minded, and informed by evidence.

For problem-solving, critical thinking helps evaluate options and decide the most effective solution. It ensures your decisions are grounded in reason and facts, and not biased or irrational assumptions.

Go Deeper: Critical Thinking Examples

22. Hypothesis Testing

Hypothesis testing usually involves formulating a claim, testing it against actual data, and deciding whether to accept or reject the claim based on the results.

In problem-solving, hypotheses often represent potential solutions. Hypothesis testing provides verification, giving a statistical basis for decision-making and problem resolution.

Usually, this will require research methods and a scientific approach to see whether the hypothesis stands up or not.

Go Deeper: Types of Hypothesis Testing

23. Cost-Benefit Analysis

A cost-benefit analysis (CBA) is a systematic process of weighing the pros and cons of different solutions in terms of their potential costs and benefits.

It allows you to measure the positive effects against the negatives and informs your problem-solving strategy.

By using CBA, you can identify which solution offers the greatest benefit for the least cost, significantly improving efficacy and efficiency in your problem-solving process.

Go Deeper: Cost-Benefit Analysis Examples

24. Simulation and Modeling

Simulations and models allow you to create a simplified replica of real-world systems to test outcomes under controlled conditions.

In problem-solving, you can broadly understand potential repercussions of different solutions before implementation.

It offers a cost-effective way to predict the impacts of your decisions, minimizing potential risks associated with various solutions.

25. Delphi Method

The Delphi Method is a structured communication technique used to gather expert opinions.

The method involves a group of experts who respond to questionnaires about a problem. The responses are aggregated and shared with the group, and the process repeats until a consensus is reached.

This method of problem solving can provide a diverse range of insights and solutions, shaped by the wisdom of a collective expert group.

26. Cross-functional Team Collaboration

Cross-functional team collaboration involves individuals from different departments or areas of expertise coming together to solve a common problem or achieve a shared goal.

When you bring diverse skills, knowledge, and perspectives to a problem, it can lead to a more comprehensive and innovative solution.

In problem-solving, this promotes communal thinking and ensures that solutions are inclusive and holistic, with various aspects of the problem being addressed.

27. Benchmarking

Benchmarking involves comparing one’s business processes and performance metrics to the best practices from other companies or industries.

In problem-solving, it allows you to identify gaps in your own processes, determine how others have solved similar problems, and apply those solutions that have proven to be successful.

It also allows you to compare yourself to the best (the benchmark) and assess where you’re not as good.

28. Pros-Cons Lists

A pro-con analysis aids in problem-solving by weighing the advantages (pros) and disadvantages (cons) of various possible solutions.

This simple but powerful tool helps in making a balanced, informed decision.

When confronted with a problem, a pro-con analysis can guide you through the decision-making process, ensuring all possible outcomes and implications are scrutinized before arriving at the optimal solution. Thus, it helps to make the problem-solving process both methodical and comprehensive.

29. 5 Whys Analysis

The 5 Whys Analysis involves repeatedly asking the question ‘why’ (around five times) to peel away the layers of an issue and discover the root cause of a problem.

As a problem-solving technique, it enables you to delve into details that you might otherwise overlook and offers a simple, yet powerful, approach to uncover the origin of a problem.

For example, if your task is to find out why a product isn’t selling your first answer might be: “because customers don’t want it”, then you ask why again – “they don’t want it because it doesn’t solve their problem”, then why again – “because the product is missing a certain feature” … and so on, until you get to the root “why”.

30. Gap Analysis

Gap analysis entails comparing current performance with potential or desired performance.

You’re identifying the ‘gaps’, or the differences, between where you are and where you want to be.

In terms of problem-solving, a Gap Analysis can help identify key areas for improvement and design a roadmap of how to get from the current state to the desired one.

31. Design Thinking

Design thinking is a problem-solving approach that involves empathy, experimentation, and iteration.

The process focuses on understanding user needs, challenging assumptions , and redefining problems from a user-centric perspective.

In problem-solving, design thinking uncovers innovative solutions that may not have been initially apparent and ensures the solution is tailored to the needs of those affected by the issue.

32. Analogical Thinking

Analogical thinking involves the transfer of information from a particular subject (the analogue or source) to another particular subject (the target).

In problem-solving, you’re drawing parallels between similar situations and applying the problem-solving techniques used in one situation to the other.

Thus, it allows you to apply proven strategies to new, but related problems.

33. Lateral Thinking

Lateral thinking requires looking at a situation or problem from a unique, sometimes abstract, often non-sequential viewpoint.

Unlike traditional logical thinking methods, lateral thinking encourages you to employ creative and out-of-the-box techniques.

In solving problems, this type of thinking boosts ingenuity and drives innovation, often leading to novel and effective solutions.

Go Deeper: Lateral Thinking Examples

34. Flowcharting

Flowcharting is the process of visually mapping a process or procedure.

This form of diagram can show every step of a system, process, or workflow, enabling an easy tracking of the progress.

As a problem-solving tool, flowcharts help identify bottlenecks or inefficiencies in a process, guiding improved strategies and providing clarity on task ownership and process outcomes.

35. Multivoting

Multivoting, or N/3 voting, is a method where participants reduce a large list of ideas to a prioritized shortlist by casting multiple votes.

This voting system elevates the most preferred options for further consideration and decision-making.

As a problem-solving technique, multivoting allows a group to narrow options and focus on the most promising solutions, ensuring more effective and democratic decision-making.

36. Force Field Analysis

Force Field Analysis is a decision-making technique that identifies the forces for and against change when contemplating a decision.

The ‘forces’ represent the differing factors that can drive or hinder change.

In problem-solving, Force Field Analysis allows you to understand the entirety of the context, favoring a balanced view over a one-sided perspective. A comprehensive view of all the forces at play can lead to better-informed problem-solving decisions.

TRIZ, which stands for “The Theory of Inventive Problem Solving,” is a problem-solving, analysis, and forecasting methodology.

It focuses on finding contradictions inherent in a scenario. Then, you work toward eliminating the contraditions through finding innovative solutions.

So, when you’re tackling a problem, TRIZ provides a disciplined, systematic approach that aims for ideal solutions and not just acceptable ones. Using TRIZ, you can leverage patterns of problem-solving that have proven effective in different cases, pivoting them to solve the problem at hand.

38. A3 Problem Solving

A3 Problem Solving, derived from Lean Management, is a structured method that uses a single sheet of A3-sized paper to document knowledge from a problem-solving process.

Named after the international paper size standard of A3 (or 11-inch by 17-inch paper), it succinctly records all key details of the problem-solving process from problem description to the root cause and corrective actions.

Used in problem-solving, this provides a straightforward and logical structure for addressing the problem, facilitating communication between team members, ensuring all critical details are included, and providing a record of decisions made.

39. Scenario Analysis

Scenario Analysis is all about predicting different possible future events depending upon your decision.

To do this, you look at each course of action and try to identify the most likely outcomes or scenarios down the track if you take that course of action.

This technique helps forecast the impacts of various strategies, playing each out to their (logical or potential) end. It’s a good strategy for project managers who need to keep a firm eye on the horizon at all times.

When solving problems, Scenario Analysis assists in preparing for uncertainties, making sure your solution remains viable, regardless of changes in circumstances.

How to Answer “Demonstrate Problem-Solving Skills” in an Interview

When asked to demonstrate your problem-solving skills in an interview, the STAR method often proves useful. STAR stands for Situation, Task, Action, and Result.

Situation: Begin by describing a specific circumstance or challenge you encountered. Make sure to provide enough detail to allow the interviewer a clear understanding. You should select an event that adequately showcases your problem-solving abilities.

For instance, “In my previous role as a project manager, we faced a significant issue when our key supplier abruptly went out of business.”

Task: Explain what your responsibilities were in that situation. This serves to provide context, allowing the interviewer to understand your role and the expectations placed upon you.

For instance, “It was my task to ensure the project remained on track despite this setback. Alternative suppliers needed to be found without sacrificing quality or significantly increasing costs.”

Action: Describe the steps you took to manage the problem. Highlight your problem-solving process. Mention any creative approaches or techniques that you used.

For instance, “I conducted thorough research to identify potential new suppliers. After creating a shortlist, I initiated contact, negotiated terms, assessed samples for quality and made a selection. I also worked closely with the team to re-adjust the project timeline.”

Result: Share the outcomes of your actions. How did the situation end? Did your actions lead to success? It’s particularly effective if you can quantify these results.

For instance, “As a result of my active problem solving, we were able to secure a new supplier whose costs were actually 10% cheaper and whose quality was comparable. We adjusted the project plan and managed to complete the project just two weeks later than originally planned, despite the major vendor setback.”

Remember, when you’re explaining your problem-solving skills to an interviewer, what they’re really interested in is your approach to handling difficulties, your creativity and persistence in seeking a resolution, and your ability to carry your solution through to fruition. Tailoring your story to highlight these aspects will help exemplify your problem-solving prowess.

Go Deeper: STAR Interview Method Examples

Benefits of Problem-Solving

Problem-solving is beneficial for the following reasons (among others):

• It can help you to overcome challenges, roadblocks, and bottlenecks in your life.
• It can save a company money.
• It can help you to achieve clarity in your thinking.
• It can make procedures more efficient and save time.
• It can strengthen your decision-making capacities.
• It can lead to better risk management.

Whether for a job interview or school, problem-solving helps you to become a better thinking, solve your problems more effectively, and achieve your goals. Build up your problem-solving frameworks (I presented over 40 in this piece for you!) and work on applying them in real-life situations.

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 101 Hidden Talents Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 15 Green Flags in a Relationship
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 15 Signs you're Burnt Out, Not Lazy
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 15 Toxic Things Parents Say to their Children

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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.

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Creative problem solving tools and skills for students and teachers

Creative Problem Solving: What Is It?

Creative Problem Solving, or CPS ,  refers to the use of imagination and innovation to find solutions to problems when formulaic or conventional processes have failed.

Despite its rather dry definition – creative problem-solving in its application can be a lot of fun for learners and teachers alike.

Why Are Creative Problem-Solving Skills Important?

By definition, creative problem-solving challenges students to think beyond the conventional and to avoid well-trodden, sterile paths of thinking.

Not only does this motivate student learning, encourage engagement, and inspire deeper learning, but the practical applications of this higher-level thinking skill are virtually inexhaustible.

For example, given the rapidly changing world of work, it is hard to conceive of a skill that will be more valuable than the ability to generate innovative solutions to the unique problems that will arise and that are impossible to predict ahead of time.

Outside the world of work, in our busy daily lives, the endless problems arising from day-to-day living can also be overcome by a creative problem-solving approach.

When students have developed their creative problem-solving abilities effectively, they will have added a powerful tool to attack problems that they will encounter, whether in school, work, or in their personal lives.

Due to its at times nebulous nature, teaching creative problem-solving in the classroom poses its own challenges. However, developing a culture of approaching problem-solving in a creative manner is possible.

In this article, we will take a look at a variety of strategies, tools, and activities that can help students improve their creative problem-solving skills.

The Underlying Principles of CPS

Before we take a look at a process for implementing creative problem solving, it is helpful to examine a few of the underlying principles of CPS. These core principles should be encouraged in the classroom. They are:

●       Assume Nothing

Assumptions are the enemy of creativity and original thinking. If students assume they already have the answer, they will not be creative in their approach to solving a problem.

●       Problems Are Opportunities

Rather than seeing problems as difficulties to endure, a shift in perspective can instead view problems as challenges that offer new opportunities. Encourage your students to shift their perspectives to see opportunities where they once saw problems.

●       Suspend Judgment

Making immediate judgments closes down the creative response and the formation of new ideas. There is a time to make judgments, but making a judgment too early in the process can be very detrimental to finding a creative solution.

Cognitive Approaches: Convergent vs Divergent Thinking

“It is easier to tame a wild idea than it is to push a closer-in idea further out.”

— Alex Osborn

The terms divergent and convergent thinking, coined by psychologist J.P. Guilford in 1956, refer to two contrasting cognitive approaches to problem-solving.

Convergent Thinking can be thought of as linear and systematic in its approach. It attempts to find a solution to a problem by narrowing down multiple ideas into a single solution. If convergent thinking can be thought of as asking a single question, that question would be ‘ Why ?’

Divergent Thinking focuses more on the generation of multiple ideas and on the connections between those ideas. It sees problems as design opportunities and encourages the use of resources and materials in original ways. Divergent thinking encourages the taking of creative risks and is flexible rather than analytical in its approach. If it was a single question, it’d be ‘ Why not ?’

While it may appear that these two modes of thinking about a problem have an essentially competitive relationship, in CPS they can work together in a complementary manner.

When students have a problem to solve and they’re looking for innovative solutions, they can employ divergent thinking initially to generate multiple ideas, then convergent thinking to analyze and narrow down those ideas.

Students can repeat this process to continue to filter and refine their ideas and perspectives until they arrive at an innovative and satisfactory solution to the initial problem.

Let’s now take a closer look at the creative problem-solving process.

The Creative Problem-Solving Process

CPS helps students arrive at innovative and novel solutions to the problems that arise in life. Having a process to follow helps to keep students focused and to reach a point where action can be taken to implement creative ideas.

Originally developed by Alex Osborn and Sid Parnes, the CPS process has gone through a number of revisions over the last 50 or so years and, as a result, there are a number of variations of this model in existence.

The version described below is one of the more recent models and is well-suited to the classroom environment.

However, things can sometimes get a little complex for some of the younger students. So, in this case, it may be beneficial to teach the individual parts of the process in isolation first.

1. Clarify:

Before beginning to seek creative solutions to a problem, it is important to clarify the exact nature of that problem. To do this, students should do the following three things:

i. Identify the Problem

The first step in bringing creativity to problem-solving is to identify the problem, challenge, opportunity, or goal and clearly define it.

ii. Gather Data

Gather data and research information and background to ensure a clear understanding.

iii. Formulate Questions

Enhance awareness of the nature of the problem by creating questions that invite solutions.

Explore new ideas to answer the questions raised. It’s time to get creative here. The more ideas generated, the greater the chance of producing a novel and useful idea. At this stage in particular, students should be engaged in divergent thinking as described above.

The focus here shifts from ideas to solutions. Once multiple ideas have been generated, convergent thinking can be used to narrow these down to the most suitable solution. The best idea should be closely analyzed in all its aspects and further ideas generated to make subsequent improvements. This is the stage to refine the initial idea and make it into a really workable solution.

4. Implement

Create a plan to implement the chosen solution. Students need to identify the required resources for the successful implementation of the solution. They need to plan for the actions that need to be taken, when they need to be taken, and who needs to take them.

Summary of Creative Problem Solving Process

In each stage of the CPS Process, students should be encouraged to employ divergent and convergent thinking in turn. Divergent thinking should be used to generate multiple ideas with convergent thinking then used to narrow these ideas down to the most feasible options. We will discuss how students go about this, but let’s first take a quick look at the role of a group facilitator.

The Importance of Group Facilitator

CPS is best undertaken in groups and, for larger and more complex projects, it’s even more effective when a facilitator can be appointed for the group.

The facilitator performs a number of useful purposes and helps the group to:

• Stay focused on the task at hand
• Move through the various stages efficiently
• Select appropriate tools and strategies

 A good facilitator does not generate ideas themselves but instead keeps the group focused on each step of the process.

Facilitators should be objective and possess a good understanding of the process outlined above, as well as the other tools and strategies that we will look at below.

The Creative Problem-Solving Process: Tools and Strategies

There are several activities available to help students move through each stage. These will help students to stay on track, remove barriers and blocks, be creative, and reach a consensus as they progress through the CPS process.

  The following tools and strategies can help provide groups with some structure and can be applied at various stages of the problem-solving process. For convenience, they have been categorized according to whether they make demands on divergent or convergent thinking as discussed earlier.

Divergent Thinking Tools:

  ●       Brainstorming

Defined by Alex Osborn as “a group’s attempt to find a solution for a specific problem by amassing ideas ”, this is perhaps the best-known tool in the arsenal of the creative problem solver.

To promote a creative collaboration in a group setting, simply share the challenge with everyone and challenge them to come up with as many ideas as possible. Ideas should be concise and specific. For this reason, it may be worth setting a word limit for recording each idea e.g. express in headline form in no more than 5 words. Post-it notes are perfect for this.

You may also set a quota on the number of ideas to generate or introduce a time limit to further encourage focus. When completed, members of the group can share and compare all the ideas in search of the most suitable.

●       5 W’s and an H

The 5 W’s and an H are Who , What , Where , Why , and How . This strategy is useful to effectively gather data. Students brainstorm questions to ask that begin with each of the question words above in turn. They then seek to gather the necessary information to answer these questions through research and discussion.

●       Reverse Assumptions

This activity is a great way to explore new ideas. Have the students begin by generating a list of up to 10 basic assumptions about the idea or concept. For each of these, students then explore the reverse of the assumption listing new insights and perspectives in the process.

The students can then use these insights and perspectives to generate fresh ideas. For example, an assumption about the concept of a restaurant might be that the food is cooked for you. The reverse of that assumption could be a restaurant where you cook the food yourself. So, how about a restaurant where patrons select their own recipes and cook their own food aided by a trained chef?

Convergent Thinking Tools

●       How-How Diagram

This is the perfect activity to use when figuring out the steps required to implement a solution.

Students write the solution on the left-hand side of a page turned landscape. Working together, they identify the individual steps required to achieve this solution and write these to the right of the solution.

When they have written these steps, they go through each step one-by-one identifying in detail each stage of achieving that step. These are written branching to the right of each step.

Students repeat this process until they have exhausted the process and ended up with a comprehensive branch diagram detailing each step necessary for the implementation of the solution.

●       The Evaluation Matrix

Making an evaluation matrix creates a systematic way of analyzing and comparing multiple solutions. It allows for a group to evaluate options against various criteria to help build consensus.

An evaluation matrix begins with the listing of criteria to evaluate potential solutions against. These can then be turned into the form of a positive question that allows for a Yes or No answer. For example, if the budget is the criteria, the evaluation question could be ‘ Is it within budget? ’

Make a matrix grid with a separate column for each of the key criteria. Write the positive question form of these criteria as headings for these columns. The different options can then be detailed and listed down the left-most column.

Students then work through each of the criteria for each option and record whether it fulfills, or doesn’t fulfill, each criteria. For more complex solutions, students could record their responses to each of the criteria on a scale from 0 to 5.

For example:

Using the example matrix above, it becomes very clear that Option 1 is the superior solution given that it completely fulfills all the criteria, whereas Option 2 and Option 3 fulfill only 2 out of the 3 criteria each.

 ●       Pair & Share

This activity is suitable to help develop promising ideas. After making a list of possible solutions or questions to pursue, each individual student writes down their top 3 ideas.

Once each student has their list of their 3 best ideas, organize students into pairs. In their pairs, students discuss their combined 6 ideas to decide on the top 3 out of the 6. Once they have agreed on these, they write the new top 3 ideas on a piece of paper.

Now, direct the pairs of students to join up with another pair to make groups of 4. In these groups of 4, students discuss their collective 6 ideas to come up with a new list of the top 3 ideas.

Repeat this process until the whole class comes together as one big group to agree on the top 3 ideas overall.

Establish a Culture of Creative Problem Solving in the Classroom

Approaching problems creatively is about establishing a classroom culture that welcomes innovation and the trial and error that innovation demands. Too often our students are so focused on finding the ‘right‘ answer that they miss opportunities to explore new ideas.

It is up to us as teachers to help create a classroom culture that encourages experimentation and creative playfulness.

To do this we need to ensure our students understand the benefits of a creative approach to problem-solving.

We must ensure too that they are aware of the personal, social, and organizational benefits of CPS.

CPS should become an integral part of their approach to solving problems whether at school, work, or in their personal lives.

As teachers, it is up to us to help create a classroom culture that encourages experimentation and creative playfulness.

To do this, we must ensure our students understand the benefits of a creative approach to problem-solving.

CPS should become an integral part of their approach to solving problems, whether at school, work or in their personal lives.

Empowering Tomorrow’s Leaders: The Crucial Role of Computational and Systems Thinking in Education

the importance of systems thinking and computational thinking strategies for students cannot be overstated, as these skills are integral to navigating the complexities of our rapidly evolving digital landscape. Computational thinking, characterized by algorithmic problem-solving and logical reasoning, equips students with the ability to approach challenges systematically. In an era dominated by technology, these skills are not limited to coding but extend to critical thinking, enabling students to dissect problems, identify patterns, and devise efficient solutions. As our world becomes increasingly interconnected and data-driven, computational thinking provides a foundational framework for students to make sense of information, fostering a generation adept at leveraging technology for innovation.

Simultaneously, systems thinking is indispensable in comprehending the intricate web of relationships within various contexts. It encourages students to view issues holistically, understanding the interdependence of components and the ripple effects of decisions. In an era marked by global challenges, such as climate change and socio-economic disparities, systems thinking instills a proactive mindset. Students equipped with these skills are better prepared to analyze multifaceted problems, appreciate diverse perspectives, and collaborate on sustainable solutions.

Together, computational and systems thinking empower students to navigate an ever-changing world with confidence, adaptability, and a profound understanding of the interconnected systems that shape our future. These skills are not just academic; they are the building blocks of a resilient, innovative, and forward-thinking society.

be sure to check out our great video guides to teaching systems thinking and computational thinking below.

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

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

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

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

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

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

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

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

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

The Problem-Solving Routine

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

Problem Solving from Two Rivers Public Charter School

Before Problem-Solving: The KWI

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

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

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

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

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

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

During Problem-Solving: The Metacognitive Moment

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

After Problem-Solving: Evaluating Solutions

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

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

Jeff Heyck-Williams (He, His, Him)

Director of the two rivers learning institute.

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

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What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

• Identify the issue : Recognize the problem that needs to be solved.
• Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
• Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
• Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
• Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
• Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
• Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

• Brainstorming with others
• Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
• Analyzing cause and effect
• Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

• Creating a list of potential ideas to solve the problem
• Grouping and categorizing similar solutions
• Prioritizing potential solutions based on feasibility, cost, and resources required
• Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

• SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
• Decision-making matrices
• Pros and cons lists
• Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

• Communicating the solution to relevant parties
• Setting timelines and milestones
• Assigning tasks and responsibilities
• Monitoring the solution and making adjustments as necessary
• Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

• Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
• Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
• SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
• Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

• Generate a diverse range of solutions
• Encourage all team members to participate
• Foster creative thinking

When brainstorming, remember to:

• Reserve judgment until the session is over
• Encourage wild ideas
• Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

• 5 Whys : Ask “why” five times to get to the underlying cause.
• Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
• Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

• List your problem’s strengths, such as relevant resources or strong partnerships.
• Identify its weaknesses, such as knowledge gaps or limited resources.
• Explore opportunities, like trends or new technologies, that could help solve the problem.
• Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

• Write the problem in the center of a blank page.
• Draw branches from the central problem to related sub-problems or contributing factors.
• Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

• Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
• Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
• Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

• Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
• Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
• Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

• Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
• Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
• Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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Manipulatives in Maths - A Classroom Guide for Teachers

Mathematical manipulatives are touted as essential tools for learning, but let's be honest—we've all experienced that moment of dread when we hand them out. Suddenly, your carefully planned lesson turns into chaos: One pupil starts building a fortress with the base ten blocks while another is hiding all the shiny counters.

Yet, despite these challenges, manipulatives play an important role in maths education. They bridge the gap between abstract concepts and tangible understanding, helping pupils grasp basic number sense. In fact, the National Curriculum emphasises their importance across all key stages, recognising that hands-on learning is vital for developing maths fluency, reasoning, and problem-solving skills.

So, how can we take advantage of these tools without losing control of the classroom? Let's explore the world of maths manipulatives—what they are, why they matter, and how to use them effectively in your primary school lessons.

What are manipulatives?

It can sound complicated, but manipulatives are simply hands-on tools that make abstract mathematical concepts concrete and visual . They're the building blocks, quite literally in some cases, that help pupils wrap their heads around tricky number ideas through good old-fashioned play, exploration, and modelling.

These learning aids come in all shapes and sizes, from the humble counter to the more elaborate Cuisenaire rods . Their key purpose? To give pupils something tangible to manipulate as they grapple with mathematical concepts. Whether it's using multilink cubes to understand place value or fraction circles to visualise parts of a whole, manipulatives help bridge the gap between 'maths on paper' and 'maths in real life'.

Common manipulatives you'll find in primary classrooms include:

Multilink cubes

Cuisenaire rods, base ten blocks, bead strings.

• Balance scales

Clock faces

Digit cards, hundred squares.

These tools align perfectly with the National Curriculum's aims of developing mathematical fluency, reasoning, and problem-solving skills. By allowing pupils to physically interact with mathematical ideas, manipulatives help build a strong foundation for more complex concepts down the line. They're not just toys or distractions—they're powerful learning tools that can transform how your pupils understand and engage with maths.

Why are they important?

Over the past two decades, research has consistently shown the positive impact of using manipulatives in the classroom. A 2013 report published in the Journal of Educational Psychology identified "statistically significant results" when teachers used manipulatives compared with when they only used abstract maths symbols. This highlights the role that manipulatives play in supporting conceptual understanding and facilitating the progression from concrete to abstract thinking.

Alignment with CPA approach

The NCETM agrees that physical manipulatives should play a central role in maths teaching. "Manipulatives are not just for young pupils, and also not just for those who can't understand something. They can always be of help to build or deepen understanding of a mathematical concept."

This approach aligns perfectly with the concrete-pictorial-abstract (CPA) progression. Once children are confident using manipulatives or 'concrete' resources, they can then move onto pictorial representations or the 'seeing' stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they just handled and the abstract pictures , diagrams or models that represent the objects from the maths problem.

Enhance problem solving

But manipulatives do more than just support understanding—they're powerful tools for enhancing problem-solving skills. By allowing pupils to physically manipulate and visualise mathematical concepts, they can more easily devise strategies to tackle complex problems. This hands-on approach often leads to those 'aha!' moments we all love to see in our classrooms.

Support engagement

Moreover, manipulatives play an important role in fostering engagement and motivation. Let's face it—maths can sometimes seem dry and abstract to young learners. But introduce some colourful counters or interlocking cubes, and suddenly you've got a room full of eager mathematicians. This increased engagement is key to developing a positive attitude towards maths, which in turn supports long-term learning.

This deep understanding allows pupils to move beyond mere memorisation of facts and procedures, towards true mathematical fluency—where they can apply their knowledge flexibly and efficiently across a range of contexts.

In essence, manipulatives are not just helpful additions to our maths teaching toolkit—they're essential components in building a comprehensive, engaging, and effective mathematics education.

Types of manipulatives in primary mathematics

In this section, we'll break it common types of manipulatives into bite-sized pieces, just like we do for our pupils.

Physical manipulatives: the classics

These are the tangible, grab-them-with-your-hands resources that have been the backbone of maths classrooms for years. They're the ones that inevitably end up stuck between classroom seats and occasionally in someone's shoe.

Below is a list of common physical manipulatives in the classroom:

Ideal for teaching place value, addition, and subtraction with regrouping.

Fraction tiles

Excellent for comparing fractions and understanding equivalence.

Great for exploring 2D shapes, symmetry, and area.

Images: Wikipedia.org

Versatile tools for counting, measuring, and understanding volume.

Fantastic for developing number sense and exploring number relationships.

Essential for basic counting, sorting, and introducing simple addition and subtraction.

Useful for teaching multiplication, division, and fractions.

Image: Pinterest

Helpful for developing number sense and practicing skip counting.

Useful for probability exercises and generating random numbers for various activities.

Great for pattern recognition, matching, and basic addition facts.

Essential for teaching time-telling and understanding intervals.

Images: Pinterest & Pinterest

Useful for place value activities and forming large numbers.

Excellent for identifying number patterns and supporting multiplication and division.

Virtual manipulatives: a new kind of tool

Manipulatives have gone digital! These are interactive, online versions of our physical favourites. Think of them as the maths equivalent of e-books.

Some popular virtual manipulatives include:

Online number lines

These number lines are zoomable, clickable, and free of the uneven lines that are often result of our hand-drawn versions.

Digital base ten blocks

All the functionality without the risk of losing pieces under desks.

Interactive fraction tools

Slice and dice up pieces in any way imaginable.

Whether physical or virtual, the best manipulative is the one that helps your pupils understand the concept at hand. Whether that's a handful of multilink cubes or a fancy online simulator, if it's making those mathematical lightbulbs flicker on, you're on the right track!

Implementing manipulatives in the classroom - let them play!

Whether you have a bumper pack of manipulatives, a shared bank of resources or your very own DIY versions, it's important to teach children how to use them independently. Here are some best practices for integrating manipulatives effectively into your lessons:

• Introduce gradually : Bring in manipulatives one at a time. If you don't have enough for each child, set up a 'maths table' where pupils can take turns exploring. This works particularly well with younger years where 'choosing tables' are common.
• Allow for exploration : Give children a chance to play with and explore the manipulatives before using them for instruction. Through this exploration, they can start to imagine how the resource might be useful.
• How could you use this?
• How might this help you when adding or subtracting?
• Why do you think they're different sizes - what could that represent?
• Model usage : Once children are familiar with a resource, introduce a simple maths problem and ask them to use the manipulatives to solve it. Model the problem-solving process step-by-step, then guide children through it.
• Scaffold learning : Start with highly structured activities, then gradually reduce support as pupils gain confidence. For instance, begin with direct instruction on how to use base ten blocks for place value, then move to guided practice, and finally independent problem-solving.
• Year 1: Using counters or number lines to support addition and subtraction within 20.
• Year 2: Use fraction tiles to help pupils recognise, find, name and write fractions of a length, shape, set of objects or quantity.
• Year 3: Utilising place value charts (physical or digital) so pupils can recognise 3-digit numbers (100s, 10s and 1s).
• Integrate into lesson plans : Don't treat manipulatives as an add-on. Instead, weave them into your lessons as essential tools for understanding. Plan specific points in your lessons where manipulatives will be most beneficial.
• Support diverse learners : Manipulatives can be particularly helpful for English Language Learners (ELLs) and pupils with learning disabilities. They provide a universal language of mathematics that transcends verbal communication barriers.

Images: The Average Teacher

Manipulatives across Key Stages 1 and 2

Next, let's breakdown more examples of manipulatives in the classroom by Key Stage.

Key Stage 1 (Years 1-2): Laying the foundations

In these early years, it's all about getting hands-on with numbers and shapes.

• Number and Place Value : Introduce counters, number lines, and base ten blocks. Pupils can observe how 10 ones form a 'ten stick', helping them grasp place value concepts.
• Addition and Subtraction : Utilise multilink cubes for hands-on learning. Pupils can physically join or separate cubes to represent addition and subtraction operations.
• Fractions : Fraction tiles can be effective tools for teaching fractions. They provide a visual and tactile representation of concepts like 'half' and 'quarter'.
• Geometry : Employ geoboards for creating 2-D shapes. Pupils can then be asked to match these shapes on a 3-D surface to enhance spatial understanding.

Key Stage 2 (Years 3-6): Progressing with Purpose

As our mathematicians-in-training grow, so does the sophistication of our manipulatives. We're not ditching the basics, just building on them.

• Multiplication and Division : Array cards and Cuisenaire rods are useful for these operations. For multiplying by 6, pupils can line up 6 rods of 4 to visualise the concept.
• Fractions, Decimals, and Percentages : Fraction circles can be used alongside decimal place value charts. The 100 square is effective for teaching percentages.
• Geometry : The geoboard is a helpful tool for teaching perimeter, area, and symmetry concepts in a hands-on manner.
• Statistics : Data can be represented using multilink cube bar charts or human pictograms, making statistics more engaging for pupils.

CPA Journey: From Concrete to Pictorial to Abstract

Remember, our end goal is for pupils to solve problems without relying on physical props. Here's how we might progress:

• Concrete : Pupils physically manipulate objects to solve a problem. For example, using counters to work out 5 + 3.
• Pictorial : They draw a picture or diagram to represent the problem. Our 5 + 3 might become five circles and three circles.
• Abstract : Finally, they use mathematical symbols and numbers alone. "5 + 3 = 8."

The beauty of this approach? Pupils can always 'go back' a stage if they're struggling with a new concept. Stuck on an abstract problem? Draw a picture! Need more practise? Grab those counters!

Remember, every child's journey through these stages is unique. Some might race through, others might linger longer at certain points. The key is to ensure they have a solid understanding at each stage before moving on.

An example of moving from the concrete, to pictorial, to abstract stages.

Manipulative manners

Once you have introduced your resources, speak as a class and explain that they should come up with a set of rules for how they are treated and used. Giving children ownership over the manipulatives as well as the respect to make their own rules will make them feel accountable and lessen the likelihood of negative behaviours when using manipulatives. Write the rules up as a class and display them so they can be referred to.

Storing manipulatives

NRICH recommends children having access to manipulatives “Give open access to all the resources and allow the children free reign in choosing what to use to model any problem they may be tackling. I would make sure that children of all ages had this access from 3 to 11 years old and beyond.” While this is exactly what teachers would like to replicate in their classrooms, not all classes learn in the same way and this isn’t always achievable due to space, budgets and children’s prior experiences of manipulatives.

Once you have introduced a manipulative, decide as a class where you should store it . You know what works best for your class, so consider different options such as communal drawers, a maths table, individual packs or a collection of manipulatives for each table. Set clear rules around using and treating manipulatives to ensure they are not broken or lost. Additionally, you could create a monitor for each resource so the children can take ownership and make sure they stay tidy and accounted for.

Creating a classroom culture that uses manipulatives will aid children’s fluency and help develop their ability to solve problems, reason mathematically and share! If manipulatives are introduced in a considered and gradual way, with clear boundaries from an early age, children should see them as part of everyday learning and they will not be a novelty. They will be seen as tools instead of toys — and hopefully no more multilink towers!

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Maths — No Problem! Community Event Conference, 28 November at The Royal Society, London.

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26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

 A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter. 

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

• Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
• Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
• Tailor your interview answer with the specific skills and qualifications outlined in the job description.
• Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills? 

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

• Critical thinking
• Analytical skills
• Decision making
• Research skills
• Technical skills
• Communication skills
• Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow. 

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve. 

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams. 

Examples of Problem-Solving in the Workplace

• Correcting a mistake at work, whether it was made by you or someone else
• Overcoming a delay at work through problem solving and communication
• Resolving an issue with a difficult or upset customer
• Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
• Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
• Troubleshooting and resolving technical issues
• Handling and resolving a conflict with a coworker
• Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
• Taking initiative when another team member overlooked or missed something important
• Taking initiative to meet with your superior to discuss a problem before it became potentially worse
• Solving a safety issue at work or reporting the issue to those who could solve it
• Using problem solving abilities to reduce/eliminate a company expense
• Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
• Changing how a process, team, or task is organized to make it more efficient
• Using creative thinking to come up with a solution that the company hasn’t used before
• Performing research to collect data and information to find a new solution to a problem
• Boosting a company or team’s performance by improving some aspect of communication among employees
• Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

• Coordinating work between team members in a class project
• Reassigning a missing team member’s work to other group members in a class project
• Adjusting your workflow on a project to accommodate a tight deadline
• Speaking to your professor to get help when you were struggling or unsure about a project
• Asking classmates, peers, or professors for help in an area of struggle
• Talking to your academic advisor to brainstorm solutions to a problem you were facing
• Researching solutions to an academic problem online, via Google or other methods
• Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. 

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description. 

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities. 

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution. 

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”  

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce. 

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence 

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

 When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

• 3 Answers to “How Do You Handle Stress?”
• How to Answer “How Do You Handle Conflict?” (Interview Question)
• Sample Answers to “Tell Me About a Time You Failed”

About the Author

Biron Clark is a former executive recruiter who has worked individually with hundreds of job seekers, reviewed thousands of resumes and LinkedIn profiles, and recruited for top venture-backed startups and Fortune 500 companies. He has been advising job seekers since 2012 to think differently in their job search and land high-paying, competitive positions. Follow on Twitter and LinkedIn .

Read more articles by Biron Clark

About the Contributor

Kyle Elliott , career coach and mental health advocate, transforms his side hustle into a notable practice, aiding Silicon Valley professionals in maximizing potential. Follow Kyle on LinkedIn .

About the Editor

Hayley Jukes is the Editor-in-Chief at CareerSidekick with five years of experience creating engaging articles, books, and transcripts for diverse platforms and audiences.

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Solving the "Blind men and the elephant problem": Additive deep learning of complex high dimensional models from partial faceted datasets

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Biological systems are complex networks involving tens of thousands of interacting molecular components, and measurable biological functions are emerging properties of these complex networks. Many quantitative studies in biology attempt to connect biological function with molecular components and genes, in the process developing mechanistic understanding. However, it is challenging to quantify the contribution of all components to the biological function simultaneously, especially at the single cell level. Instead, in typical experiments, only a subset of the variables (or facet) is measured. This makes it difficult to obtain a complete and unbiased understanding of the network and how different components of the network cooperatively contribute to the biological function. In this paper, we explore a machine learning approach to combine different facets of data and obtain a complete picture of the biological system based on conditional distributions from faceted data subsets. Both a polynomial regression approach and a neural network approach are developed and examined with two set of concrete examples: A mechanical spring network system deforming under external forces and a small (8-dimensions) biological network including the cellular senescence marker P53. In the later example, single cell data is collected to validate the machine learning approach. We find that the full system is successfully reconstructed from faceted data in both examples. We further discuss the additive property of the model, where the model predictive accuracy increases with increasing number of simultaneously measured variables (dimension of subsets). Our model provides a systematic and novel approach to integrate different pieces of experimental information to reconstruct complex high dimensional systems, arriving at an unbiased and wholistic model of biological function.

Competing Interest Statement

The authors have declared no competing interest.

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